{"id":170,"date":"2014-08-12T03:10:05","date_gmt":"2014-08-12T03:10:05","guid":{"rendered":"https:\/\/courses.candelalearning.com\/cheminter\/?post_type=chapter&#038;p=170"},"modified":"2017-08-28T21:26:29","modified_gmt":"2017-08-28T21:26:29","slug":"measurements","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/measurements\/","title":{"raw":"Measurements","rendered":"Measurements"},"content":{"raw":"<h3>SI Base Units<\/h3>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-NTc1MmZmMGU2ZjgzMzM0MGQ5NGU0MjBiZDIxZGJkYTc.-rtj\">\r\n \t<li>Define the SI system of units.<\/li>\r\n \t<li>List the seven base units of measurement.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How long is a yard?<\/h3>\r\nIt depends on whom you ask and when you asked the question. Today we have a standard definition of the yard, which you can see marked on every football field. If you move the ball ten yards, you get a first down and it doesn\u2019t matter whether you are playing in Los Angeles, Dallas, or Green Bay. But at one time that yard was arbitrarily defined as the distance from the tip of the king\u2019s nose to the end of his outstretched hand. Of course, the problem there is simple: new king, new distance (and then you have to remark all those football fields).\r\n\r\n<\/div>\r\n<h3>SI Base Units<\/h3>\r\n<p id=\"x-ck12-YzUxZDA1OTk2MWM5ODQyNWVmMTRiZGNlYTViMjg5MDY.-sp2\">All measurements depend on the use of units that are well known and understood. The <strong> English system <\/strong> of measurement units (inches, feet, ounces, etc.) are not used in science because of the difficulty in converting from one unit to another. The <strong> metric system <\/strong> is used because all metric units are based on multiples of 10, making conversions very simple. The metric system was originally established in France in 1795. <strong> The International System of Units <\/strong> is a system of measurement based on the metric system. The acronym <strong> SI <\/strong> is commonly used to refer to this system and stands for the French term, <em> Le Syst\u00e8me International d\u2019Unit\u00e9s <\/em> . The SI was adopted by international agreement in 1960 and is composed of seven base units, as shown in <strong> Table <\/strong> below .<\/p>\r\n\r\n<table id=\"x-ck12-MjRjMzVmMWM5MzM5ODliYjM5MGE4ZWI3MjVlZWRhN2I.-t8j\" class=\"x-ck12-nofloat\" border=\"1\"><caption>SI Base Units of Measurement<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Quantity <\/strong><\/td>\r\n<td><strong> SI Base Unit <\/strong><\/td>\r\n<td><strong> Symbol <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Length<\/td>\r\n<td>meter<\/td>\r\n<td>m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mass<\/td>\r\n<td>kilogram<\/td>\r\n<td>kg<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Temperature<\/td>\r\n<td>kelvin<\/td>\r\n<td>K<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Time<\/td>\r\n<td>second<\/td>\r\n<td>s<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Amount of a Substance<\/td>\r\n<td>mole<\/td>\r\n<td>mol<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Electric Current<\/td>\r\n<td>ampere<\/td>\r\n<td>A<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Luminous Intensity<\/td>\r\n<td>candela<\/td>\r\n<td>cd<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"x-ck12-MWEwN2I3YzI5YWRkNWFiNTg4ZmJhMTNmYzY2YjI5ZDQ.-m75\">\r\n<p id=\"x-ck12-ZDBlZGE5ZGU1ZGU2MTI4ZTQ5M2I5ZTdjMzlkN2VkMjY.-xjt\">The first five units are frequently encountered in chemistry. All other measurement quantities, such as volume, force, and energy, can be derived from these seven base units.<\/p>\r\n\r\n<div id=\"x-ck12-ZTcyOWI2Zjg2M2U1ZmQxZjc3NzFmY2FhZjU1YjAwMGE.-1ec\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-azi\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2NTk1OC0zMi04OS1JbWFnZS0tLTI5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210659\/20140811155029197942.jpeg\" alt=\"The meter standard\" longdesc=\"Meter%20standard.\" \/><\/p>\r\n<strong> Figure 3.1 <\/strong>\r\n<p id=\"x-ck12-NWRkYmEyZmFkMTdkODI3NDQ1Y2MyMWM4Mjk1OGNkZjA.-lkg\">Meter standard.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NWYzOGU0MzI3NGVkOTM1ZjU2MmU1ZGQwY2YxZjQ0YmM.-wim\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-lky\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2NjAwMi02OC0zOC1JbWFnZS0tLTMw\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210700\/20140811155029328243.jpeg\" alt=\"The kilogram standard\" longdesc=\"Kilogram%20standard\" \/><\/p>\r\n<strong> Figure 3.2 <\/strong>\r\n<p id=\"x-ck12-NTExOTVjY2U3MTMxNThlYWQ2MDdkZDg1NjlkNGFiOTg.-cuk\">Kilogram standard<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-MDM1ZDRjN2Y1N2YzYTc3YjcwZGE0OWVjNTM2OTI1NTI.-e3g\">\u00a0The map in <strong> Figure <\/strong> below shows the adoption of the SI units in countries around the world. The United States has legally adopted the metric system for measurements, but does not use it in everyday practice. Great Britain and much of Canada use a combination of metric and imperial units.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NTYyMDljZTk5M2IxMWNmZTYzY2QzMjA4YmI2MjU0Zjk.-3td\">\r\n<div id=\"x-ck12-MzI1ZTY0NDI2NGU3ZWFjNmQ3MmU4YWI2YjkwMGRkYWM.-ovu\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n<p id=\"x-ck12-3eu\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2NjA2MS03My0zMC1JbWFnZS0tLTMx\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210701\/20140811155029406394.png\" alt=\"Map of the world that uses the metric system\" longdesc=\"Areas%20of%20world%20using%20metric%20system.\" \/><\/p>\r\n<strong> Figure 3.3 <\/strong>\r\n<p id=\"x-ck12-MDViOTYzZjI5MDIwODA5YzhmOWFiNjI4NDg0NGFjMjU.-ea4\">Areas of world using metric system.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-OWVhN2RjYTQyZGIyZjc4OTE4N2JmNGYyZGRmZTlkZjM.-wv3\">\r\n<ul id=\"x-ck12-OWVhN2RjYTQyZGIyZjc4OTE4N2JmNGYyZGRmZTlkZjM.-e5j\">\r\n \t<li>The SI system is based on multiples of ten.<\/li>\r\n \t<li>There are seven basic units in the SI system.<\/li>\r\n \t<li>Five of these units are commonly used in chemistry.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-xwo\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-xwo\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jta\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-yfi\">\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-vls\">Use the link below to answer the following questions:<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NTA2NmM1Nzk5YWZhNmFlYzJiNmQwMTFkZWQ4MTVhOTg.-mqt\">\r\n<p id=\"x-ck12-NTA2NmM1Nzk5YWZhNmFlYzJiNmQwMTFkZWQ4MTVhOTg.-ftx\"><a href=\"http:\/\/physics.nist.gov\/cuu\/Units\/history.html\"> http:\/\/physics.nist.gov\/cuu\/Units\/history.html <\/a><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MTZhYzM0YjFhOGQ0ZWQyZWYwNDBmMDU0YzJjMTZmNWE.-wip\">\r\n<ol id=\"x-ck12-MTZhYzM0YjFhOGQ0ZWQyZWYwNDBmMDU0YzJjMTZmNWE.-jbp\">\r\n \t<li>When was the metric system created?<\/li>\r\n \t<li>What was deposited in the Archives de la R\u00e9publique in Paris?<\/li>\r\n \t<li>What was the CGS system based on?<\/li>\r\n \t<li>When was the name <em> International System of Units <\/em> ( <em> SI <\/em> ) assigned?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-wnz\">\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-wnz\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-hkl\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-YWNjZmQ2MjQzNjEyMjFhNGYwNWFhMzk3M2ZiOGYyNDU.-7li\">\r\n<ol id=\"x-ck12-YWNjZmQ2MjQzNjEyMjFhNGYwNWFhMzk3M2ZiOGYyNDU.-ywl\">\r\n \t<li>What does SI stand for?<\/li>\r\n \t<li>When was this system adopted by the international community?<\/li>\r\n \t<li>Which of the units are commonly used in chemistry?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div id=\"x-ck12-Yzk0MmYwMDU1NTk1Y2EwNjdmYmZjN2MwM2Q1MmE1NTA.-q61\" class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-Y2Y0YmNiM2VkMDFiZjEyZjk1NTk5NjYzZGIwYmQ3NTg.-026\">\r\n \t<li><strong>English system: <\/strong> A system of measurements based on feet inches, and other somewhat arbitrary units.<\/li>\r\n \t<li><strong> The International System of Units: <\/strong> Based on the metric system of measurements.<\/li>\r\n \t<li><strong> Metric system <\/strong> : Based on units of 10.<\/li>\r\n \t<li><strong> SI: <\/strong> The metric system and stands for the French term, <em> Le Syst\u00e8me International d\u2019Unit\u00e9s. <\/em><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-TWV0cmljIFByZWZpeGVz\">Metric Prefixes<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>List common metric prefixes and their exponential values.<\/li>\r\n \t<li>Convert from one exponential factor to another for a given unit.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>What do Latin and Greek have to do with modern science?<\/h3>\r\n<p id=\"x-ck12-NDAxYTVlMGNhYjQ1ZGU3YmU4ZWI5YWFlNzhmZWY1NTE.-kav\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210702\/20140811155029529152.jpeg\" alt=\"Drawing of ancient scientist\" width=\"250\" \/><\/span><\/p>\r\n<p id=\"x-ck12-ZWFjMWZkMGRlNDQ0ZWRkODRlZTYyOWNjZmNhZjZhNzM.-x6i\">Isn\u2019t it hard enough to learn English terms? For hundreds of years, the languages of the educated class were Latin and Greek. In part, because the literature of philosophy was Latin and Greek. Even the medieval Bibles were written in those two languages \u2013 the first English translation was in the late 1380s. Using Latin and Greek allowed scholars from different countries to communicate more easily with one another. Today we still see many Latin phrases in legal communications (\u201cpro bono\u201d meaning to do something \u201cfor the good\u201d and not charge legal fees), scientific naming of biological species, and Latin is used for the annual student speech at Harvard University graduations. Not bad for a \u201cdead\u201d language.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Metric Prefixes <strong>\r\n<\/strong><\/h3>\r\n<p id=\"x-ck12-YTFhYTRlZmIzYzFlZDAxM2Q4YTZiZjM0ODNlNzkwZmQ.-y8h\">Conversions between metric system units are straightforward because the system is based on powers of ten. For example, meters, centimeters, and millimeters are all metric units of length. There are 10 millimeters in 1 centimeter and 100 centimeters in 1 meter. <strong> Metric prefixes <\/strong> are used to distinguish between units of different size. These prefixes all derive from either Latin or Greek terms. For example, <em> mega <\/em> comes from the Greek word <img id=\"x-ck12-MTM3ODMxODg1OTc5MQ..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210704\/3632ee411a7fe20a46f5041dee4bbbd8.png\" alt=\"mu acute{varepsilon} gammaalphavarsigma\" width=\"49\" height=\"16\" \/> , meaning \u201cgreat\u201d<\/p>\r\n<p id=\"x-ck12-MWI1MzM5MTVlY2QzYTI1ZGQ0NGVmMzgxNGFlZDIxNjk.-txa\"><strong> Table <\/strong> below lists the most common metric prefixes and their relationship to the central unit that has no prefix. Length is used as an example to demonstrate the relative size of each prefixed unit.<\/p>\r\n\r\n<table id=\"x-ck12-YjY1MzI0NmRlMDU2Yjk4OTcyZDAwZDBiMDc3ZTc0NDk.-ye0\" class=\"x-ck12-nofloat\" border=\"1\"><caption>SI Prefixes<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Prefix <\/strong><\/td>\r\n<td><strong> Unit Abbrev. <\/strong><\/td>\r\n<td><strong> Meaning <\/strong><\/td>\r\n<td><strong> Example <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>giga<\/td>\r\n<td>G<\/td>\r\n<td>1,000,000,000<\/td>\r\n<td>1 gigameter (Gm) = 10 <sup> 9 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>mega<\/td>\r\n<td>M<\/td>\r\n<td>1,000,000<\/td>\r\n<td>1 megameter (Mm) = 10 <sup> 6 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilo<\/td>\r\n<td>k<\/td>\r\n<td>1000<\/td>\r\n<td>1 kilometer (km) = 1000 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>hecto<\/td>\r\n<td>h<\/td>\r\n<td>100<\/td>\r\n<td>1 hectometer (hm) = 100 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>deka<\/td>\r\n<td>da<\/td>\r\n<td>10<\/td>\r\n<td>1 dekameter (dam) = 10 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong> 1 <\/strong><\/td>\r\n<td><strong> 1 meter (m) <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>deci<\/td>\r\n<td>d<\/td>\r\n<td>1\/10<\/td>\r\n<td>1 decimeter (dm) = 0.1 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centi<\/td>\r\n<td>c<\/td>\r\n<td>1\/100<\/td>\r\n<td>1 centimeter (cm) = 0.01 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>milli<\/td>\r\n<td>m<\/td>\r\n<td>1\/1000<\/td>\r\n<td>1 millimeter (mm) = 0.001 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>micro<\/td>\r\n<td>\u03bc<\/td>\r\n<td>1\/1,000,000<\/td>\r\n<td>1 micrometer (\u03bcm) = 10 <sup> -6 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>nano<\/td>\r\n<td>n<\/td>\r\n<td>1\/1,000,000,000<\/td>\r\n<td>1 nanometer (nm) = 10 <sup> -9 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>pico<\/td>\r\n<td>p<\/td>\r\n<td>1\/1,000,000,000,000<\/td>\r\n<td>1 picometer (pm) = 10 <sup> -12 <\/sup> m<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"x-ck12-NzY2ZTA4NmZlNDVmNGE2NTA2NGI3MGU0MzY4ZGM1NzI.-8o4\">\r\n<div class=\"textbox\">There are more prefixes - some of them rarely used. Have you ever heard of a zeptometer? You can learn more about prefixes at <a href=\"https:\/\/web.archive.org\/web\/20070310221329\/http:\/\/www.essex1.com\/people\/speer\/large.html\" target=\"_blank\" rel=\"noopener\"> http:\/\/www.essex1.com\/people\/speer\/large.html<\/a>.<\/div>\r\n<\/div>\r\n<div id=\"x-ck12-NGU0NGE1MjJkYjA5YzZkYTkwYTI1YzE3MWM3MzA4ZTc.-lle\">\r\n<p id=\"x-ck12-NGU0NGE1MjJkYjA5YzZkYTkwYTI1YzE3MWM3MzA4ZTc.-muw\">There are a couple of odd little practices with the use of metric abbreviations. Most abbreviations are lower-case. We use \u201cm\u201d for meter and not \u201cM\u201d. However, when it comes to volume, the base unit \u201cliter\u201d is abbreviated as \u201cL\u201d and not \u201cl\u201d. So we would write 3.5 milliliters as 3.5 mL.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MTZiZTdhNTkwMWU3YjliMGUyNDQ2ZDVmMjQ0NmI3MzE.-ctc\">\r\n<p id=\"x-ck12-MTZiZTdhNTkwMWU3YjliMGUyNDQ2ZDVmMjQ0NmI3MzE.-sy3\">As a practical matter, whenever possible you should express the units in a small and manageable number. If you are measuring the weight of a material that weighs 6.5 kg, this is easier than saying it weighs 6500 g or 0.65 dag. All three are correct, but the kg units in this case make for a small and easily managed number. However, if a specific problem needs grams instead of kilograms, go with the grams for consistency.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-a6q\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-ZTY2OWUzM2ZmYmQyMDc4ODRhYjFkZTFmNTBmY2RmYjM.-nyq\">\r\n<ul id=\"x-ck12-ZTY2OWUzM2ZmYmQyMDc4ODRhYjFkZTFmNTBmY2RmYjM.-anh\">\r\n \t<li>Metric prefixes derive from Latin or Greek terms.<\/li>\r\n \t<li>The prefixes are used to make the units manageable.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-f61\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-f61\">\r\n<p id=\"x-ck12-YzUwYWQ3ZDZhZTEyMTg1YTg5ZmVhMWQxNmU1YmNmM2E.-pqr\">Do the online metric system crossword puzzle at<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NGY4ZDEzMzEyNTQ4NzZiYTc2ZGRlZGMwYmE5Y2EwNDE.-soz\">\r\n<p id=\"x-ck12-NGY4ZDEzMzEyNTQ4NzZiYTc2ZGRlZGMwYmE5Y2EwNDE.-ydj\"><a href=\"http:\/\/education.jlab.org\/sciencecrossword\/index.html\"> http:\/\/education.jlab.org\/sciencecrossword\/index.html <\/a><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZjA2MzhhNTg2NWJhZmU3ZWIyZWY2M2EzZWZlOGE3ODc.-2ya\">\r\n<p id=\"x-ck12-ZjA2MzhhNTg2NWJhZmU3ZWIyZWY2M2EzZWZlOGE3ODc.-vnk\">Click on \u201cmetric system\u201d to get to the puzzle<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-myj\"><\/div>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-myj\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ded\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OWQ1MzVmYTJmMWJmOTBhYmRiYjU5YzBlMWVlMTA3NzI.-qwz\">\r\n<ol id=\"x-ck12-OWQ1MzVmYTJmMWJmOTBhYmRiYjU5YzBlMWVlMTA3NzI.-d7i\">\r\n \t<li>What is the prefix for \u201cthousand\u201d?<\/li>\r\n \t<li>What is the prefix for 0.01?<\/li>\r\n \t<li>How would you write 500 milliliters?<\/li>\r\n \t<li>How many decimeters in one meter?<\/li>\r\n \t<li>You have a mass that weighs 1.2 hectograms. How many grams does it weigh?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-NzRiZGJlNTIyM2ZkYjE4MjU3ZmE0OGE2NDE2YzI5NjU.-bh9\">\r\n \t<li><strong> metric prefixes: <\/strong> Prefixes used to distinguish between metric units of different sizes.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U2NpZW50aWZpYyBOb3RhdGlvbiBpbiBDaGVtaXN0cnk.\">Scientific Notation in Chemistry<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define scientific (exponential) notation.<\/li>\r\n \t<li>Use this notation to simplify very large or very small numbers.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-MmNhOWZkMTY2NmFlYjA4YWEwZWIxZjFkOWIyMDYzZjY.-3jk\">\r\n \t<li>\r\n<div class=\"textbox examples\">\r\n<h3>How far is the Sun from Earth?<\/h3>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<p id=\"x-ck12-MWNmYWViNWIyMmMxZTQ1NGUxM2VjODE0NDc4OWI2YTg.-s6k\"><span class=\"x-ck12-img-inline\"> <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210704\/20140811155029702638.jpeg\" alt=\"A picture of the sun\" width=\"300\" \/><\/span><\/p>\r\n<p id=\"x-ck12-NWE4Y2Q4MjMzN2YzYjM1MWZmZGM0ZTFmNjg0NWEyYmQ.-sc3\">Astronomers are used to really big numbers.\u00a0 While the moon is only 406,697 km from earth at its maximum distance, the sun is much further away (150 million km).\u00a0 Proxima Centauri, the star nearest the earth, is 39, 900, 000, 000, 000 km away and we have just started on long distances.\u00a0 On the other end of the scale, some biologists deal with very small numbers: a typical fungus could be as small as 30 \u03bcmeters (0.000030 meters) in length and a virus might only be 0.03 \u03bcmeters (0.00000003 meters) long.<\/p>\r\n\r\n<\/div>\r\n&nbsp;<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Scientific Notation<\/h3>\r\n<p id=\"x-ck12-NGQ2OWJiODQ5ZTFkN2M5Yzc1NDc1Y2I0ZDJlZDBiNDI.-nda\">Scientific notation is a way to express numbers as the product of two numbers: a coefficient and the number 10 raised to a power. It is a very useful tool for working with numbers that are either very large or very small. \u00a0As an example, the distance from Earth to the Sun is about 150,000,000,000 meters \u2013 a very large distance indeed.\u00a0 In scientific notation, the distance is written as 1.5\u00a0\u00d7 10 <sup> 11 <\/sup> m. The coefficient is the 1.5 and must be a number greater than or equal to 1 and less than 10.\u00a0 The power of 10, or exponent, is 11 because you would have to multiply 1.5 by 10 <sup> 11 <\/sup> to get the correct number.\u00a0 Scientific notation is sometimes referred to as exponential notation. A summary of SI units is given in <strong> Table <\/strong> below .<\/p>\r\n\r\n<div id=\"x-ck12-NDBhMThjZjYyOGFkNDIyOTM5MmIwZWIxZTZjNzA3YTU.-acv\">\r\n<table id=\"x-ck12-YTg4MjEwODcxYmM1YzljMGQ5YjQ2NTU5NDMxNDkxYmI.-4yo\" class=\"x-ck12-nofloat\" border=\"1\"><caption>SI Prefixes<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Prefix <\/strong><\/td>\r\n<td><strong> Unit Abbrev. <\/strong><\/td>\r\n<td><strong> Exponential Factor <\/strong><\/td>\r\n<td><strong> Meaning <\/strong><\/td>\r\n<td><strong> Example <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>giga<\/td>\r\n<td>G<\/td>\r\n<td>10 <sup> 9 <\/sup><\/td>\r\n<td>1,000,000,000<\/td>\r\n<td>1 gigameter (Gm) = 10 <sup> 9 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>mega<\/td>\r\n<td>M<\/td>\r\n<td>10 <sup> 6 <\/sup><\/td>\r\n<td>1,000,000<\/td>\r\n<td>1 megameter (Mm) = 10 <sup> 6 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilo<\/td>\r\n<td>k<\/td>\r\n<td>10 <sup> 3 <\/sup><\/td>\r\n<td>1000<\/td>\r\n<td>1 kilometer (km) = 1000 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>hecto<\/td>\r\n<td>h<\/td>\r\n<td>10 <sup> 2 <\/sup><\/td>\r\n<td>100<\/td>\r\n<td>1 hectometer (hm) = 100 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>deka<\/td>\r\n<td>da<\/td>\r\n<td>10 <sup> 1 <\/sup><\/td>\r\n<td>10<\/td>\r\n<td>1 dekameter (dam) = 10 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong> 10 <sup> 0 <\/sup><\/strong><\/td>\r\n<td><strong> 1 <\/strong><\/td>\r\n<td><strong> 1 meter (m) <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>deci<\/td>\r\n<td>d<\/td>\r\n<td>10 <sup> -1 <\/sup><\/td>\r\n<td>1\/10<\/td>\r\n<td>1 decimeter (dm) = 0.1 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centi<\/td>\r\n<td>c<\/td>\r\n<td>10 <sup> -2 <\/sup><\/td>\r\n<td>1\/100<\/td>\r\n<td>1 centimeter (cm) = 0.01 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>milli<\/td>\r\n<td>m<\/td>\r\n<td>10 <sup> -3 <\/sup><\/td>\r\n<td>1\/1000<\/td>\r\n<td>1 millimeter (mm) = 0.001 m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>micro<\/td>\r\n<td>\u03bc<\/td>\r\n<td>10 <sup> -6 <\/sup><\/td>\r\n<td>1\/1,000,000<\/td>\r\n<td>1 micrometer (\u03bcm) = 10 <sup> -6 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>nano<\/td>\r\n<td>n<\/td>\r\n<td>10 <sup> -9 <\/sup><\/td>\r\n<td>1\/1,000,000,000<\/td>\r\n<td>1 nanometer (nm) = 10 <sup> -9 <\/sup> m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>pico<\/td>\r\n<td>p<\/td>\r\n<td>10 <sup> -12 <\/sup><\/td>\r\n<td>1\/1,000,000,000,000<\/td>\r\n<td>1 picometer (pm) = 10 <sup> -12 <\/sup> m<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"x-ck12-NmIwM2E0NDJhNWViZDdiZjA2NGQ4NDkxZTE1ZjI1ODQ.-qjy\">When working with small numbers, we use a negative exponent.\u00a0 So 0.1 meters is\u00a01\u00a0\u00d7\u00a010 <sup> -1 <\/sup> meters, 0.01 is\u00a01\u00a0\u00d7\u00a010 <sup> -2 <\/sup> and so forth.\u00a0 <strong> Table <\/strong> above gives examples of smaller units.\u00a0 Note the use of the <strong> leading zero <\/strong> (the zero to the left of the decimal point). That digit is there to help you see the decimal point more clearly.\u00a0 The figure 0.01 is less likely to be misunderstood than .01 where you may not see the decimal.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-6wj\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-ODA4OTM3ZjUyMGRiOWM4ZDk3YjZiYjMxOTY1NTUxMmY.-uqo\">\r\n<ul id=\"x-ck12-ODA4OTM3ZjUyMGRiOWM4ZDk3YjZiYjMxOTY1NTUxMmY.-s2t\">\r\n \t<li>Scientific notation allows us to express very large or very small numbers in a convenient way.<\/li>\r\n \t<li>This notation uses a coefficient (a number between 1 and 10) and a power of ten sufficient for the actual number.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-e5p\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-YTYxNmQ0OTgyYWU3ZmNlMWRkODA5Y2ZlMzM3YWY4NmQ.-rkj\">\r\n<p id=\"x-ck12-YTYxNmQ0OTgyYWU3ZmNlMWRkODA5Y2ZlMzM3YWY4NmQ.-fss\">Practice scientific notation using the link below:<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-ure\">\r\n<p id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-bq5\"><a href=\"http:\/\/www.mathsisfun.com\/numbers\/scientific-notation.html\"> http:\/\/www.mathsisfun.com\/numbers\/scientific-notation.html<\/a><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-ure\"><\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-qep\">\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-qep\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-6kt\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MDUyYzU3NmZlNGJiYmRlM2FiYjQwYTcyNmMxOWQyMzE.-j4p\">\r\n<ol id=\"x-ck12-MDUyYzU3NmZlNGJiYmRlM2FiYjQwYTcyNmMxOWQyMzE.-jjz\">\r\n \t<li>What is scientific notation?<\/li>\r\n \t<li>What do we use scientific notation for?<\/li>\r\n \t<li>What is a leading zero?<\/li>\r\n \t<li>Express 150,000,000 in scientific notation.<\/li>\r\n \t<li>Express 0.000043 in scientific notation.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div id=\"x-ck12-ZjM2NTVkMWFhYWQyYmM0YWUwYjE3OTRkYTJkZGVmZGE.-iz0\" class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZjM2NTVkMWFhYWQyYmM0YWUwYjE3OTRkYTJkZGVmZGE.-9sl\">\r\n \t<li><strong> exponent: <\/strong> A number placed to the right and above another number, symbol, or expression to indicate the power to which the expression is raised.<\/li>\r\n \t<li><strong> leading zero: <\/strong> The zero to the left of the decimal point which is there to help you see the decimal point more clearly.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U0kgTGVuZ3RoIGFuZCBWb2x1bWUgVW5pdHM.\">SI Length and Volume Units<\/h1>\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\r\n \t<li>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\r\n \t<li>Define length.<\/li>\r\n \t<li>Define volume.<\/li>\r\n \t<li>Describe standard measure of length and volume.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"x-ck12-OGM1M2EwY2M0OGNlMDBjMTQ3MWQyNzhlODg1OWRkOWU.-km6\"><\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How were sailors able to measure the depths of seas?<\/h3>\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\r\n \t<li><img style=\"line-height: 1.5;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210706\/20140811155029876586.jpeg\" alt=\"Ships used fathoms to measure depth\" width=\"500\" \/><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h4 id=\"x-ck12-MDA0YjY5NDNjMjFiNzAzYjExNDAwMWUzZjZlMWQ1NWU.-uvc_3-tgf\">How were sailors able to measure the depths of seas?<\/h4>\r\n<p id=\"x-ck12-MWM5NTBlYjBkMmI0MDM0ZGExZGVkNzI2ZGEyODgxMDM.-3yz\">Back in the days before all the electronic gadgets for measuring depth and locating undersea objects existed, the \"fathom\" was the unit of measurement for depth. A rope was knotted every six feet and the end was dropped over the side of the ship. You could tell how deep the water was by how many knots went under the water before the rope hit bottom. Today we just turn on an instrument and read the depth to a high level of accuracy.<\/p>\r\n\r\n<\/div>\r\n&nbsp;<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Length and Volume<\/h3>\r\n<p id=\"x-ck12-ZmZmYWZkNmE2NmZlZmZmMjg3MTFlNjg2NThjZGFjYzM.-bt9\"><strong> Length <\/strong> is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or linear measure, is the <strong> meter <\/strong> (m). All measurements of length may be made in meters, though the prefixes listed in various tables will often be more convenient. The width of a room may be expressed as about 5 meters (m), whereas a large distance, such as the distance between New York City and Chicago, is better expressed as 1150 kilometers (km). Very small distances can be expressed in units such as the millimeter or the micrometer. The width of a typical human hair is about 20 micrometers (\u03bcm).<\/p>\r\n<p id=\"x-ck12-MTM4OWY3NWE2MjczNWQ0ODdjOTg0NDM5ZWFiY2U4NDc.-7cy\"><strong> Volume <\/strong> is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length. The SI unit of volume is the cubic meter (m <sup> 3 <\/sup> ), which is the volume occupied by a cube that measures 1 m on each side. This very large volume is not very convenient for typical use in a chemistry laboratory. A liter (L) is the volume of a cube that measures 10 cm (1 dm) on each side. A liter is thus equal to both 1000\u00a0cm <sup> 3 <\/sup> (10\u00a0cm \u00d7 10\u00a0cm \u00d7 10\u00a0cm) and to 1 dm <sup> 3 <\/sup> . A smaller unit of volume that is commonly used is the milliliter (mL \u2013 note the capital L which is a standard practice). A milliliter is the volume of a cube that measures 1 cm on each side. Therefore, a milliliter is equal to a cubic centimeter (cm <sup> 3 <\/sup> ). There are 1000 mL in 1 L, which is the same as saying that there are 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> .<\/p>\r\n\r\n<div id=\"x-ck12-ZGVjOWFhNmRlY2NhOGVjZGE2ZTM5NmI0NjZiZWE0Yjk.-eoi\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-13b\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2OTYwNi00MS02MS1JbWFnZS0tLTM1\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210707\/20140811155030027703.jpeg\" alt=\"Picture of a water bottle\" longdesc=\"A%20typical%20water%20bottle%20is%201%20liter%20in%20volume\" \/><\/p>\r\n<strong> Figure 3.4 <\/strong>\r\n<p id=\"x-ck12-NjlmYjg2ZjJmODFmZGU2MGE1YmViYzNkODg4ZTcwNTY.-bfu\">A typical water bottle is 1 liter in volume<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZTA1YTE1NTNiZjZkZDJkNmYxNDYzMTJjMWYxMzEyMGU.-lyu\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-5zm\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2OTY0Ni00OS00Mi1JbWFnZS0tLTM3\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210708\/20140811155030108980.jpeg\" alt=\"Picture of a Rubik's Cube\" longdesc=\"Rubik%E2%80%99s%20cube.%20This%20Rubik%E2%80%99s%20cube%20is%205.7%20cm%20on%20each%20side%20and%20has%20a%20volume%20of%20185.2%20cm%3Csup%3E3%3C%2Fsup%3E%20or%20185.2%20mL.\" \/><\/p>\r\n<strong> Figure 3.5 <\/strong>\r\n<p id=\"x-ck12-NjkyMjZhNDgwMzBiYTFjNTI2NmM4ZjU3NGI5ZjVhZDI.-56n\">Rubik\u2019s cube. This Rubik\u2019s cube is 5.7 cm on each side and has a volume of 185.2 cm <sup> 3 <\/sup> or 185.2 mL.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NThiNTZmMmVjNTA1NTgzZWFjMTliMDBiZDVmYmUzMWQ.-ynh\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-jwr\"><img id=\"x-ck12-OTgwNDUtMTM2MzE2OTY4Ny05My0yMC1JbWFnZS0tLTM2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210708\/20140811155030192453.jpeg\" alt=\"A graduated cylinder is used to measure volume\" longdesc=\"Graduated%20cylinder.%20Volume%20in%20the%20laboratory%20is%20often%20measured%20with%20a%20graduated%20cylinder%2C%20which%20come%20in%20a%20variety%20of%20sizes.\" \/><\/p>\r\n<strong> Figure 3.6 <\/strong>\r\n<p id=\"x-ck12-NWFmMzU0M2RjZDAxNDhiODM1OTkwOGY2NTEyMTVkZDk.-keg\">Graduated cylinder. Volume in the laboratory is often measured with a graduated cylinder, which come in a variety of sizes.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-MmMxZjRlMGM3NTUzN2VhNmYzNjZhODBmNjAxMDU2Mjc.-ojn\">\r\n \t<li>Length is the measurement of the extent of something along its greatest dimension.<\/li>\r\n \t<li>Volume is the amount of space occupied by a sample of matter.<\/li>\r\n \t<li>Volume can be determined by knowing the length of each side of the item.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-atu\"><em> Questions <\/em><\/p>\r\n<p id=\"x-ck12-OTQzODgyNWNmMWIwNTM0OTIzOWYwNGYyM2VjMzE4ZmM.-zsu\"><a href=\"https:\/\/web.archive.org\/web\/20130306094916\/http:\/\/www.montgomerycollege.edu\/Departments\/biotp\/Metric.html\" target=\"_blank\" rel=\"noopener\">Read the section of length and volume in this link<\/a> and answer the following questions:<\/p>\r\n\r\n<ol id=\"x-ck12-NWE2N2E0NDVjN2ViNTU1YWQwMmQ1Mjk0ZGEyZWMyOWE.-vna\">\r\n \t<li>What are some units of length in the metric system?<\/li>\r\n \t<li>Do the first three length conversions.<\/li>\r\n \t<li>Where on the meniscus do you measure volume in a graduated cylinder?<\/li>\r\n \t<li>Do the first two conversion examples for volume.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-3ps\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-NmFjZjZiZTYwMmJiMDFiY2QyNDRkNTdkZWI4MDJjY2M.-chp\">\r\n \t<li>Define length.<\/li>\r\n \t<li>Define volume.<\/li>\r\n \t<li>An object measures <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210709\/808661f1aaa48dfb18454f12290d5df0.png\" alt=\"6.2 cm times 13.7 cm times 26.9 cm\" width=\"220\" height=\"14\" \/> . Which value is the length of the object?<\/li>\r\n \t<li>How big is a mL?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-NTgwNjQ2NzQ4ZjAxMGEzYTU5ODEyNWViOWI5ZmU5NDU.-jve\">\r\n \t<li><strong> length: <\/strong> The measurement of the extent of something along its greatest dimension<\/li>\r\n \t<li><strong> meter: <\/strong> The SI basic unit of length, or linear measure<\/li>\r\n \t<li><strong> volume: <\/strong> The amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U0kgTWFzcyBhbmQgV2VpZ2h0IFVuaXRz\">SI Mass and Weight Units<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nType your learning objectives here.\r\n<ul>\r\n \t<li>Define mass.<\/li>\r\n \t<li>Define weight.<\/li>\r\n \t<li>Explain the difference between mass and weight.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How is he floating?<\/h3>\r\n<p id=\"x-ck12-ZDZjMDI3NWMxNWNhNWMzNTA5MjZhNTJiZmZlMmQ3MjA.-07p\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210710\/20140811155030340053.jpeg\" alt=\"An astronaut floating in space\" width=\"500\" \/><\/span><\/p>\r\n<p id=\"x-ck12-MjE5MjM5ZmVlMjEzNGE0OTYzNGE4ZDhlZmZmMzMwNTU.-rop\"><strong>\u00a0<\/strong><\/p>\r\n<p id=\"x-ck12-YTE2ODNhNDM0MWQxYTliZDcxYTQ0ZGQ4YjhhMDAyODU.-gtt\">One of the many interesting things about travel in outer space is the idea of weightlessness. If something is not fastened down, it will float in mid-air. Early astronauts learned that weightlessness had bad effects on bone structure. If there was no pressure on the legs, those bones would begin to lose mass. Weight provided by gravity is needed to maintain healthy bones. Specially designed equipment is now a part of every space mission so the astronauts can maintain good body fitness.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Mass and Weight<\/h3>\r\n<p id=\"x-ck12-MmU2NjU2Y2FjM2FhNTg3NDMyYjkwMWU5Y2E5NGQ2ODA.-igr\"><strong> Mass <\/strong> is a measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram. The kilogram was originally defined as the mass of 1 L of liquid water at 4\u00b0C (volume of a liquid changes slightly with temperature). In the laboratory, mass is measured with a balance ( <strong> Figure <\/strong> below ), which must be calibrated with a standard mass so that its measurements are accurate.<\/p>\r\n\r\n<div id=\"x-ck12-ZjQ2MjJmNDg5NDI3N2M2ZWVhNWQ1MDAxZDMzNTVhODI.-2qx\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-gix\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MDI2Mi0xNS03OC1JbWFnZS0tLTM5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210713\/20140811155030427294.jpeg\" alt=\"An analytical balance is used to precisely measure weight\" longdesc=\"An%20analytical%20balance%20makes%20very%20sensitive%20mass%20measurements%20in%20a%20laboratory%2C%20usually%20in%20grams.\" \/><\/p>\r\n<strong> Figure 3.7 <\/strong>\r\n<p id=\"x-ck12-Nzc1MjlkOGM5ZDUzMWY2MTFhODNkZTYzMGNiZDIxOTg.-ibf\">An analytical balance makes very sensitive mass measurements in a laboratory, usually in grams.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-ZmVkNzMxZjA3MDIxZDkzODMzNGU4OGYwNzY1MDE1YTY.-zut\">Other common units of mass are the gram and the milligram. A gram is 1\/1000th of a kilogram, meaning that there are 1000 g in 1 kg. A milligram is 1\/1000th of a gram, so there are 1000 mg in 1 g.<\/p>\r\n<p id=\"x-ck12-ZmI2ZGFjOTgxYjdkODZiNjJmMzFhNzQ1NTA1YWE0OWI.-evb\">Mass is often confused with the term weight. <strong> Weight <\/strong> is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the force due to <strong> gravity <\/strong> is about one sixth that of the gravitational force on Earth. Therefore, a given object will weigh six times more on Earth than it does on the moon. Since mass is dependent only on the amount of matter present in an object, mass does not change with location. Weight measurements are often made with a spring scale by reading the distance that a certain object pulls down and stretches a spring.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-M2JmZTM4MmZlYWVjZmY2ZDZiOWYzYWY4MTQxMjcyNzQ.-xow\">\r\n \t<li>Mass is a measure of the amount of matter that an object contains.<\/li>\r\n \t<li>Weight is a measure of force that is equal to the gravitational pull on an object.<\/li>\r\n \t<li>Mass is independent of location, while weight depends on location.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-qw9\"><em> Questions <\/em><\/p>\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-bom\">Use the link below to answer the following questions:<\/p>\r\n<p id=\"x-ck12-MmNmZWRjYmJhMWQ2N2RmNWU5MGQ3NTI3ZTliNjAyNzU.-vtq\"><a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/mass.html\"> http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/mass.html <\/a><\/p>\r\n\r\n<ol id=\"x-ck12-YzgxMmVkNjIzOTYzZjg5NzAzODVhNjYzNTdiNWNlZDY.-cyr\">\r\n \t<li>The mass of an object is a __________ measure of its inertia.<\/li>\r\n \t<li>What is the SI unit for mass?<\/li>\r\n \t<li>How is weight different from mass?<\/li>\r\n \t<li>What is the unit of weight in the United States?<\/li>\r\n<\/ol>\r\n<h4><\/h4>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3><span style=\"line-height: 1.5;\">Review<\/span><\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-bwf\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-ZWVmNmUwNDQwZjUzOGEzMWM5MmU5ZjVlOTdjNjkwNTQ.-oz8\">\r\n \t<li>Define mass.<\/li>\r\n \t<li>Define weight.<\/li>\r\n \t<li>If I weigh 180 pounds on Earth, what will I weigh on the moon?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-NGU2YWRiZDc4NTEyMGI0MDc1NzZlYmI1MGFkNzRjMWE.-ipt\">\r\n \t<li><strong> gravity: <\/strong> The force that causes two particles to pull towards each other<\/li>\r\n \t<li><strong> mass: <\/strong> A measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram.<\/li>\r\n \t<li><strong> weight: <\/strong> A measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U0kgS2luZXRpYyBFbmVyZ3kgVW5pdHM.\">SI Kinetic Energy Units<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nType your learning objectives here.\r\n<ul>\r\n \t<li>Define kinetic energy.<\/li>\r\n \t<li>Define potential energy.<\/li>\r\n \t<li>Write the expression for calculating energy in joules.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Have you ever watched a cat in action?<\/h3>\r\n<p id=\"x-ck12-MzVjYzMyOTY2MjBkNzU5ODQ3MzRkYWU5MDgzY2YyMjc.-9tg\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210714\/20140811155030561341.jpeg\" alt=\"A picture of a cat\" width=\"500\" \/><\/span><\/p>\r\n<p id=\"x-ck12-NzcxMzg3MWMwOTUxMWI0NzQ4MTY3MGNjZmI4MmMzODY.-ics\"><strong>\u00a0\u00a0<\/strong><\/p>\r\n<p id=\"x-ck12-MGFkNWNlNzAwNTg4NWI5NDNjN2YyMmM2ODFjNmUwOWU.-a2g\">When cats are chasing something, they move very fast. We may comment, \u201cThat cat has a lot of energy\u201d. In saying that, we are more correct than we realize. One form of energy is seen when an object is moving and this type of energy is the basis for many chemical processes.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>SI Kinetic Energy Units<\/h3>\r\n<p id=\"x-ck12-MDhkYzZmYjc3M2JjZWIzYzU1ZmQxNzU1MTRhYmNlZTk.-t4f\">An object\u2019s <strong> kinetic <\/strong> <strong> energy <\/strong> is the energy due to motion. Kinetic energy can be defined mathematically as<\/p>\r\n<p id=\"x-ck12-vyg\" class=\"x-ck12-indent\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210715\/4576a6e07a6c6f2907195af2aaa5c534.png\" alt=\"text{KE} = frac{1}{2} text{mv}^2\" width=\"99\" height=\"37\" \/><\/p>\r\n<p id=\"x-ck12-N2RlNTcxY2FlYjNjNWNmOGFmMTk2Mzg2NTNiOGY2ZTI.-tld\">where <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210716\/3d9d87196b2a6db0461bb9f77b72b047.png\" alt=\"text{KE} = text{kinetic energy}\" width=\"160\" height=\"16\" \/><\/p>\r\n<p id=\"x-ck12-NzQxMWNmZjI0MWFiMzZkOGRhYmQ3YmE3NGVlYTkyMmY.-dyk\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210717\/28a7eb890220fe9154fd452a3539274a.png\" alt=\"text{m} = text{mass}\" width=\"77\" height=\"9\" \/><\/p>\r\n<p id=\"x-ck12-M2E1MTA0ODMzNGY0NmU2ZDYyMTE2ZjVmZGYzZjU1YjQ.-9ja\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210717\/4484d6e0c4455f52264f1e0498e3b149.png\" alt=\"text{v} = text{velocity}\" width=\"94\" height=\"16\" \/><\/p>\r\n<p id=\"x-ck12-MDQ1YjM3OGZlNDc0ODAzZWE2ODgwNzc5MWU3ZjAwOTk.-gjp\"><strong> Energy <\/strong> is defined as the capacity to do work or to produce heat. As discussed previously, kinetic energy is one type of energy and is associated with motion. Another frequently encountered energy is <strong> potential energy <\/strong> , a type of energy that is stored in matter and released during a chemical reaction. The <strong> joule <\/strong> (J) is the SI unit of energy and is named after English physicist James Prescott Joule (1818-1889). If we go back to the equation for kinetic energy written above, we can put units in (kg for mass and m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> for velocity squared). Then, in terms of SI base units a joule is equal to a kilogram times meter squared divided by a second squared (kg\u00a0\u2022\u00a0m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> ). Another common unit of energy that is often used is the <strong> calorie <\/strong> (cal), which is equivalent to 4.184 J.<\/p>\r\n\r\n<div id=\"x-ck12-Mjc4Y2UwZmRlZTBhNzM1OTI2OWM5MWI1NmY3Mjk3MWY.-qv2\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-rbr\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MDcyNS0yNy0xOC1JbWFnZS0tLTQx\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210718\/20140811155030763669.jpeg\" alt=\"Picture of James Prescott Joule\" longdesc=\"James%20Prescott%20Joule.\" \/><\/p>\r\n<strong> Figure 3.8 <\/strong>\r\n<p id=\"x-ck12-ZDI1MzIxYzFhODRiMDgwMzM5NGE3NDdhN2Y1ZWRmZTY.-icf\">James Prescott Joule.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZTJiOWExYmViZjk4NTE1Y2UzOTFkNzIxZDI0M2RlNjc.-sle\">\r\n \t<li>Energy is the capacity to do work or to produce heat.<\/li>\r\n \t<li>Kinetic energy is the energy due to motion.<\/li>\r\n \t<li>Potential energy is energy stored in matter.<\/li>\r\n \t<li>The joule (J) is the SI unit of energy and equals kg\u00a0\u2022\u00a0m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> .<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<h4><em> Questions <\/em><\/h4>\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-jia\">Read <a href=\"https:\/\/web.archive.org\/web\/20160114103204\/http:\/\/chemwiki.ucdavis.edu\/Physical_Chemistry\/Thermodynamics\/State_Functions\/Kinetic_Energy\" target=\"_blank\" rel=\"noopener\">Kinetic Energy<\/a> to answer the following questions:<\/p>\r\n\r\n<ol id=\"x-ck12-YzU3NGE4MzFmYTQ1ZDg2N2QzZDliMGM3YTgwYjE3NTE.-hh5\">\r\n \t<li>What is kinetic energy dependent upon?<\/li>\r\n \t<li>Do molecules at a higher temperature move faster or slower than molecules at a lower temperature?<\/li>\r\n \t<li>What happens when a chemical reaction releases energy?<\/li>\r\n \t<li>What happens when a chemical reaction absorbs energy?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<h4><em> Questions <\/em><\/h4>\r\n<ol id=\"x-ck12-MWRiZGZhNWEwYjIyMDkyNzdkZDJjZGU4N2RkZWIyMjE.-q9y\">\r\n \t<li>What is kinetic energy?<\/li>\r\n \t<li>What is the mathematical equation for kinetic energy?<\/li>\r\n \t<li>What is potential energy?<\/li>\r\n \t<li>What is the SI unit for energy?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-MTMyNDhmZmZmZWNlMmE1MjdkNjkxN2JmZGZmZGEzODA.-eqk\">\r\n \t<li><strong> calorie: <\/strong> common unit of energy, which is equal to 4.184 J.<\/li>\r\n \t<li><strong> energy: <\/strong> As the capacity to do work or to produce heat.<\/li>\r\n \t<li><strong> joule: <\/strong> The SI unit of energy and is named after English physicist James Prescott Joule (1818-1889).<\/li>\r\n \t<li><strong> kinetic energy: <\/strong> The energy due to motion.<\/li>\r\n \t<li><strong> potential energy: <\/strong> A type of energy that is stored in matter and released during a chemical reaction.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-VGVtcGVyYXR1cmUgYW5kIFRlbXBlcmF0dXJlIFNjYWxlcw..\">Temperature and Temperature Scales<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define temperature.<\/li>\r\n \t<li>Describe the Fahrenheit temperature scale.<\/li>\r\n \t<li>Describe the Celsius temperature scale.<\/li>\r\n \t<li>Describe the Kelvin temperature scale.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\nTouch the top of the stove after it has been on and it feels hot. Hold an ice cube in your hand and it feels cold. Why? The particles of matter in a hot object are moving much faster than the particles of matter in a cold object. An object\u2019s <strong> kinetic energy <\/strong> is the energy due to motion. The particles of matter that make up the hot stove have a greater amount of kinetic energy than those in the ice cube.\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Temperature and Temperature Scales<\/h3>\r\n<p id=\"x-ck12-ZWFmMzViZTRiODI5YTBiZjNkNzRhYzgyOTEzOTI5MTQ.-ead\"><strong> Temperature <\/strong> is a measure of the average kinetic energy of the particles in matter. In everyday usage, temperature indicates a measure of how hot or cold an object is. Temperature is an important parameter in chemistry. When a substance changes from solid to liquid, it is because there was an increase in the temperature of the material. Chemical reactions usually proceed faster if the temperature is increased. Many unstable materials (such as enzymes) will be viable longer at lower temperatures.<\/p>\r\n\r\n<div id=\"x-ck12-MWUzODc2ZWU3NjI3ODlkMGI3ZWFmMzQyZGE5Njc1NTY.-csy\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n<p id=\"x-ck12-s4h\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MTE4Mi0xMy04OS1JbWFnZS0tLTQy\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210719\/20140811155030968001.png\" alt=\"Charcoal and snow have two very different temperatures\" longdesc=\"The%20glowing%20charcoal%20on%20the%20left%20represents%20high%20kinetic%20energy%2C%20while%20the%20snow%20and%20ice%20on%20the%20right%20are%20of%20much%20lower%20kinetic%20energy.\" \/><\/p>\r\n<strong> Figure 3.9 <\/strong>\r\n<p id=\"x-ck12-ZTdkYTgzMzgxNzQ3YmZkNGU2M2E5NWMxMWE2ZjhkNTA.-v3u\">The glowing charcoal on the left represents high kinetic energy, while the snow and ice on the right are of much lower kinetic energy.<\/p>\r\n\r\n<\/div>\r\n<h4>Temperature Scales <strong>\r\n<\/strong><\/h4>\r\n<p id=\"x-ck12-ZTBmOTZiMzExMjU4Y2MwZjk0YzMwNTEzNDM1YTQwMDM.-ank\">The first thermometers were glass and contained alcohol, which expanded and contracted as the temperature changed. The German scientist, Daniel Gabriel Fahrenheit used mercury in the tube, an idea put forth by Ismael Boulliau. The Fahrenheit scale was first developed in 1724 and tinkered with for some time after that. The main problem with this scale is the arbitrary definitions of temperature. The freezing point of water was defined as 32\u00b0F and the boiling point as 212\u00b0F. The Fahrenheit scale is typically not used for scientific purposes.<\/p>\r\n\r\n<div id=\"x-ck12-NGY2MzQxZjkwZjk5MmJmNDc4MWUyM2VhMTc4OTdhOTU.-duv\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-gbh\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MTIxNy0zMS00MC1JbWFnZS0tLTQz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210720\/20140811155031131280.jpeg\" alt=\"Portrait of Daniel Gabriel Fahrenheit\" longdesc=\"Daniel%20Gabriel%20Fahrenheit.\" \/><\/p>\r\n<strong> Figure 3.10 <\/strong>\r\n<p id=\"x-ck12-MWIyY2UzNjJhZDU5YjUzY2ZiZTAwN2M3MGMwYmNmNzc.-gbe\">Daniel Gabriel Fahrenheit.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-MjAyZjMzNTMwOTM1NTQ2N2ViZTM5ZGJmNWQyNzdhYTM.-vom\">The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius (1701-1744). The Celsius scale sets the freezing point and boiling point of water at 0\u00b0C and 100\u00b0C respectively. The distance between those two points is divided into 100 equal intervals, each of which is one degree. Another term sometimes used for the Celsius scale is \u201ccentigrade\u201d because there are 100 degrees between the freezing and boiling points of water on this scale. However, the preferred term is \u201cCelsius.\u201d<\/p>\r\n\r\n<div id=\"x-ck12-NjAxNmI3MmY2YzE2YzNkN2NjMDE2ZjA0ZThhZDkxY2Q.-xiz\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-wg9\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MTI4OC0yNC00Ny1JbWFnZS0tLTQ0\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210721\/20140811155031266060.jpeg\" alt=\"Portrait of Andres Celsius\" longdesc=\"Anders%20Celsius.\" \/><\/p>\r\n<strong> Figure 3.11 <\/strong>\r\n<p id=\"x-ck12-MTM5ZjU5MzQyM2Q3NmVjNTRjMjhlYWJhN2MzNTNjZTk.-8s0\">Anders Celsius.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-YTI3MGFkN2Y3MTRlMmYzNTIxMDMwZDkxYTYzYTE2ZmM.-qkc\">The Kelvin temperature scale is named after Scottish physicist and mathematician Lord Kelvin (1824-1907). It is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases. The freezing point of water on the Kelvin scale is 273.15 K, while the boiling point is 373.15 K. Notice that here is no \u201cdegree\u201d used in the temperature designation. Unlike the Fahrenheit and Celsius scales where temperatures are referred to as \u201cdegrees F\u201d or \u201cdegrees C,\u201d we simply designated temperatures in the Kelvin scale as kelvins.<\/p>\r\n\r\n<div id=\"x-ck12-YmI5MWQ0YmFiNTk4MmYyNWYyZDc0M2MxOTJlMjJiYTY.-3el\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-h9i\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3MTMyOS0wNS03LUltYWdlLS0tNDU.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210721\/20140811155031349933.jpeg\" alt=\"Portrait of Lord Kelvin\" longdesc=\"Lord%20Kelvin.\" \/><\/p>\r\n<strong> Figure 3.12 <\/strong>\r\n<p id=\"x-ck12-YmFjZTdmMDVjOGY1NDE0ODE4YzA1MmI0NDEwOWM5OWU.-cic\">Lord Kelvin.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-YjNhZmJmNzJhNzQ2NTcxNTdlODA2N2U1YWI4OGY2YzM.-zsl\">As can be seen by the 100 kelvin difference between the two, a change of one degree on the Celsius scale is equivalent to the change of one kelvin on the Kelvin scale. Converting from the Kelvin scale to the Celsius scale or vice versa is easy, as you simply add or subtract 273.<\/p>\r\n&nbsp;\r\n<div id=\"x-ck12-ZWQ1MmNiNzA3Y2ZlNmYwNWQ5OTkwOTc4MjkzN2JhYzk.-gyl\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/24175829\/3-Temperature-Scales-K-C-F1.jpg\"><img class=\"alignnone size-medium wp-image-2765\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/24175829\/3-Temperature-Scales-K-C-F1-300x269.jpg\" alt=\"3 Temperature Scales K-C-F\" width=\"300\" height=\"269\" \/><\/a>\r\n\r\n<strong>Figure 3.13 <\/strong>\r\n<p id=\"x-ck12-MDE4OGRkZTYyYTdkY2NkNDc4ZTUxZGQ1NDVkNzgzMTg.-afq\">Comparing the three different\u00a0temperature scales.<\/p>\r\nConverting between the Celsius and Fahrenheit temperature scales is a little bit trickier but still not too difficult. \u00a0To convert from Fahrenheit to Celsius, first multiply the temperature in Celsius (T<sub>C<\/sub>) by 1.8 and then add 32, in that order.\r\n\r\nT<sub>F<\/sub> = 1.8 X T<sub>C<\/sub> + 32\r\n\r\n<\/div>\r\nTo convert from Celsius to Farenheit, first subtract 32 from the temperature in Farenheit then divide by 1.8, in that order.\r\n\r\nT<sub>C<\/sub> = (T<sub>F<\/sub> - 32)\/1.8\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZjJkZjE2Yzk5NTc4M2E0OGY0NGFlNzc0NDk1ZDg2MWQ.-cf7\">\r\n \t<li>Temperature is a measure of the average kinetic energy of the particles in matter.<\/li>\r\n \t<li>The Fahrenheit scale defines the freezing point of water as 32\u00b0F and the boiling point as 212\u00b0F.<\/li>\r\n \t<li>The Celsius scale sets the freezing point and boiling point of water at 0\u00b0C and 100\u00b0C respectively.<\/li>\r\n \t<li>The Kelvin scale is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-cby\"><em> Questions <\/em><\/p>\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-avl\">Use the link below to answer the following questions:<\/p>\r\n<p id=\"x-ck12-ZDk1OTZhNTE2ZmRlZTM3NzA5NmE1N2MxN2E4YTNhNjM.-7tp\"><a href=\"http:\/\/www.visionlearning.com\/library\/module_viewer.php?mid=48\"> http:\/\/www.visionlearning.com\/library\/module_viewer.php?mid=48 <\/a><\/p>\r\n\r\n<ol id=\"x-ck12-OGQwYWJlMmFjNzg2YTVlZGUwZWMwNDI5MTc0MDlhYmI.-huq\">\r\n \t<li>What mixture did Fahrenheit use to set his thermometer at zero degrees?<\/li>\r\n \t<li>Why is the Celsius scale preferred in scientific work over the Fahrenheit scale?<\/li>\r\n \t<li>What was the idea behind the establishment of the Kelvin temperature scale?<\/li>\r\n \t<li>What is the advantage of using the Kelvin scale at low temperatures?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-x6q\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-NjU2ZWRiYjNmMmRkZTYxYTExYzRlMTNjODhjYzlmNjQ.-xjs\">\r\n \t<li>What is absolute zero on the Celsius temperature scale?<\/li>\r\n \t<li>What are the freezing and boiling points of water in the Celsius scale?<\/li>\r\n \t<li>Convert the following Kelvin temperatures to degrees Celsius.\r\n<ol id=\"x-ck12-YjJkOTJlM2UwOWQyYzJhMGU2Mzc4NjI1ZjIwYzgwOTE.-psu\">\r\n \t<li>188 K<\/li>\r\n \t<li>631 K<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Temperature in degrees Fahrenheit can be converted to Celsius by first subtracting 32, then dividing by 1.8. What is the Celsius temperature outside on a warm day (88\u00b0F)?<\/li>\r\n \t<li>Why is the Celsius scale sometimes called \u201ccentigrade\u201d?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZWYwMWEyNWJmZDQwODM2NDY3ODM4NWE3YzlhYTc1ZTU.-7me\">\r\n \t<li><strong> kinetic energy: <\/strong> The energy due to motion<\/li>\r\n \t<li><strong> temperature: <\/strong> A measure of the average kinetic energy of the particles in matter. In everyday usage, temperature is how hot or cold an object is<\/li>\r\n \t<li><strong> temperature scale: <\/strong> A way of measuring temperature quantitatively. There are three major scales used today.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U2NpZW50aWZpYyBEaW1lbnNpb25hbCBBbmFseXNpcw..\">Scientific Dimensional Analysis<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define dimensional analysis.<\/li>\r\n \t<li>Use dimensional analysis in solving problems.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<h3>Conversion Factors<\/h3>\r\n<p id=\"x-ck12-MDMwNDY1ODhmZDQ5MzI0MmJjOWNkNThlYmNkMTg2Yzk.-1cw\" class=\"x-ck12-math\">Many quantities can be expressed in several different ways. The English system measurement of 4 cups is also equal to 2 pints, 1 quart, and \u00bc of a gallon.<\/p>\r\n<p id=\"x-ck12-YjNhYTdkMWZmNjYxOGE3YzFkOWZmYThkMjEwZmE0NmY.-co9\" class=\"x-ck12-indent\">4 cups = 2 pints = 1 quart = 0.25 gallon<\/p>\r\n<p id=\"x-ck12-MjEzYmI4NmZiNGI0YzdkNzg3MGU4NjQ4ZGE1NjM3N2Y.-l0e\">Notice that the numerical component of each quantity is different, while the actual amount of material that it represents is the same. That is because the units are different. We can establish the same set of equalities for the metric system:<\/p>\r\n<p id=\"x-ck12-ZTMyYzBjNTJmNDAxYjllODExMWZmMDVmNTRkMmQxZjc.-lyx\" class=\"x-ck12-indent\">1 meter = 10 decimeters = 100 centimeters = 100 millimeters<\/p>\r\n<p id=\"x-ck12-ZmZkMmE4ZDJkMzJjNzVlNTg1YzMwNmRhYTcwY2Y3MDI.-kl0\">The metric system\u2019s use of powers of 10 for all conversions makes this quite simple.<\/p>\r\n<p id=\"x-ck12-YzMxZWRjZGM1Y2E2MDUwNTEzNmVjMWI1OGE1ZWI5MDY.-mij\">Whenever two quantities are equal, a ratio can be written that is numerically equal to 1. Using the metric examples above:<\/p>\r\n<p id=\"x-ck12-4fp\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210722\/ae4352c20b2cfe66c4c7529e5ce63449.png\" alt=\"frac{1 text{m}}{100 text{cm}}=frac{100 text{cm}}{100 text{cm}}=frac{1 text{m}}{1 text{m}}=1\" width=\"196\" height=\"24\" \/><\/p>\r\n<p id=\"x-ck12-MzJjZjVkNmE2NDJjZGI3NjI4NjE1NDI1NzNjNGI5ODI.-kwf\">The <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210723\/2c0a32e16a39f8df5841a8fdcd09c6e8.png\" alt=\"frac{1 text{m}}{100 text{cm}}\" width=\"42\" height=\"24\" \/> is called a <strong> conversion factor <\/strong> . A conversion factor is a ratio of equivalent measurements. Because both 1 m and 100 cm represent the exact same length, the value of the conversion factor is 1. The conversion factor is read as \u201c1 meter per 100 centimeters\u201d. Other conversion factors from the cup measurement example can be:<\/p>\r\n<p id=\"x-ck12-u8p\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210724\/08fa91bb7883a50f0d8c8a89c6b0ac51.png\" alt=\"frac{4 text{cups}}{2 text{pints}}=frac{2 text{pints}}{1 text{quart}}=frac{1 text{quart}}{0.25 text{gallon}}=1\" width=\"235\" height=\"27\" \/><\/p>\r\n<p id=\"x-ck12-M2ZhOTRhMWQwNmMwMWRhNWNkZDk2MGQ5MDk2YTRkY2I.-kwh\">Since the numerator and denominator represent equal quantities in each case, all are valid conversion factors.<\/p>\r\n\r\n<h3>Scientific Dimensional Analysis<\/h3>\r\n<p id=\"x-ck12-OTRhMWE0MjJkYTg5MzU1ZGRmNmQzZWJiNmVhM2EzODM.-prt\">Conversion factors are used in solving problems in which a certain measurement must be expressed with different units. When a given measurement is multiplied by an appropriate conversion factor, the numerical value changes, but the actual size of the quantity measured remains the same. <strong> Dimensional analysis <\/strong> is a technique that uses the units (dimensions) of the measurement in order to correctly solve problems. Dimensional analysis is best illustrated with an example.<\/p>\r\n\r\n<h4>Sample Problem: Dimensional Analysis<\/h4>\r\n<p id=\"x-ck12-ZjBhNTRmMWJlZDQxNDU0Njg5MDU2NzQxZTdkOTBlNWI.-tem\">How many seconds are in a day?<\/p>\r\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-pvz\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-qeu\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-OWE4ZjcyM2U4NjVhYTJkM2QxOTI2OGI3OGZlMzAzMmQ.-h7e\">\r\n \t<li>1 day = 24 hours<\/li>\r\n \t<li>1 hour = 60 minutes<\/li>\r\n \t<li>1 minute = 60 seconds<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-xvj\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-MDI0ZThjOTExMjJiMDkxNjFmODk0OGU5NjBkYTJiZmU.-fqr\">\r\n \t<li>1 day = ? seconds<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-YzQ4ZGRjZDY4M2FiODZhMjczYTRmZWVmNmEzMDQ0YWE.-dr6\">The known quantities above represent the conversion factors that we will use. The first conversion factor will have day in the denominator so that the \u201cday\u201d unit will cancel. The second conversion factor will then have hours in the denominator, while the third conversion factor will have minutes in the denominator. As a result, the unit of the last numerator will be seconds and that will be the units for the answer.<\/p>\r\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-uk8\"><em> Step 2: Calculate <\/em><\/p>\r\n<p id=\"x-ck12-g3l\" class=\"x-ck12-indent\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210725\/9e11e5a18ed11ef727045fd9a63c4ed7.png\" alt=\"1 text{d} times frac{24 text{h}}{1 text{d}} times frac{60 text{min}}{1 text{h}} times frac{60 text{s}}{1 text{min}}=86, 400 text{s}\" width=\"323\" height=\"39\" \/><\/p>\r\n<p id=\"x-ck12-ZjlmNWE5ZGNjY2U4OTc3MWU3NDkxZWJmMjllOGU4YWY.-hsp\">Applying the first conversion factor, the \u201cd\u201d unit cancels and 1\u00a0\u00d7\u00a024\u00a0=\u00a024. Applying the second conversion factor, the \u201ch\u201d unit cancels and 24\u00a0\u00d7 60 = 1440. Applying the third conversion factor, the \u201cmin\u201d unit cancels and 1440\u00a0\u00d7\u00a060\u00a0=\u00a086,400. The unit that remains is \u201cs\u201d for seconds.<\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-2b4\"><em> Step 3: Think about your result. <\/em><\/p>\r\n<p id=\"x-ck12-NGFmYjM2ZGJhNzc0MjFlNTNiM2VlYjlmMWM3ZGVlOWM.-8bk\">Seconds is a much smaller unit of time than a day, so it makes sense that there are a very large number of seconds in one day.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-N2Y4ZWYyMjhjMTFlZjg3OWRhOGY2MzM4ZTAyM2QyMTk.-pwu\">\r\n \t<li>A conversion factor is a ratio of equivalent measurements.<\/li>\r\n \t<li>Dimensional analysis is a technique that uses the units (dimensions) of the measurement in order to correctly solve problems.<\/li>\r\n<\/ul>\r\n<h4><\/h4>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3><span style=\"line-height: 1.5;\">Practice<\/span><\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ddg\"><em> Questions <\/em><\/p>\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-cut\">Use the link below to answer the following questions:<\/p>\r\n<a href=\"http:\/\/www.felderbooks.com\/papers\/units.html\" target=\"_blank\" rel=\"noopener\">http:\/\/www.felderbooks.com\/papers\/units.html<\/a>\r\n<ol id=\"x-ck12-NjkyYWZmZGVjMDJlNzU3NTM1MDZiMTFiM2IyMzE4NWI.-wv9\">\r\n \t<li>What do we always need to express measurements correctly?<\/li>\r\n \t<li>What does dimensional analysis tell you?<\/li>\r\n \t<li>How do you know that you have set the problem up incorrectly?<\/li>\r\n \t<li>How do you know that you have set the problem up correctly?<\/li>\r\n<\/ol>\r\n<h4><\/h4>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3><strong>Review<\/strong><\/h3>\r\n<em>Questions <\/em>\r\n<ol id=\"x-ck12-ZTIyM2ZhYTQ5NTA3MWQ4ODEwMDc0MmVjZmVmYWUzOTI.-d1m\">\r\n \t<li>What is a conversion factor?<\/li>\r\n \t<li>What is dimensional analysis?<\/li>\r\n \t<li>How many meters are in 3.7 km?<\/li>\r\n \t<li>How many kg in 12980 g?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-YTcyZWU5NzBlNjk1YWUwOTI3MTIzMWMxYjRlMGFmZmE.-axc\">\r\n \t<li><strong> conversion factor: <\/strong> A ratio of equivalent measurements.<\/li>\r\n \t<li><strong> dimensional analysis: <\/strong> A technique that uses the units (dimensions) of the measurement in order to correctly solve problems.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Metric Unit Conversions<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Use dimensional analysis to carry out metric unit conversions.<\/li>\r\n<\/ul>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How can a number of track laps be converted to a distance in meters?<\/h3>\r\n<p id=\"x-ck12-N2Q2OTgzYTNjNTBiMmYyY2MwZDk4YTVhNDZmNDJjNDI.-rve\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210727\/20140811155031590883.jpeg\" alt=\"Runners on a track\" width=\"250\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-ZDE4MzczNjhkMDY2MDY2OWFmZGI2ZDhlZWY3ZGI1YmU.-3hf_8-mwf\"><\/h4>\r\n<p id=\"x-ck12-ZDZkNDI0NDQzOThiZGIzYzM3NDUyMDAyYzJlNzVjNmQ.-a8h\">You are training for a 10-kilometer run by doing laps on a 400-meter track. You ask yourself \u201cHow many times do I need to run around this track in order to cover ten kilometers?\u201d (more than you realize). By using dimensional analysis, you can easily determine the number of laps needed to cover the 10 k distance.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Metric Unit Conversions<\/h3>\r\n<p id=\"x-ck12-MTgyNzdiZTQyMDU3MWUzMWJhYmYxYjE2MWMyYzNhNjU.-je9\">The metric system\u2019s many prefixes allow quantities to be expressed in many different units. Dimensional analysis is useful to convert from one metric system unit to another.<\/p>\r\n<p id=\"x-ck12-YTY3MzE3MzhlY2I0ZDYzZTJkNTZlYTExOTRiY2NlZmI.-enf\"><strong> Sample Problem: Metric Unit Conversions <\/strong><\/p>\r\n<p id=\"x-ck12-Zjc2ZjBlYzc4ZTYzNzQxZTcwZmQzZTkzOTJkY2JkMGY.-qbt\">A particular experiment requires 120 mL of a solution. The teacher knows that he will need to make enough solution for 40 experiments to be performed throughout the day. How many liters of solution should he prepare?<\/p>\r\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-prq\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-kcd\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-OGZlNjNjMmYxMmI3ZDQ0NjFmNzdlZjU0MzVjNjdmMTE.-pst\">\r\n \t<li>1 exp requires 120 mL<\/li>\r\n \t<li>1 L = 1000 mL<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-d1i\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZTk1MTU5YmU4MmZlZWQwNGFiNjY4Y2JiYmJhMjE0MTQ.-wdk\">\r\n \t<li>L of solution for 40 exp<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-YmVkNDRiNDZiOTRmYWQxNmIyMjgzOGVmMGE3ZWNjYzI.-6me\">Since each experiment requires 120 ml of solution and the teacher needs to prepare enough for 40 experiments, multiply 120 by 40 to get 4800 mL of solution needed. Now you must convert ml to L by using a conversion factor.<\/p>\r\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-ycs\"><em> Step 2: Calculate <\/em><\/p>\r\n<p id=\"x-ck12-dxg\" class=\"x-ck12-indent\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210728\/f1f58c6c9d42b60d0cb77e8f1f28fa5a.png\" alt=\"4800 text{mL} times frac{1 text{L}}{1000 text{mL}}=4.8 text{L}\" width=\"226\" height=\"39\" \/><\/p>\r\n<p id=\"x-ck12-ZjE0MzM2ZDFiMTU1YzUzMmMzZmY1MmM5OTFmYTQxZjA.-aej\">Note that conversion factor is arranged so that the mL unit is in the denominator and thus cancels out, leaving L as the remaining unit in the answer.<\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-ydr\"><em> Step 3: Think about your result. <\/em><\/p>\r\n<p id=\"x-ck12-YTYxZDk5NGRiYjFiZmRkMDljOGFjYjJkZmEwMjljMGY.-fzh\">A liter is much larger than a milliliter, so it makes sense that the number of liters required is less than the number of milliliters.<\/p>\r\n\r\n<h4>Two-Step Metric Unit Conversions<\/h4>\r\n<p id=\"x-ck12-MmE0ZmE2MDZkZWE4NDkyOGE4YTFhM2FjMDg3NmRmYWI.-j2l\">Some metric conversion problems are most easily solved by breaking them down into more than one step. When both the given unit and the desired unit have prefixes, one can first convert to the simple (unprefixed) unit, followed by a conversion to the desired unit. An example will illustrate this method.<\/p>\r\n<p id=\"x-ck12-YmVhOTVhZmE5NDg2YjA2NzI3Yzc1NzZkMjQ4MTVkMjk.-tug\"><strong> <em> Sample Problem 3.3: Two-Step Metric Conversion <\/em> <\/strong><\/p>\r\n<p id=\"x-ck12-OWI0MDVmZmJjOTJkOTVhY2VjOGNiMWVjNTEwMTVmMTk.-kei\">Convert 4.3 cm to \u03bcm.<\/p>\r\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-s6x\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-ina\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-NmEwMWJmNmQxYjY3MjA3MTBmMWQxYTBkMTkzNjgwMGM.-9ba\">\r\n \t<li>1 m = 100 cm<\/li>\r\n \t<li>1 m = 10 <sup> 6 <\/sup> \u03bcm<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-8sm\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-NDg1MGQ5NTUwZDI4MmU0ZmQ5MjA5NzIxYjQ0ODIxNGQ.-o5k\">\r\n \t<li>4.3 cm = ?\u00a0\u03bcm<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-YThmNzE5MWI1N2Y1YWE0ZDMxNzgwZTJhZjhlODAyYWU.-6dz\">You may need to consult a table for the multiplication factor represented by each metric prefix. First convert cm to m, followed by a conversion of m to \u03bcm.<\/p>\r\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-4zp\"><em> Step 2: Calculate <\/em><\/p>\r\n<p id=\"x-ck12-fv8\" class=\"x-ck12-indent\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210729\/0ec8d310fedb14f0af22dd4a8d0d93a9.png\" alt=\"4.3 text{cm} times frac{1 text{m}}{100 text{cm}} times frac{10^6 mu text{m}}{1 text{m}}=43, 000 mu text{m}\" width=\"325\" height=\"42\" \/><\/p>\r\n<p id=\"x-ck12-NmJjMjMzZDgzOGI1MmJmZmI0NTMxMzZhNzEwZjRhMTk.-kan\">Each conversion factor is written so that unit of the denominator cancels with the unit of the numerator of the previous factor.<\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-urj\"><em> Step 3: Think about your result. <\/em><\/p>\r\n<p id=\"x-ck12-NjExZThmM2UyMGFhMGRhN2MyYmNhYmQyOGIzMTFiMTQ.-qdl\">A micrometer is a smaller unit of length than a centimeter, so the answer in micrometers is larger than the number of centimeters given.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-MTVlZTllZmY4ZGJhYTAwNTMyMjlkZDJhZmM3ZTU0Y2I.-jkw\">\r\n \t<li>Dimensional analysis can be used to carry out metric unit conversions.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-mld\"><em> Questions <\/em><\/p>\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-k5n\">Use the link below to answer the following questions:<\/p>\r\n<p id=\"x-ck12-YTk2MTBiODcyNDI4YTY4MmQ0MjBlZjdkMzMxM2MzZjc.-c5d\"><a href=\"http:\/\/www.purplemath.com\/modules\/metric.htm\"> http:\/\/www.purplemath.com\/modules\/metric.htm <\/a><\/p>\r\n\r\n<ol id=\"x-ck12-NzRhMTQ4OTExYzg1ZTFiZGU5NDQ0YTU1M2NjY2Q5ZGQ.-e5k\">\r\n \t<li>Why are metric units nice to work with?<\/li>\r\n \t<li>What are the basic metric units?<\/li>\r\n \t<li>To move to a smaller unit, which direction do you move the decimal?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ybc\"><em> Question <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-MDkyYTI4MTA2MmJjNzBlZGE1OWIzNGUzMjhiMDQ4NjA.-vu0\">\r\n \t<li>Perform the following conversions.\r\n<ol id=\"x-ck12-YmYyNTIwYTQwNWU4NmU1NDg3ZDBlMTc3MzQ0Y2I1YzM.-rzi\">\r\n \t<li>0.074 km to m<\/li>\r\n \t<li>24,600 \u03bcg to g<\/li>\r\n \t<li>4.9 \u00d7 10 <sup> 7 <\/sup> \u00a0\u03bcg to kg<\/li>\r\n \t<li>84 dm to mm<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-YTBiOWFmODk5ZjVlNjU3NTY5N2NkZTQ4MzljNDE4MTQ.-ryc\">\r\n \t<li><strong> unit conversion: <\/strong> Conversion factors between different units of measurement for the same quantity.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-RGVyaXZlZCBVbml0cw..\">Derived Units<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define derived unit.<\/li>\r\n \t<li>Carry out unit conversions using derived units.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How has farming evolved?<\/h3>\r\n<p id=\"x-ck12-MTQ0M2I0N2Y3M2Y4OTdiZDNlNWVlNGM0OTcyODkzMWM.-ge9\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210731\/20140811155031753897.jpeg\" alt=\"Picture of a farm\" width=\"450\" \/><\/span><\/p>\r\n\r\n<h4>How has farming evolved?<\/h4>\r\n<p id=\"x-ck12-YjUzMmY5ZWY2NzgxZTIxNTRmY2ZjMzQ3ZWQwYTcyNWM.-pjg\">As farming becomes more expensive and less profitable (at least for small farms), many families will sell the land to builders who want to erect either commercial or residential properties. In order to sell, an accurate property tile is needed. The dimensions of the farm must be determined and the acreage calculated from those dimensions.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Dimensional Analysis and Derived Units<\/h2>\r\n<p id=\"x-ck12-ZDE5MjQ2OTEzNzJiNjM2YTk2N2QxY2Y5OTM2OTFmMGY.-bny\">Some units are combinations of SI base units. A <strong> derived unit <\/strong> is a unit that results from a mathematical combination of SI base units. We have already discussed volume and energy as two examples of derived units.\u00a0 Some others are listed in the <strong> Table <\/strong> below :<\/p>\r\n\r\n<div id=\"x-ck12-MzEyY2ZkNzliN2YwY2E5MzM5NWY2ZWNmYWI5YmI2Mjk.-qoc\">\r\n<table id=\"x-ck12-NWI0ZGM3NDVlYzQ2ZDg4ZDljYmM3NDMwZmZhOWMyNTQ.-gld\" class=\"x-ck12-nofloat\" border=\"1\"><caption>Derived SI Units<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Quantity <\/strong><\/td>\r\n<td><strong> Symbol <\/strong><\/td>\r\n<td><strong> Unit <\/strong><\/td>\r\n<td><strong> Unit Abbreviation <\/strong><\/td>\r\n<td><strong> Derivation <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Area<\/td>\r\n<td>A<\/td>\r\n<td>square meter<\/td>\r\n<td>m <sup> 2 <\/sup><\/td>\r\n<td>length \u00d7 width<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Volume<\/td>\r\n<td>V<\/td>\r\n<td>cubic meter<\/td>\r\n<td>m <sup> 3 <\/sup><\/td>\r\n<td>length \u00d7 width \u00d7 height<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Density<\/td>\r\n<td>D<\/td>\r\n<td>kilograms\/cubic meter<\/td>\r\n<td>kg\/m <sup> 3 <\/sup><\/td>\r\n<td><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/9ede8d0e286966a5308df7c6c1b6dfe7.png\" alt=\"frac{text{mass}}{text{volume}}\" width=\"41\" height=\"21\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Concentration<\/td>\r\n<td>c<\/td>\r\n<td>moles\/liter<\/td>\r\n<td>mol\/L<\/td>\r\n<td><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/79546fcbac576cbd074ab94e37430eae.png\" alt=\"frac{text{amount}}{text{volume}}\" width=\"43\" height=\"24\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Speed (velocity)<\/td>\r\n<td>v<\/td>\r\n<td>meters\/second<\/td>\r\n<td>m\/s<\/td>\r\n<td><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/abb6627e8b97fb49ee7a4785b2487278.png\" alt=\"frac{text{length}}{text{time}}\" width=\"36\" height=\"26\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Acceleration<\/td>\r\n<td>a<\/td>\r\n<td>meters\/second\/second<\/td>\r\n<td>m\/s <sup> 2 <\/sup><\/td>\r\n<td><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210733\/19947f47ee444e653f80065eec57bf2e.png\" alt=\"frac{text{speed}}{text{time}}\" width=\"32\" height=\"26\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Force<\/td>\r\n<td>F<\/td>\r\n<td>newton<\/td>\r\n<td>N<\/td>\r\n<td>mass \u00d7 acceleration<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Energy<\/td>\r\n<td>E<\/td>\r\n<td>joule<\/td>\r\n<td>J<\/td>\r\n<td>force \u00d7 length<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"x-ck12-MWRiZTRjNTA5NDAyNTJhZmI3MzM5MDA3MTUyNWUzZmY.-flg\">Using dimensional analysis with derived units requires special care. When units are squared or cubed as with area or volume, the conversion factors themselves must also be squared. Shown below is the conversion factor for cubic centimeters and cubic meters.<\/p>\r\n<p id=\"x-ck12-6af\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210733\/01413b2a3f5bef18cc62ebe66feeee74.png\" alt=\"left(frac{1 text{m}}{100 text{cm}}right)^3=frac{1 text{m}^3}{10^6 text{cm}^3}=1\" width=\"176\" height=\"27\" \/><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZThmYzM2YjRlYWM2NGU5NjljZjdhYzhiMWY4OTM0MTY.-wpy\">\r\n<p id=\"x-ck12-ZThmYzM2YjRlYWM2NGU5NjljZjdhYzhiMWY4OTM0MTY.-kp3\">Because a cube has 3 sides, each side is subject to the conversion of 1 m to 100 cm. Since 100 cubed is equal to 1 million (10 <sup> 6 <\/sup> ), there are 10 <sup> 6 <\/sup> cm <sup> 3 <\/sup> in 1 m <sup> 3 <\/sup> . Two convenient volume units are the liter, which is equal to a cubic decimeter, and the milliliter, which is equal to a cubic centimeter. The conversion factor would be:<\/p>\r\n<p id=\"x-ck12-bqk\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210734\/2199e3a669a1868fe67664a976fa947f.png\" alt=\"left(frac{1 text{dm}}{10 text{cm}}right)^3 = frac{1 text{dm}^3}{1000 text{cm}^3}=1\" width=\"176\" height=\"27\" \/><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-Mzk2NmE0MTI5NzE2ZWIyMmUyMmFhNmQ1ZGY3MzMwMzI.-hft\">\r\n<p id=\"x-ck12-Mzk2NmE0MTI5NzE2ZWIyMmUyMmFhNmQ1ZGY3MzMwMzI.-qce\">There are thus 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> , which is the same thing as saying there are 1000 mL in 1 L<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZjA1ZDQ0YzYwMzlkMmQxYjZkNjQ1OTMwZjJkOTU0YjM.-t4s\">\r\n<div id=\"x-ck12-YWEwNWYzYTkyNDM1YzFjNDBmNWY5ZjVkZGI3OWI2YzU.-ff1\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n<p id=\"x-ck12-mxt\"><img id=\"x-ck12-OTgwNDUtMTM2MzE3NDAzNi0zNy04Ni1JbWFnZS0tLTQ5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210734\/20140811155031845423.png\" alt=\"1000\u00a0milliliter cubes are in\u00a0a\u00a0liter cube\" longdesc=\"There%20are%201000%20cm%3Csup%3E3%3C\/sup%3E%20in%201%20dm%3Csup%3E3%3C\/sup%3E.%20Since%20a%20cm%3Csup%3E3%3C\/sup%3E%20is%20equal%20to%20a%20mL%20and%20a%20dm%3Csup%3E3%3C\/sup%3E%20is%20equal%20to%20a%20L%2C%20we%20can%20say%20that%20there%20are%201000%20mL%20in%201%20L.\" \/><\/p>\r\n<strong> Figure 3.14 <\/strong>\r\n<p id=\"x-ck12-NDg4NWQ0NWVkMjFiOGQ3ODI1ZTY2ODY5MmQxZDU5NzM.-ob1\">There are 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> . Since a cm <sup> 3 <\/sup> is equal to a mL and a dm <sup> 3 <\/sup> is equal to a L, we can say that there are 1000 mL in 1 L.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-YmVjYTM1ZWMwMjEyZDQzZmMzMGY1YmVjMzYyOTY3MzY.-os3\"><strong> <em> Sample Problem:\u00a0 <\/em> <\/strong> <strong> <em> Derived Unit Conversion <\/em> <\/strong><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MTcyYzhlNjhjMDJhN2MxYTg5MWFkNTkxODVlOWRkNDM.-ef8\">\r\n<p id=\"x-ck12-MTcyYzhlNjhjMDJhN2MxYTg5MWFkNTkxODVlOWRkNDM.-vch\">Convert 3.6 \u00d7 10 <sup> 8 <\/sup> mm <sup> 3 <\/sup> to mL.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZjNlNGYwZmFiMDA2MzFhMmViM2Y1ZjhkMTEyOTgxNWY.-c6r\">\r\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-qxu\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-qfy\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-YzI1YWQyOTEwNDAyYWYzMjRhNzNkZDc2MDRjZTZjZWE.-wpn\">\r\n \t<li>1 m = 1000 mm<\/li>\r\n \t<li>1 ml = 1 cm <sup> 3 <\/sup><\/li>\r\n \t<li>1 m = 100 cm<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-vpw\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZGFhNzgwZWU3M2YwMjVhZjEwNzBiYTQwMWQ2ZWZlZWM.-tfl\">\r\n \t<li>3.6 mm <sup> 3 <\/sup> = ? mL<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div id=\"x-ck12-YjZiMjJlZWExMzFkZTIxZGU3YmVjZDJiMmI3YTdiNTE.-mg9\">\r\n<p id=\"x-ck12-YjZiMjJlZWExMzFkZTIxZGU3YmVjZDJiMmI3YTdiNTE.-yog\">This problem requires multiple steps and the technique for converting with derived units.\u00a0 Simply proceed one step at a time: mm <sup> 3 <\/sup> to m <sup> 3 <\/sup> to cm <sup> 3 <\/sup> = mL.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-xdi\">\r\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-nb3\"><em> Step 2: Calculate <\/em><\/p>\r\n<p id=\"x-ck12-znq\" class=\"x-ck12-indent\"><em> <img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210736\/6ba3d5895e340e0946e87dc89590ce6f.png\" alt=\"3.6 text{mm}^3 times left(frac{1 text{m}}{1000 text{mm}}right)^3 times left(frac{100 text{cm}}{1 text{m}}right)^3 times frac{1 text{mL}}{1 text{cm}^3}=0.0036 text{mL}\" width=\"490\" height=\"49\" \/><\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OTcxNjFmYjk5YzBiMGNlNjk3MDU5ZWZkZjhhMWMxMjc.-m6y\">\r\n<p id=\"x-ck12-OTcxNjFmYjk5YzBiMGNlNjk3MDU5ZWZkZjhhMWMxMjc.-ki3\">Numerically, the steps are to divide 3.6 by 10 <sup> 9 <\/sup> , followed by multiplying by 10 <sup> 6 <\/sup> .\u00a0 You may find that you can shorten the problem by a step by first determining the conversion factor from mm to cm and using that instead of first converting to m. There are 10 mm in 1 cm.<\/p>\r\n<p id=\"x-ck12-qew\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210737\/11806a72633f700675cc5cf0a50a915e.png\" alt=\"3.6 text{mm}^3 times left(frac{1 text{cm}}{10 text{mm}}right)^3 times frac{1 text{mL}}{1 text{cm}^3}=0.0036 text{mL}\" width=\"323\" height=\"27\" \/><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MDk2NjVlMWZjZmVhYTEwMTQxNWZlMzE5ODQ0Nzg1ZDA.-koy\">\r\n<p id=\"x-ck12-MDk2NjVlMWZjZmVhYTEwMTQxNWZlMzE5ODQ0Nzg1ZDA.-twp\">In this case 3.6 \/ 1000 gives the same result of 0.0036.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-jxf\">\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-xad\"><em> Step 3: Think about your result. <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NTlkOTQ3N2YxMGRmNjA0ZDJlOTA2NmE4NGVlMWRiODY.-uyd\">\r\n<p id=\"x-ck12-NTlkOTQ3N2YxMGRmNjA0ZDJlOTA2NmE4NGVlMWRiODY.-cgt\">Cubic millimeters are much smaller than cubic centimeters, so the final answer is much less than the original number of mm <sup> 3 <\/sup> .<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-xld\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-YmIxYTAzNTIzYzFmYmY0YjhmNGMwMGE1MDg4M2VlMDM.-3c2\">\r\n<ul id=\"x-ck12-YmIxYTAzNTIzYzFmYmY0YjhmNGMwMGE1MDg4M2VlMDM.-ech\">\r\n \t<li>A derived unit is a unit that results from a mathematical combination of SI base units.<\/li>\r\n \t<li>Calculations involving derived units follow the same principles as other unit conversion calculations.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-qxf\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-qxf\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-atw\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-zay\">\r\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-rvr\">Use the link below to answer the following questions:<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MDdiNGIzM2I4ZjBmNTU2YjZlZmIwNWY5Zjg3ZGY3ZTE.-7mj\">\r\n<p id=\"x-ck12-MDdiNGIzM2I4ZjBmNTU2YjZlZmIwNWY5Zjg3ZGY3ZTE.-bk9\"><a href=\"http:\/\/www.unc.edu\/~rowlett\/units\/siderive.html\"> http:\/\/www.unc.edu\/~rowlett\/units\/siderive.html <\/a><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGQxNTVkOTE0OGU4Nzc2YjMxMGNkZGIyMTc3NTJmMWY.-hru\">\r\n<ol id=\"x-ck12-OGQxNTVkOTE0OGU4Nzc2YjMxMGNkZGIyMTc3NTJmMWY.-nsj\">\r\n \t<li>How many derived units are there?<\/li>\r\n \t<li>Who established these units?<\/li>\r\n \t<li>What derived unit gives rise to the definition of the watt?<\/li>\r\n \t<li>What derived units are defined by the newton?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-2vi\">\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-2vi\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-tu3\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZDk5ZmJiYTBjODk4ZWEzNjlhZTNhZDYxZDJmZmFlNmY.-ibh\">\r\n<ol id=\"x-ck12-NzdlYTgzZDM3ZTU1MTJlZGM5ODdlMzI4YTIxZDc0ZTk.-nmd\">\r\n \t<li>What is a derived unit?<\/li>\r\n \t<li>Convert 0.00722 km <sup> 2 <\/sup> to m <sup> 2 <\/sup><\/li>\r\n \t<li>Convert 129 cm <sup> 3 <\/sup> to L<\/li>\r\n \t<li>Convert 4.9 \u00d7 10 <sup> 5 <\/sup> \u03bcm <sup> 3 <\/sup> to mm <sup> 3 <\/sup> .<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZTdkMWEwZGU1OTE5YTlmNGU5ZmUwOGY2ODFkNjU3YzA.-njq\">\r\n \t<li><strong>derived unit: <\/strong> A unit that results from a mathematical combination of SI base units.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-RGVuc2l0eQ..\">Density<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define density.<\/li>\r\n \t<li>Use physical measurements to calculate density.<\/li>\r\n \t<li>Use density values to calculate mass or volume.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox examples\">\r\n<h3>How do logs stay afloat in water?<\/h3>\r\n<p id=\"x-ck12-NzI5ZTI5ZmQzMDA3MzFiNTc4MGRiYjhiMGVjMTBiNDE.-lxy\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210739\/20140811155031985542.jpeg\" alt=\"Logs floating in a river\" width=\"200\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-NTc2ZWY0MzA3ZTdhMjFkYjYzNGE4NWU4ODc4Nzc2MjQ.-j85_10-rtq\">How do logs stay afloat in water?<\/h4>\r\n<p id=\"x-ck12-NTc2ZWY0MzA3ZTdhMjFkYjYzNGE4NWU4ODc4Nzc2MjQ.-3cl\">After trees are cut, logging companies often move these materials down a river to a sawmill where they can be shaped into building materials or other products.\u00a0 The logs float on the water because they are less dense than the water they are in.\u00a0 Knowledge of density is important in the characterization and separation of materials.\u00a0 Information about density allows us to make predictions about the behavior of matter.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Density<\/h3>\r\n<p id=\"x-ck12-MGZiOTIxODQ3ZDI3YjJiY2NiZmIxNWVmMDI1MTQ2NGU.-cfk\">A golf ball and a table tennis ball are about the same size. However, the golf ball is much heavier than the table tennis ball. Now imagine a similar size ball made out of lead. That would be very heavy indeed! What are we comparing? By comparing the mass of an object relative to its size, we are studying a property called <strong> density. <\/strong> Density is the ratio of the mass of an object to its volume.<\/p>\r\n<p id=\"x-ck12-olz\" class=\"x-ck12-indent\"><img id=\"x-ck12-MTM5NjU4ODQ5NjkzNg..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210740\/09fef6cb6260d14ca9756d1b69d3b68c.png\" alt=\"text{Density} = frac{text{mass}}{text{volume}}\" width=\"141\" height=\"34\" \/><\/p>\r\n<p id=\"x-ck12-MWZjYmJmNDRlNzgwOTgwZmU4YzFlMzAyYjYzMGNlMzQ.-ual\">Density is an intensive property, meaning that it does not depend on the amount of material present in the sample. Water has a density of 1.0 g\/mL. That density is the same whether you have a small glass of water or a swimming pool full of water. Density is a property that is constant for the particular identity of the matter being studied.<\/p>\r\n<p id=\"x-ck12-YWUwM2ZhMTUzNGZjOThiYzE1YzY4OTQ0YzE4ZDM0OTA.-xha\">The SI units of density are kilograms per cubic meter (kg\/m <sup> 3 <\/sup> ), since the kg and the m are the SI units for mass and length respectively. In everyday usage in a laboratory, this unit is awkwardly large. Most solids and liquids have densities that are conveniently expressed in grams per cubic centimeter\u00a0(g\/cm <sup> 3 <\/sup> ). Since a cubic centimeter is equal to a milliliter, density units can also be expressed as g\/mL. Gases are much less dense than solids and liquids, so their densities are often reported in g\/L. Densities of some common substances at 20\u00b0C are listed in the <strong> Table <\/strong> below.<\/p>\r\n\r\n<table id=\"x-ck12-Njc3MmU1NjYzZTFjMDM5NTAwNjZjNGMxYTZjZjc0MDQ.-lec\" class=\"x-ck12-nofloat\" border=\"1\"><caption>Densities of Some Common Substances<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Liquids and Solids <\/strong><\/td>\r\n<td><strong> Density at 20\u00b0C (g\/ml) <\/strong><\/td>\r\n<td><strong> Gases <\/strong><\/td>\r\n<td><strong> Density at 20\u00b0C (g\/L) <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Ethanol<\/td>\r\n<td>0.79<\/td>\r\n<td>Hydrogen<\/td>\r\n<td>0.084<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Ice (0\u00b0C)<\/td>\r\n<td>0.917<\/td>\r\n<td>Helium<\/td>\r\n<td>0.166<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Corn oil<\/td>\r\n<td>0.922<\/td>\r\n<td>Air<\/td>\r\n<td>1.20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Water<\/td>\r\n<td>0.998<\/td>\r\n<td>Oxygen<\/td>\r\n<td>1.33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Water (4\u00b0C)<\/td>\r\n<td>1.000<\/td>\r\n<td>Carbon dioxide<\/td>\r\n<td>1.83<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Corn syrup<\/td>\r\n<td>1.36<\/td>\r\n<td>Radon<\/td>\r\n<td>9.23<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Aluminum<\/td>\r\n<td>2.70<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Copper<\/td>\r\n<td>8.92<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Lead<\/td>\r\n<td>11.35<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mercury<\/td>\r\n<td>13.6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Gold<\/td>\r\n<td>19.3<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"x-ck12-YjMxMzk2ODU2OTIwZWVlMmRiYTU4N2NiZGM0YTdjN2M.-mr8\">Since most materials expand as temperature increases, the density of a substance is temperature dependent and usually decreases as temperature increases.<\/p>\r\n<p id=\"x-ck12-MWMxNjI3NWRlZTY5NDM0YmZiMTdmZmRhMjhlN2U3NjU.-hoh\">You know that ice floats in water and it can be seen from the table that ice is less dense. Alternatively, corn syrup, being denser, would sink if placed into water.<\/p>\r\n\r\n<h4>Sample Problem: Density Calculations<\/h4>\r\n<p id=\"x-ck12-NTZhZTYzODIwY2JiMTU2M2ViODQwOGRlOTdkMmYwY2U.-xbi\">An 18.2 g sample of zinc metal has a volume of 2.55 cm <sup> 3 <\/sup> . Calculate the density of zinc.<\/p>\r\n<p id=\"x-ck12-OGU2YWEyYzY0NzAwMDUxZjI4NjFjY2E4MjYyNmNhN2I.-qvm\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-7bk\"><span class=\"x-ck12-underline\"> Known <em>\r\n<\/em> <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-YzdlMjI3Nzk3NGQwZDAxYWQwYmRiNjliM2ViMGE5YTk.-ck8\">\r\n \t<li>mass = 18.2 g<\/li>\r\n \t<li>volume = 2.55 cm <sup> 3 <\/sup><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-o7p\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZmYwMGQ4Yjc0N2JiMWZlMzU5NmVjNTM4NzBmYmI5YzM.-n8p\">\r\n \t<li>density =\u00a0? g\/cm <sup> 3 <\/sup><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-NzgyMjc2ZWJiYzM3YTJlNWIwOTE0OWFhYmU1MDgzZTc.-dop\">Use the equation for density, <img id=\"x-ck12-MTM5NjU4ODQ5NjkzNw..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/6a010143d9bbda127ddf0081214df314.png\" alt=\"D = frac{m}{V}\" width=\"53\" height=\"20\" \/> , to solve the problem.<\/p>\r\n<p id=\"x-ck12-YjlmZWM1OTI2ZTA2NThkOTk4OGE4NWE0N2EyOWY0OWE.-9ay\"><em> Step 2: Calculate <\/em><\/p>\r\n<p id=\"x-ck12-vqa\" class=\"x-ck12-indent\"><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/55158119dd4315ab0dd90b8ec2cba188.png\" alt=\"D=frac{m}{V}=frac{18.2 text{g}}{2.55 text{cm}^3}=7.14 text{g}\/text{cm}^3\" width=\"243\" height=\"24\" \/><\/p>\r\n<p id=\"x-ck12-ZGJmYWE4NWM0YmIyZGJiOTdhZTZmY2NmYmJmYjM1MjI.-pk3\"><em> Step 3: Think about your result. <\/em><\/p>\r\n<p id=\"x-ck12-ZTNhY2IzNWMwZGIxMzU0M2MzMmIzNDM3ODEyZmNjY2Q.-nq6\">If 1 cm <sup> 3 <\/sup> of zinc has a mass of about 7 grams, then 2 and a half cm <sup> 3 <\/sup> will have a mass about 2 and a half times as great. Metals are expected to have a density greater than that of water and zinc\u2019s density falls within the range of the other metals listed above<\/p>\r\n<p id=\"x-ck12-NGFhNDcyMGNkNjYxMjEzNDFiOWYwZGYyMTM1YjQ3NDY.-sqe\">Since density values are known for many substances, density can be used to determine an unknown mass or an unknown volume. Dimensional analysis will be used to ensure that units cancel appropriately.<\/p>\r\n\r\n<h4>Sample Problem: Using Density to Determine Mass and Volume<\/h4>\r\n<ol id=\"x-ck12-MGFhNWYwNWFjZTk5YzEyYzkzNzQ5MzJiODBjNGIzNWE.-ngn\">\r\n \t<li>What is the mass of 2.49 cm <sup> 3 <\/sup> of aluminum?<\/li>\r\n \t<li>What is the volume of 50.0 g of aluminum?<\/li>\r\n<\/ol>\r\n<p id=\"x-ck12-OGU2YWEyYzY0NzAwMDUxZjI4NjFjY2E4MjYyNmNhN2I.-ezv\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-piw\"><span class=\"x-ck12-underline\"> Known <\/span> <em>\r\n<\/em><\/p>\r\n\r\n<ul id=\"x-ck12-MjUyMjRiNDQ1MjExNzhhMmI2NzgxMTEzZWQyNTJmZDA.-qnh\">\r\n \t<li>density = 2.70 g\/cm <sup> 3 <\/sup><\/li>\r\n \t<li>1. volume = 2.49 cm <sup> 3 <\/sup><\/li>\r\n \t<li>2. mass = 50.0 g<\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-j1l\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZGE2NGM5ZDI5NzJmMDNjYjM4YjM1NDAyZDgzM2MyNDc.-0nc\">\r\n \t<li>1. mass =\u00a0? g<\/li>\r\n \t<li>2. volume =\u00a0? cm <sup> 3 <\/sup><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ZDMyMDcxMDg2OWM2MzAxNzRiZGU5Y2I3NjJiNTNiNTE.-cyh\">Use the equation for density, <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/6a010143d9bbda127ddf0081214df314.png\" alt=\"D = frac{m}{V}\" width=\"53\" height=\"20\" \/> , and dimensional analysis to solve each problem.<\/p>\r\n<p id=\"x-ck12-YjlmZWM1OTI2ZTA2NThkOTk4OGE4NWE0N2EyOWY0OWE.-dle\"><em> Step 2: Calculate <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-vnb\">\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210742\/bcc345b6877bcde5c3928c4c72797269.png\" alt=\"2.49 text{cm}^3 times frac{2.70 text{g}}{1 text{cm}^3}=6.72 text{g}\" width=\"200\" height=\"25\" \/><\/li>\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210743\/8127a940e36a3a22c6d08e57a1863520.png\" alt=\"50.0 text{g} times frac{1 text{cm}^3}{2.70 text{g}}=18.5 text{cm}^3\" width=\"199\" height=\"27\" \/><\/li>\r\n<\/ol>\r\n<p id=\"x-ck12-YzFhOWFhYjZlMmEzZjA4Mzg5Nzk3N2E5NjI1Y2EwNjY.-cfh\">In problem 1, the mass is equal to the density multiplied by the volume. In problem 2, the volume is equal to the mass divided by the density.<\/p>\r\n<p id=\"x-ck12-NWI4MjExZjgzODRhNTExMjdjNTVlYWMwNmQ1MTRmYjM.-m0k\"><em> Step 3: Think about your results. <\/em><\/p>\r\n<p id=\"x-ck12-N2ZhNjcyMGZiMzI5M2U2MWUzYjExNjFkNjcyNDBlMGY.-3kb\">Because a mass of 1 cm <sup> 3 <\/sup> of aluminum is 2.70 g, the mass of about 2.5 cm <sup> 3 <\/sup> should be about 2.5 times larger. The 50 g of aluminum is substantially more than its density, so that amount should occupy a relatively large volume.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-MDU3MTg2MzA2ZTU0MTI3MWU3MzlhMmIyZWQ1MTBiMzY.-jfk\">\r\n \t<li>Density is the ratio of the mass of an object to its volume.<\/li>\r\n \t<li>Gases are less dense that either solids or liquids<\/li>\r\n \t<li>Both liquid and solid materials can have a variety of densities<\/li>\r\n \t<li>For liquids and gases, the temperature will affect the density to some extent.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-ODJhYjQ2NzVkOWE0NWI2MTAwY2UxZjIxNTJhMjhkYTI.-fuh\">You can perform a density experiment to identify a mystery object online. Find this simulation at\u00a0<a href=\"https:\/\/phet.colorado.edu\/en\/simulation\/density\" target=\"_blank\" rel=\"noopener\">https:\/\/phet.colorado.edu\/en\/simulation\/density<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-woj\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-NWI3NmUyMGI2NzdjYWRhNjFhYzFhMTM2YWM2NTIwNjk.-8lt\">\r\n \t<li>Define \u201cdensity.\u201d<\/li>\r\n \t<li>Are gases more or less dense that liquids or solids at room temperature?<\/li>\r\n \t<li>How does temperature affect the density of a material?<\/li>\r\n \t<li>A certain liquid sample has a volume of 14.7 mL and a mass of 22.8 grams. Calculate the density.<\/li>\r\n \t<li>A material with a density of 2.7 grams\/mL occupies 35.6 mL. How many grams of the material are there?<\/li>\r\n \t<li>A certain material has a density of 19.3 g\/mL. What is the material?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-MDI1MWE5NzEyMmUxMmFlN2ZjMWZjN2RlZjI2YjE3NDM.-g80\">\r\n \t<li><strong>density: <\/strong> The ratio of the mass of an object to its volume. <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210744\/539a0d1b39b487f97368ee471ac72aa9.png\" alt=\"text{Density} = frac{text{mass}}{text{volume}}\" width=\"127\" height=\"21\" \/> . Density is an intensive property, meaning that it does not depend on the amount of material present in the sample.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-QWNjdXJhY3kgYW5kIFByZWNpc2lvbg..\">Accuracy and Precision<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define accuracy.<\/li>\r\n \t<li>Define precision.<\/li>\r\n \t<li>Describe situations with varying levels of accuracy and precision.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How do professional basketball players improve their shooting accuracy?<\/h3>\r\n<p id=\"x-ck12-YTdhNDZhYjEwYmU1NDQxMjI1ZmQ2OTc2ZjRhYWU3Y2I.-e1v\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210744\/20140811155032103310.jpeg\" alt=\"A basketball game requires shooting accuracy\" width=\"400\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-ODA2NzE4YmQ2M2FmOGIzNjY2N2RkYjBlYTEzZWQ5OTM.-9fc_11-pyl\">How do professional basketball players improve their shooting accuracy?<\/h4>\r\n<p id=\"x-ck12-ODA2NzE4YmQ2M2FmOGIzNjY2N2RkYjBlYTEzZWQ5OTM.-c4p\">Basketball is one of those sports where you need to hit the target.\u00a0 A football field goal kicker might have room for some deviation from a straight line \u2013 for college and pro football there is an 18 foot 6 inch space for the ball to go through.\u00a0 In basketball, the basket is only 18 inches across and the ball is a little less than 10 inches across \u2013 not much room for error.\u00a0 The ball has to be on target in order to go into the basket and score.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Accuracy and Precision<\/h3>\r\n<p id=\"x-ck12-N2MxNDcwODhiYzQ1ZGNhOWE2OTA1ODkxZmRmMDQ5MzY.-cfe\">In everyday speech, the terms <strong> accuracy <\/strong> and <strong> precision <\/strong> are frequently used interchangeably.\u00a0 However, their scientific meanings are quite different.\u00a0 Accuracy is a measure of how close a measurement is to the correct or accepted value of the quantity being measured.\u00a0 Precision is a measure of how close a series of measurements are to one another. \u00a0Precise measurements are highly reproducible, even if the measurements are not near the correct value.<\/p>\r\n<p id=\"x-ck12-ZTEwZGEzMzY0NDM0NWIzYThkYWIzYmJhZTEwNWQ2ZGU.-nui\">Darts thrown at a dartboard are helpful in illustrating accuracy and precision<\/p>\r\n\r\n<div id=\"x-ck12-NDU2ZGJhMDFlYjI0YjFjMjgzNDI4NWU0Y2EwYzU0NDY.-ekm\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n<p id=\"x-ck12-sn8\"><img id=\"x-ck12-OTgwNDUtMTM2MzI0Mzc5OS01NC0yNS1JbWFnZS0tLTUy\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210746\/20140811155032248757.png\" alt=\"A basketball game requires shooting accuracy\" longdesc=\"The%20distribution%20of%20darts%20on%20a%20dartboard%20shows%20the%20difference%20between%20accuracy%20and%20precision.\" \/><\/p>\r\n<strong> Figure 3.15 <\/strong>\r\n<p id=\"x-ck12-NTcxMGJhODJmMWQxOGVmMzk3MWRhZDhiYTczYzZjZjk.-bhg\">The distribution of darts on a dartboard shows the difference between accuracy and precision.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-NWY1MzU0YTAxYWQxY2UzMmFiZDZlMTc5YmY1OWY3MWQ.-da4\">Assume that three darts are thrown at the dartboard, with the bulls-eye representing the true, or accepted, value of what is being measured.\u00a0 A dart that hits the bulls-eye is highly accurate, whereas a dart that lands far away from the bulls-eye displays poor accuracy.\u00a0 The <strong> Figure <\/strong> above demonstrates four possible outcomes.<\/p>\r\n\r\n<ol id=\"x-ck12-ZDc5M2IwMWE1YzlkMzVmMjAxNDI1MzUyYmUzMGJmNDY.-gn9\" class=\"x-ck12-lower-alpha\">\r\n \t<li>The darts have landed far from each other and far from the bulls-eye.\u00a0 This grouping demonstrates measurements that are neither accurate, nor precise.<\/li>\r\n \t<li>The darts are close to one another, but far from the bulls-eye.\u00a0 This grouping demonstrates measurements that are precise, but not accurate.\u00a0 In a laboratory situation, high precision with low accuracy often results from a systematic error.\u00a0 Either the measurer makes the same mistake repeatedly or the measuring tool is somehow flawed.\u00a0 A poorly calibrated balance may give the same mass reading every time, but it will be far from the true mass of the object.<\/li>\r\n \t<li>The darts are not grouped very near to each other, but are generally centered around the bulls-eye.\u00a0 This demonstrates poor precision, but fairly high accuracy.\u00a0 This situation is not desirable in a lab situation because the \u201chigh\u201d accuracy may simply be random chance and not a true indicator of good measuring skill.<\/li>\r\n \t<li>The darts are grouped together and have hit the bulls-eye.\u00a0 This demonstrates high precision and high accuracy.\u00a0 Scientists always strive to maximize both in their measurements.<\/li>\r\n<\/ol>\r\n<div id=\"x-ck12-Mzc5NDc2NTIxNzJkMzNjNzY4ZTQwY2JiNmM1NTQ2MjQ.-bls\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\r\n<p id=\"x-ck12-vaz\"><img id=\"x-ck12-OTgwNDUtMTM2MzI0Mzg5OC01Ny01MS1JbWFnZS0tLTUz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210747\/20140811155032366639.jpeg\" alt=\"Students in a lab using volumetric flasks\" longdesc=\"Students%20in%20a%20chemistry%20lab%20are%20making%20careful%20measurements%20with%20a%20series%20of%20volumetric%20flasks.%20Accuracy%20and%20precision%20are%20critical%20in%20every%20experiment.\" \/><\/p>\r\n<strong> Figure 3.16 <\/strong>\r\n\r\nStudents in a chemistry lab are making careful measurements with a series of volumetric flasks. Accuracy and precision are critical in every experiment.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-N2M1MmZhOWQwNjgxMmMyYmVhOWNlNDkzZmIxMDhkZDA.-bqy\">\r\n \t<li>Accuracy is a measure of how close a measurement is to the correct or accepted value of the quantity being measured.<\/li>\r\n \t<li>Precision is a measure of how close a series of measurements are to one another.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NDI4ZWZlYjIzODA1Zjg1YmYwNjkxYzZhZDc1MDgxNTA.-lra\">Take the quiz at the link below:<\/p>\r\n<p id=\"x-ck12-MzQ0YzA4Zjg4OGI1YmFjMzM2MTUzNTFjYWJkMTEzMmM.-cqm\"><a href=\"http:\/\/www.quia.com\/quiz\/1863743.html?AP_rand=980502951\"> http:\/\/www.quia.com\/quiz\/1863743.html?AP_rand=980502951<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-m8s\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-NTRkMWI2NWUzN2Q3NGUwZGYwNThmMWNjMWQ1MzZhZTE.-l6p\">\r\n \t<li>Define accuracy.<\/li>\r\n \t<li>Define precision.<\/li>\r\n \t<li>What can be said about the reproducibility of precise values?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-YzQ3MGMyMGRkNjMzZDM1NTc0Y2U1NThhNTJlZjhlNjk.-i9k\">\r\n \t<li><strong>accuracy: <\/strong> A measure of how close a measurement is to the correct or accepted value of the quantity being measured<\/li>\r\n \t<li><strong> precision: <\/strong> A measure of how close a series of measurements are to one another. Precise measurements are highly reproducible, even if the measurements are not near the correct value.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Percent Error<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define accepted value.<\/li>\r\n \t<li>Define experimental value.<\/li>\r\n \t<li>Define error and calculate the error given appropriate data.<\/li>\r\n \t<li>Define percent error and calculate the error given appropriate data.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How does an electrical circuit work?<\/h3>\r\n<p id=\"x-ck12-ODA0NTRjMDNlOTliZWI2YjY4NGExNzdkMmQ2NzdiNTY.-okf\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210749\/20140811155032515994.jpeg\" alt=\"Resistors have a percent error indicated by a colored band\" width=\"450\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-ZjVjNzI5NThkY2NkMGM2NWFmZTUyZmQ1ZDBiNTkwNTg.-vjk_12-r3d\">How does an electrical circuit work?<\/h4>\r\n<p id=\"x-ck12-ZjVjNzI5NThkY2NkMGM2NWFmZTUyZmQ1ZDBiNTkwNTg.-94f\">A complicated piece of electronics equipment may contain several resistors whose role is to control the voltage and current in the electrical circuit.\u00a0 Too much current and the apparatus malfunctions.\u00a0 Too little current and the system simply does not perform.\u00a0 The resistors values are always given with an error range.\u00a0 A resistor may have a stated value of 200 ohms, but a 10% error range, meaning the resistance could be anywhere between 195-205 ohms.\u00a0 By knowing these values, an electronics person can design and service the equipment to make sure it functions properly.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Percent Error<\/h3>\r\n<p id=\"x-ck12-MjMyNjI3YWZmZjdkZGZmZjYzZDkwNDI1NDE5YWM0YjY.-1mx\">An individual measurement may be accurate or inaccurate, depending on how close it is to the true value.\u00a0 Suppose that you are doing an experiment to determine the density of a sample of aluminum metal.\u00a0 The <strong> accepted value <\/strong> of a measurement is the true or correct value based on general agreement with a reliable reference.\u00a0 For aluminum the accepted density is 2.70 g\/cm <sup> 3 <\/sup> .\u00a0 The <strong> experimental value <\/strong> of a measurement is the value that is measured during the experiment.\u00a0 Suppose that in your experiment you determine an experimental value for the aluminum density to be 2.42 g\/cm <sup> 3 <\/sup> .\u00a0 The <strong> error <\/strong> of an experiment is the difference between the experimental and accepted values.<\/p>\r\n<p id=\"x-ck12-lvc\" class=\"x-ck12-indent\"><img id=\"x-ck12-MTM5NjU4ODUxNTAyMw..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210750\/b61ee1e78e24ac187558913c39c54f89.png\" alt=\"text{Error}=text{experimental value}-text{accepted value}\" width=\"349\" height=\"17\" \/><\/p>\r\n<p id=\"x-ck12-NDkwNjZhYzRhNTBhYjhiMGQ1MjQxY2QzMDg2NDg0ZTU.-csx\">If the experimental value is less than the accepted value, the error is negative.\u00a0 If the experimental value is larger than the accepted value, the error is positive.\u00a0 Often, error is reported as the absolute value of the difference in order to avoid the confusion of a negative error.\u00a0 The <strong> percent error <\/strong> is the absolute value of the error divided by the accepted value and multiplied by 100%.<\/p>\r\n<p id=\"x-ck12-ih5\" class=\"x-ck12-indent\"><img id=\"x-ck12-MTM5NjU4ODUxNTAyNA..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210751\/3168e89be27137f5d2fc86683460c77b.png\" alt=\"% text{Error}=frac{|text{experimental value}-text{accepted value}|}{text{accepted value}} times 100 %\" width=\"447\" height=\"43\" \/><\/p>\r\n<p id=\"x-ck12-ZmJlZDk4ZGEwOGI2NGFhMTE1ODc3MDE5MDk4NmZkM2Q.-csm\">To calculate the percent error for the aluminum density measurement, we can substitute the given values of 2.45 g\/cm <sup> 3 <\/sup> for the experimental value and 2.70 g\/cm <sup> 3 <\/sup> for the accepted value.<\/p>\r\n<p id=\"x-ck12-ja5\" class=\"x-ck12-indent\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210753\/0f40e186c0d644f76be7d3103d772f83.png\" alt=\"% text{Error}=frac{|2.45 text{g}\/text{cm}^3-2.70 text{g}\/text{cm}^3|}{2.70 text{g}\/text{cm}^3} times 100 % = 9.26 %\" width=\"428\" height=\"46\" \/><\/p>\r\n<p id=\"x-ck12-YmJiNGI1ZGI1M2IyYTViYmU5MDY5MGY0NDJjMzFiODE.-bqm\">If the experimental value is equal to the accepted value, the percent error is equal to 0.\u00a0 As the accuracy of a measurement decreases, the percent error of that measurement rises.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-Mzk0YjgyMTFhNGY5MDRhMTJhYmJiY2M4NjlkYzZhYjc.-pze\">\r\n \t<li>Definitions of accepted value and experimental value are given.<\/li>\r\n \t<li>Calculations of error and percent error are demonstrated.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-ZDBiNTFhODU4YWM5NDVlNjI5Yjk5NzkxZTU4NDcxZTY.-nyw\">Read the material at the link below and then do \u201cYour Turn\u201d questions to see how well you did.<\/p>\r\n<p id=\"x-ck12-MTUxYjM5YTZkZjUyNmVhNGVkNmFhNzY0ZTI2MTA5MjU.-sav\"><a href=\"http:\/\/www.mathsisfun.com\/numbers\/percentage-error.html\"> http:\/\/www.mathsisfun.com\/numbers\/percentage-error.html<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-7wt\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-NzlkNGMwZDUxNWFkNTZhZWVkOTNhYWRmMzE4ODcyOTc.-2mi\">\r\n \t<li>Define accepted value.<\/li>\r\n \t<li>Define experimental value<\/li>\r\n \t<li>What happens as the accuracy of the measurement decreases?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-Y2RjYjg0NDNlOGUxYTI4YWZhNzUzZDIzY2U1NDc3NDM.-2hz\">\r\n \t<li><strong> accepted value: <\/strong> \u00a0The true or correct value based on general agreement with a reliable reference.<\/li>\r\n \t<li><strong> error: <\/strong> \u00a0The difference between the experimental and accepted values.<\/li>\r\n \t<li><strong> experimental value: <\/strong> \u00a0The value that is measured during the experiment.<\/li>\r\n \t<li><strong> percent error: <\/strong> The absolute value of the error divided by the accepted value and multiplied by 100%.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-TWVhc3VyZW1lbnQgVW5jZXJ0YWludHk.\">Measurement Uncertainty<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Describe uncertainty in measurements.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How do police officers identify criminals?<\/h3>\r\n<p id=\"x-ck12-MzVmYTE4MzRlMzhiMmM1YmYyYjI0MWM5ODYxZmZlN2I.-gis\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210755\/20140811155032812983.jpeg\" alt=\"Police arresting man\" width=\"450\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-OTRjNzM0ZGZlNjAzOWQzNzQzYzZlNzBhMjlhNzlmMzc.-sd6_13-evq\">How do police officers identify criminals?<\/h4>\r\n<p id=\"x-ck12-OWY5NTA1NjQ2YmM1NTllNWIxN2UwZDhiMjEwYzc3NmY.-x6r\">After a bank robbery has been committed, police will ask witnesses to describe the robbers. They will usually get some answer such as \u201cmedium height.\u201d Others may say \u201cbetween 5 foot 8 inches and 5 foot 10 inches.\u201d In both cases, there is a significant amount of uncertainty about the height of the criminals.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Measurement Uncertainty<\/h2>\r\n<p id=\"x-ck12-MzVmYTE4MzRlMzhiMmM1YmYyYjI0MWM5ODYxZmZlN2I.-gis\">Some error or <strong> uncertainty <\/strong> always exists in any measurement. The amount of uncertainty depends both upon the skill of the measurer and upon the quality of the measuring tool. While some balances are capable of measuring masses only to the nearest 0.1 g, other highly sensitive balances are capable of measuring to the nearest 0.001 g or even better. Many measuring tools such as rulers and graduated cylinders have small lines which need to be carefully read in order to make a measurement. The figure below shows two rulers making the same measurement of an object (indicated by the blue arrow).<\/p>\r\n\r\n<div id=\"x-ck12-YTA4MjdkNWMyMTY0Y2YxZWUxZjdjYTc3OWEyMWViMjg.-2k1\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-mlk\"><img id=\"x-ck12-OTgwNDUtMTM2MzI0NDg0Ny0yMy02Mi1JbWFnZS0tLTU2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210757\/20140811155032979963.png\" alt=\"Uncertainty in measurement on a ruler\" longdesc=\"Uncertainty%20in%20measurement.\" \/><\/p>\r\n<strong> Figure 3.17 <\/strong>\r\n<p id=\"x-ck12-MWQ4ZDI0N2U5MGVjM2Y2ZGZiZDYyZGZiN2ZjY2JkYmE.-twk\">Uncertainty in measurement.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-OGI1OGMxNTdhM2QwNTQ0N2MwZTI5MzI4YWMxMjEzMjE.-z76\">With either ruler, it is clear that the length of the object is between 2 and 3 cm. The bottom ruler contains no millimeter markings. With that ruler, the tenths digit can be estimated and the length may be reported as 2.5 cm.\u00a0 However, another person may judge that the measurement is 2.4 cm or perhaps 2.6 cm. While the 2 is known for certain, the value of the tenths digit is uncertain.<\/p>\r\n<p id=\"x-ck12-OTJiYTU4ODYyNDcyNTBmN2NmYzczMWZmOTczN2IzNTg.-arw\">The top ruler contains marks for tenths of a centimeter (millimeters). Now the same object may be measured as 2.55 cm. The measurer is capable of estimating the hundredths digit because he can be certain that the tenths digit is a 5. Again, another measurer may report the length to be 2.54 cm or 2.56 cm. In this case, there are two certain digits (the 2 and the 5), with the hundredths digit being uncertain. Clearly, the top ruler is a superior ruler for measuring lengths as precisely as possible.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZTVmNDE3Y2RlOGQ4Y2EzMmU4MWRiNGVmZTU4NDcxMzk.-wls\">\r\n \t<li>Uncertainty exists in all measurements.<\/li>\r\n \t<li>The degree of uncertainty is affected in part by the quality of the measuring tool.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-NGMwYzQ1ODU1ODE4MDU5MmY0OTY1YzBmYjczNjc1Yjk.-qmm\">Read the material at the link below and answer the questions on the web site:<\/p>\r\n<p id=\"x-ck12-OGRmNGYxNDMzYTYyMTJjYzg3ZjllODM5MzhjZDViYzI.-u1i\"><a href=\"http:\/\/www2.southeastern.edu\/Academics\/Faculty\/rallain\/plab194\/error.html\"> http:\/\/www2.southeastern.edu\/Academics\/Faculty\/rallain\/plab194\/error.html<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-med\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-Mzc0MDMyMjc5YzYyMzE4Yzg3ZmYyZjE1NDk2YmI1YzY.-efj\">\r\n \t<li>What is uncertainty in measurements?<\/li>\r\n \t<li>Why is the top ruler more reliable in measuring length than the bottom ruler?<\/li>\r\n \t<li>How could the top ruler be made more accurate?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<h2>Glossary<\/h2>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZmExNjAyMjVmMDMwYWQ4MGJlZmYzNTA0YzMxNzY5NjE.-gce\">\r\n \t<li><strong>uncertainty: <\/strong> lack of sureness about something.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-U2lnbmlmaWNhbnQgRmlndXJlcw..\">Significant Figures<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Define significant figures.<\/li>\r\n \t<li>Use significant figure rules to express numerical values correctly.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How fast do you drive?<\/h3>\r\n<p id=\"x-ck12-MDExNGQ4ODM0Y2E5YTRiZjI0ZDA1NTc5OTRiZGU0OTk.-7xs\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210758\/20140811155033084790.jpeg\" alt=\"Speed limits have uncertainty built into it\" width=\"400\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-YTg5YzcyY2YwMjVhMTQ3OTNhYTUxYzIzZGIwYzdmNmU.-e5a_14-7qx\">How fast do you drive?<\/h4>\r\n<p id=\"x-ck12-NmJjYzNjMGE1MjQ4Y2NhMWFmYWM0YTRjZjQyODY2MWM.-bx8\">As you enter the town of Jacinto City, Texas, the sign below tells you that the speed limit is 30 miles per hour. But what if you happen to be driving 31 miles an hour? Are you in trouble? Probably not, because there is a certain amount of leeway built into enforcing the regulation. Most speedometers do not measure the vehicle speed very accurately and could easily be off by a mile or so (on the other hand, radar measurements are much more accurate). So, a couple of miles\/hour difference won\u2019t matter that much. Just don\u2019t try to stretch the limits any further unless you want a traffic ticket.<\/p>\r\n\r\n<\/div>\r\n<h2>Significant Figure<\/h2>\r\n<p id=\"x-ck12-MDExNGQ4ODM0Y2E5YTRiZjI0ZDA1NTc5OTRiZGU0OTk.-7xs\"><span style=\"line-height: 1.5;\">\u00a0<\/span><\/p>\r\n<p id=\"x-ck12-NDU3YmJmMGMzNmExYjIwZmU2NjBlZDgxZWI2MjQ1MzI.-s0m\">The <strong> significant figures <\/strong> in a measurement consist of all the certain digits in that measurement plus one uncertain or estimated digit. In the ruler illustration below, the bottom ruler gave a length with 2 significant figures, while the top ruler gave a length with 3 significant figures. In a correctly reported measurement, the final digit is significant but not certain. Insignificant digits are not reported. With either ruler, it would not be possible to report the length as 2.553 cm as there is no possible way that the thousandths digit could be estimated. The 3 is not significant and would not be reported.<\/p>\r\n\r\n<div id=\"x-ck12-ZmQ1YTcxYjM5OWE1NmY4NTE0YTAyNGUxODM5OWY5M2I.-c9z\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<p id=\"x-ck12-nkr\"><img id=\"x-ck12-OTgwNDUtMTM2MzI0NTIyOC02Mi00LUltYWdlLS0tNTg.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210759\/20140811155033245807.png\" alt=\"Uncertainty in measurement on a ruler\" longdesc=\"Measurement%20with%20two%20different%20rulers.\" \/><\/p>\r\n<strong> Figure 3.18 <\/strong>\r\n<p id=\"x-ck12-MDdmODRlNzQ2MzYxNjU2OGI1NjRiYTkxNzRiNDEyYjQ.-jy2\">Measurement with two different rulers.<\/p>\r\n\r\n<\/div>\r\n<p id=\"x-ck12-YWY1M2FiY2NkN2QwMGEzZWI1ZjZjMTExMTZiN2VhNjE.-yph\">When you look at a reported measurement, it is necessary to be able to count the number of significant figures.\u00a0 The <strong> Table <\/strong> below details the rules for determining the number of significant figures in a reported measurement. For the examples in the table,\u00a0assume that the quantities are correctly reported values of a measured quantity.<\/p>\r\n\r\n<div id=\"x-ck12-N2ExOWRhYTcwMTJlNjJkMDBkNjM3NzE2NTZkNDBlYzY.-c1f\">\r\n<table id=\"x-ck12-NmQ3ZjhlNWIxZjBjYmQxYzY2ZjQyNGMwZGRmMGE1Njg.-oqf\" class=\"x-ck12-nofloat\" border=\"1\"><caption>Significant Figure Rules<\/caption>\r\n<tbody>\r\n<tr>\r\n<td><strong> Rule <\/strong><\/td>\r\n<td><strong> Examples <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1. All nonzero digits in a measurement are significant<\/td>\r\n<td>\r\n<p id=\"x-ck12-MTViODUwNTQ3OTBhZmUzYTRiZDU1OTFkYzkyNjczMzY.-k0h\">A. 237 has three significant figures.<\/p>\r\n<p id=\"x-ck12-NzBiNzJhYmVhZmI5ZTJjMmYwNjdhOGZlMTgzNjExOTY.-2et\">B. 1.897 has four significant figures.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2. Zeros that appear between other nonzero digits are always significant.<\/td>\r\n<td>\r\n<p id=\"x-ck12-MmZiOGQwZjkzMTNjNGI5NzFlZDdiMDNhOTQ0ZmQ4NmE.-ih3\">A. 39,004 has five significant figures.<\/p>\r\n<p id=\"x-ck12-YmM3Mzc0NjVkZTM5M2ZiNGM3OTk2OGJiYzFmYzEzZmQ.-lb9\">B. 5.02 has three significant figures<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3. Zeros that appear in front of all of the nonzero digits are called left-end zeros.\u00a0 Left-end zeros are never significant<\/td>\r\n<td>\r\n<p id=\"x-ck12-NmE3NWM4ZmJjMGUyYTQxOWZkNjBkZjU5MGMyMDY1Yjc.-ik6\">A. 0.008 has one significant figure.<\/p>\r\n<p id=\"x-ck12-OGYxYmZlYzNlYWZlMDE3M2VhZWYwZGEzNGJhYTBkYjA.-ueb\">B. 0.000416 has three significant figures.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4. Zeros that appear after all nonzero digits are called right-end zeros.\u00a0 Right-end zeros in a number that lacks a decimal point are not significant.<\/td>\r\n<td>\r\n<p id=\"x-ck12-NjEzYjI3NDExM2Y1ZDQ4MGM5NWFiODg4NzQxNzA1ZWI.-1cx\">A. 140 has two significant figures.<\/p>\r\n<p id=\"x-ck12-MDEwNzZiMjA3MzNkNmExMTkzNzA5NjljYmY1NjQxMGE.-aq1\">B. 75,210 has four significant figures.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5. Right-end zeros in a number with a decimal point are significant.\u00a0 This is true whether the zeros occur before or after the decimal point.<\/td>\r\n<td>\r\n<p id=\"x-ck12-MGM5ZTJkODcxMDhkMDhlYmY0Yzc0ZGJjNzdmYzIwNGE.-qga\">A. 620.0 has four significant figures.<\/p>\r\n<p id=\"x-ck12-NGQxOTlhNjRlMTYzMzdiMWNhNzAyODFiYjcxYTYyYmY.-vne\">B. 19.000 has five significant figures<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"x-ck12-ZTg0YzJlMGE3ZTE2NGMwMjMzNzVmYzgyZDBlNjAyMGE.-cpa\">It needs to be emphasized that to say a certain digit is not significant does not mean that it is not important or can be left out. Though the zero in a measurement of 140 may not be significant, the value cannot simply be reported as 14. An insignificant zero functions as a placeholder for the decimal point. When numbers are written in scientific notation, this becomes more apparent. The measurement 140 can be written as 1.4 \u00d7 10 <sup> 2 <\/sup> with two significant figures in the coefficient. For a number with left-end zeros, such as 0.000416, it can be written as 4.16 \u00d7 10 <sup> \u22124 <\/sup> with 3 significant figures. In some cases, scientific notation is the only way to correctly indicate the correct number of significant figures. In order to report a value of 15,000,000 with four significant figures, it would need to be written as 1.500 \u00d7 10 <sup> 7 <\/sup> . The right-end zeros after the 5 are significant. The original number of 15,000,000 only has two significant figures.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-x1k\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-MGU0YTdlY2ZmYWZmOWEwMTBkN2UxZWFmZWNmNWE0NWQ.-kat\">\r\n<ul id=\"x-ck12-MGU0YTdlY2ZmYWZmOWEwMTBkN2UxZWFmZWNmNWE0NWQ.-36i\">\r\n \t<li>Significant figures give an indication of the certainty of a measurement.<\/li>\r\n \t<li>Rules allow decisions to be made about how many digits to use in any given situation.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-u6w\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-NzQ5MTA5ZWE5NTI3MzhkYmNiNTFiNmQzN2IxNGZlMmI.-8ot\">\r\n<p id=\"x-ck12-NzQ5MTA5ZWE5NTI3MzhkYmNiNTFiNmQzN2IxNGZlMmI.-djy\">Take a quiz at the link below:<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-nz2\">\r\n<p id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-bpw\"><a href=\"http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/sigfigs.htm\"> http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/sigfigs.htm<\/a><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-nz2\"><\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-1zi\">\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-1zi\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jsg\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-ZDc4NGNkNDc5NTI0NTg5Y2E0ZGNiNTk4MTFjNGE5YmM.-xuc\">\r\n<ol id=\"x-ck12-ZDc4NGNkNDc5NTI0NTg5Y2E0ZGNiNTk4MTFjNGE5YmM.-e1m\">\r\n \t<li>What does a significant figure tell us?<\/li>\r\n \t<li>What is a left-end zero?<\/li>\r\n \t<li>What is a right-end zero?<\/li>\r\n \t<li>What does an insignificant zero do?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-YTc2NjMyZDkzNzQ5OWYzNWUwZGUwYTIzYjAzY2Y5YjY.-2s3\">\r\n \t<li><strong> significant figures: <\/strong> All the certain digits in that measurement plus one uncertain or estimated digit.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-Um91bmRpbmc.\">Rounding<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Learn and apply rules for rounding numbers.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Have you ever been fishing?<\/h3>\r\n<p id=\"x-ck12-NTNiNjgxNzM3OTRiYjc1ZTMzZGIxOTE0NDE5OTU3YWQ.-8ts\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210800\/20140811155033332051.jpeg\" alt=\"People fishing\" width=\"450\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-NDcxMWIzZDk2ODA5OWYyZjVhMjQ0MTU3NTQyOTBmZWU.-mj1_15-gam\">Have you ever been fishing?<\/h4>\r\n<p id=\"x-ck12-YjM2MDA1MWIzZWY0YjJlMzQ0ZWZlZjgxNjdlNzMzNmI.-cz4\">People who fish often are a little unreliable when it comes to describing what they caught and how much it weighed. It\u2019s easier to say your fish weighed ten pounds than it is to accurately describe the weight of 8 pounds 11 ounces. Ten pounds is \u201cclose enough\u201d when you are talking about your catch.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Rounding <strong>\r\n<\/strong><\/h3>\r\n<p id=\"x-ck12-ZDAyYjAxZmQ2NTNhNzMyN2I5MTIxY2NhYzU3YmQzOTY.-ax1\">Before dealing with the specifics of the rules for determining the significant figures in a calculated result, we need to be able to round numbers correctly. To <strong> round <\/strong> a number, first decide how many significant figures the number should have. Once you know that, round to that many digits, starting from the left. If the number immediately to the right of the last significant digit is less than 5, it is dropped and the value of the last significant digit remains the same. If the number immediately to the right of the last significant digit is greater than or equal to 5, the last significant digit is increased by 1.<\/p>\r\n<p id=\"x-ck12-MDQwNzRmODQzNzNhYWM3NTY4ZmVlM2RhNDUwZTk2MDY.-pi4\">Consider the measurement 207.518 m. Right now, the measurement contains six significant figures. How would we successively round it to fewer and fewer significant figures? Follow the process as outlined in <strong> Table <\/strong> below .<\/p>\r\n\r\n<div id=\"x-ck12-ODA4MWJlNDNkMTE4Y2IyMDUxMDBjMGRjYTdlZDhjYWU.-kps\">\r\n<table id=\"x-ck12-ZjU5NTAzMDc4YjYyOGJmZDA3ZTNhNDk2ODVjMmIyZTU.-xtq\" class=\"x-ck12-nofloat\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td><strong> Number of Significant Figures <\/strong><\/td>\r\n<td><strong> Rounded Value <\/strong><\/td>\r\n<td><strong> Reasoning <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>207.518<\/td>\r\n<td>All digits are significant<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>207.52<\/td>\r\n<td>8 rounds the 1 up to 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>207.5<\/td>\r\n<td>2 is dropped<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>208<\/td>\r\n<td>5 rounds the 7 up to 8<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>210<\/td>\r\n<td>8 is replaced by a 0 and rounds the 0 upto 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>200<\/td>\r\n<td>1 is replaced by a 0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"x-ck12-ZmE5ZjkzMjFhMzJmNzA4M2NkNmNhZTAyMTFiZDk2YzQ.-5xh\">Notice that the more rounding is done, the less reliable to figure is. An approximate value may be sufficient for some purposes, but scientific work requires a much higher level of detail.<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-kx7\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<div id=\"x-ck12-NTFjNTE1YTI4OWUxMDUwMDE2MTQxYTM0Yjk2ODcyMTI.-jaz\">\r\n<ul id=\"x-ck12-NTFjNTE1YTI4OWUxMDUwMDE2MTQxYTM0Yjk2ODcyMTI.-iff\">\r\n \t<li>Rounding involves the adjustment of a value to account for the proper number of significant digits.<\/li>\r\n \t<li>Rules exist for rounding of numbers.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-2nv\">\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-2nv\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-lte\">Practice rounding numbers using the following link:<\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-YjEwZjVjYzkxZWM2NWZmNmJjNDdiZGRiZDhmY2JkZTY.-g0z\">\r\n<p id=\"x-ck12-YmFiZDNhNGEwZDg0ODAyMDg4ZDk4MmFlYWQ4ZGZmM2E.-n4g\"><a href=\"http:\/\/www.mathscore.com\/math\/practice\/Rounding%20Numbers\/\" target=\"_blank\" rel=\"noopener\">http:\/\/www.mathscore.com\/math\/practice\/Rounding%20Numbers\/<\/a><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-tlb\">\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-tlb\">\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ut8\"><em> Questions <\/em><\/p>\r\n\r\n<\/div>\r\n<div id=\"x-ck12-MzJiMjFjYThjOTdlNTk2OGY1OTZhMjJkMzM4YTMxNDQ.-hoy\">\r\n<ol id=\"x-ck12-MzJiMjFjYThjOTdlNTk2OGY1OTZhMjJkMzM4YTMxNDQ.-sg6\">\r\n \t<li>Why do we round numbers?<\/li>\r\n \t<li>What do we need to know before we round a number?<\/li>\r\n \t<li>What is \u201crounding up\u201d?<\/li>\r\n \t<li>What is \u201crounding down\u201d?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"x-ck12-data-problem-set\">\r\n<h2>Glossary<\/h2>\r\n<\/div>\r\n<div id=\"x-ck12-ZWIzMjM1MzFiOGViOGVmODExNjk5NTBhOTgxYTVlOTU.-kuj\" class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZWIzMjM1MzFiOGViOGVmODExNjk5NTBhOTgxYTVlOTU.-sfv\">\r\n \t<li><strong>round: <\/strong> Adjust a value to reflect the actual number of significant figures.<\/li>\r\n \t<li><strong> rounding down: <\/strong> Adjusting a value to less than the original value.<\/li>\r\n \t<li><strong> rounding up: <\/strong> Adjusting a value to more than the original value.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1 id=\"x-ck12-VW5jZXJ0YWludHkgaW4gTXVsdGlwbGljYXRpb24gYW5kIERpdmlzaW9u\">Uncertainty in Multiplication and Division<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>State the rule for rounding values obtained by multiplication or division.<\/li>\r\n \t<li>Apply the rule to appropriate problems.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"x-ck12-data-objectives\"><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Who should report the number - you or your calculator?<\/h3>\r\n<p id=\"x-ck12-MzFmZTBmODRlOGI3MDFkODhkNmRlYTQyMjA3NGE1MmQ.-tqt\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210802\/20140811155033473901.jpeg\" alt=\"Calculators do not keep track of significant figures\" width=\"300\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-ODQzOTVkMzlhYWU2NjQ0ODM0ZDU2ZTg3ZmM1NGIyNmI.-ozy_16-c5w\">Who should report the numbers - you or your calculator?<\/h4>\r\n<p id=\"x-ck12-ODQzOTVkMzlhYWU2NjQ0ODM0ZDU2ZTg3ZmM1NGIyNmI.-byi\">Calculators do just what you ask of them, no more and no less.\u00a0 However, they sometimes can get a little out of hand.\u00a0 If I multiply 2.48 times 6.3, I get an answer of 15.687, a value that ignores the number of significant figures in either number.\u00a0 Division with a calculator is even worse. When I divide 12.2 by 1.7, the answer I obtain is\u00a0 7.176470588.\u00a0 Neither piece of data is accurate to nine decimal places, but the calculator doesn\u2019t know that.\u00a0 The human being operating the instrument has to make the decision about how many places to report.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Uncertainty in Multiplication and Division<\/h3>\r\n<p id=\"x-ck12-MzA3YTdiMzVkYmY5ODVlYzA2OTA5Nzg4ZmFiNmIxZmU.-vcp\">The density of a certain object is calculated by dividing the mass by the volume.\u00a0 Suppose that a mass of 37.46 g is divided by a volume of 12.7 cm <sup> 3 <\/sup> .\u00a0 The result on a calculator would be:<\/p>\r\n<p id=\"x-ck12-fgj\" class=\"x-ck12-indent\"><img id=\"x-ck12-MTM5NjU4ODU3Njk1Mw..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210803\/2ec47941246b37af7b95030a4e61e163.png\" alt=\"D=frac{m}{V}=frac{37.46 text{g}}{12.7 text{cm}^3}=2.949606299 text{g}\/text{cm}^3\" width=\"325\" height=\"39\" \/><\/p>\r\n<p id=\"x-ck12-OWU0MTEzMDE3MTZiZTIzZTJhNzE5NTU3ODYyNGJhZGE.-ymt\">The value of the mass measurement has four significant figures, while the value of the volume measurement has only three significant figures.\u00a0 For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.\u00a0 Applying this rule results in a density of 2.95 g\/cm <sup> 3 <\/sup> , for three significant figures \u2013 the same as the volume measurement.<\/p>\r\n\r\n<h4>Sample Problem:\u00a0 Significant Figures in Calculations<\/h4>\r\n<p id=\"x-ck12-OWI5MTc0YmU2Y2ZjOTY2NGNjZDU0YTc2ZDk3YTE1MjU.-5l0\">Perform the following calculations, rounding the answers to the appropriate number of significant figures.<\/p>\r\n\r\n<ol id=\"x-ck12-ff4\" class=\"x-ck12-upper-alpha\">\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210804\/9f8361320e1e8d6f294697e451567dab.png\" alt=\"0.048 text{m} times 32.97 text{m}\" width=\"146\" height=\"14\" \/><\/li>\r\n \t<li><img id=\"x-ck12-MTM5NjU4ODU3Njk1NA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210805\/b04417fd0bca3bf75738436e1bced6fd.png\" alt=\"14,570 text{kg} div 5.81 text{L}\" width=\"147\" height=\"17\" \/><\/li>\r\n<\/ol>\r\n<p id=\"x-ck12-M2ZkZjY4NDZkODRkNWJlNjEwM2JlZjVhOWQwZGFlMTU.-xau\"><em> Step 1:\u00a0 Plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-NjcxYWI2ZGUxODZlMDZhZjA2N2E5Y2RiODFkZmJmNzI.-zko\">Analyze each of the measured values to determine how many significant figures should be in the result.\u00a0 Perform the calculation and round appropriately.\u00a0 Apply the correct units to the answer. When multiplying or dividing, the units are also multiplied or divided.<\/p>\r\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-04n\"><em> Step 2:\u00a0 Calculate <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-MmFmNDE4ZmM4ODk1YTA1MTZkNzE4ODFlZmYxMjk3OGM.-65y\" class=\"x-ck12-upper-alpha\">\r\n \t<li><sup><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210806\/566dd18a8eb080a8f60e472c4e2efddc.png\" alt=\"0.048 text{m} times 32.97 text{m} = 1.6 text{m}^2\" width=\"219\" height=\"16\" \/> \u00a0 <\/sup> Round to two significant figures because 0.048 has two.<\/li>\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210807\/a3ad0272ba73f28950d5452c88fa5f55.png\" alt=\"14,570 text{kg} div 5.81 text{L} = 2510 text{kg}\/ text{L}\" width=\"252\" height=\"18\" \/> \u00a0Round to three significant figures because 5.81 has three.<\/li>\r\n<\/ol>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-OWM0NTNmMWY1ZjVjMzRkNTRiNDA3N2M3NjJkZDZlN2M.-mpv\">\r\n \t<li>For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-MDBhNjIzYzY5MDM2MGM4NWY4NzMyMzJmODYyMDdkYWM.-lty\"><a href=\"https:\/\/web.archive.org\/web\/20150316195329\/http:\/\/sigfigscalculator.appspot.com\/tutorial\/multiply_and_divide\" target=\"_blank\" rel=\"noopener\">Read the information and work on the problems on this web site.<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-z8k\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-ZjBlYzFlMDdmZTM0MzM4OTE4YjRkNDExN2JkODE3ODQ.-dyr\">\r\n \t<li>What is the basic principle involved in working with multiplication and division?<\/li>\r\n \t<li>What happens to units in multiplication and division problems?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"x-ck12-data-problem-set\"><\/div>\r\n<div class=\"x-ck12-data-vocabulary\"><\/div>\r\n<h1 id=\"x-ck12-VW5jZXJ0YWludHkgaW4gQWRkaXRpb24gYW5kIFN1YnRyYWN0aW9u\">Uncertainty in Addition and Subtraction<\/h1>\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n&nbsp;\r\n<ul>\r\n \t<li>State the rule for rounding values obtained by addition or subtraction.<\/li>\r\n \t<li>Apply the rule to appropriate problems.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox examples\">\r\n<h3>How old do you think this calculator?<\/h3>\r\n<p id=\"x-ck12-NDY1ZjU5YjczYjg0NDk4ZDFkNjI1ODc5NjczYTk0YjE.-jhr\"><span class=\"x-ck12-img-inline\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210808\/20140811155033588269.jpeg\" alt=\"Watch calculator\" width=\"300\" \/><\/span><\/p>\r\n\r\n<h4 id=\"x-ck12-NDAzYzllNDBkODFjN2JkYTQ1OTQ2YjcwYzFlOTZjNmY.-d3u_17-axc\">How old do you think this calculator is?<\/h4>\r\n<p id=\"x-ck12-M2VkNjEzMmEwNmRmNjRmZDg1MjEwZDQyYzAxMzkxZmM.-q5d\">Calculators are great devices. Their invention has allowed for quick computation at work, school, or other places where manipulation of numbers needs to be done rapidly and accurately. But they are only as good as the numbers put into them. The calculator cannot determine how accurate each of a set of numbers is and the answer given on the screen must be assessed by the user for reliability.<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Uncertainty in Addition and Subtraction<\/h2>\r\n<p id=\"x-ck12-NTQyYjI5MTIxZWE0NWE2YjY4ZmM0MjY3NjQ1ODhkZjk.-2jv\">Consider two separate mass measurements: 16.7 g and 5.24 g. The first mass measurement (16.7 g) is known only to the tenths place or to one digit after the decimal point. There is no information about its hundredths place and so that digit cannot be assumed to be zero. The second measurement (5.24 g) is known to the hundredths place or to two digits after the decimal point.<\/p>\r\n<p id=\"x-ck12-OGFkYjc4NGEwZDhlODdhNmYwYjQzM2Q5Y2E5NmExZTg.-evp\">When these masses are added together, the result on a calculator is 16.7 + 5.24 = 21.94 g. Reporting the answer as 21.94 g suggests that the sum is known all the way to the hundredths place. However that cannot be true because the hundredths place of the first mass was completely unknown. The calculated answer needs to be rounded in such a way as to reflect the certainty of each of the measured values that contributed to it. For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places. The sum of the above masses would be properly rounded to a result of 21.9 g.<\/p>\r\n<p id=\"x-ck12-MWE5NmE0YzU2NmRmODUxYzNkMmE3NGFkZGEwMjE3Yjg.-yqc\">When working with whole numbers, pay attention to the last significant digit that is to the left of the decimal point and round your answer to that same point. For example, consider the subtraction: 78,500 m \u2013 362 m. The calculated result is 78,138 m. However, the first measurement is known only to the hundreds place, as the 5 is the last significant digit. Rounding the result to that same point means that the correct result is 78,100 m.<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZWFmOGVkOGYwZTE3ODJmNWM5YmMzMjRjMjM4YTliNzA.-jwv\">\r\n \t<li>For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-MDBhNjIzYzY5MDM2MGM4NWY4NzMyMzJmODYyMDdkYWM.-1vm\"><a href=\"https:\/\/web.archive.org\/web\/20150316175012\/http:\/\/sigfigscalculator.appspot.com\/tutorial\/add_and_subtract\" target=\"_blank\" rel=\"noopener\">Read the information and work on the problems at this web site.<\/a><\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jxp\"><em> Questions <\/em><\/p>\r\n\r\n<ol id=\"x-ck12-OWU2ZDQ3OTU3MTA5ZmViYTJhNjM3ZWI3MTBlMDkxZDc.-rog\">\r\n \t<li>What is the basic principle to use in working with addition and subtraction?<\/li>\r\n \t<li>What do you pay attention to when working with whole numbers?<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n\r\n[reveal-answer q=\"836080\"]Show References[\/reveal-answer]\r\n[hidden-answer a=\"836080\"]\r\n<h2>References<\/h2>\r\n<ol>\r\n \t<li>Courtesy of US Department of Commerce. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:US_National_Length_Meter.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:US_National_Length_Meter.JPG <\/a> .<\/li>\r\n \t<li>Courtesy of National Institute of Standards and Technology . <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Standard_kilogram,_2.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Standard_kilogram,_2.jpg <\/a> .<\/li>\r\n \t<li>User:Canuckguy\/Wikipedia and User:AzaToth\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Metric_system_adoption_map.svg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Metric_system_adoption_map.svg <\/a> .<\/li>\r\n \t<li>Joseph Wright of Derby. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:JosephWright-Alchemist.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:JosephWright-Alchemist.jpg <\/a> .<\/li>\r\n \t<li>Courtesy of NASA. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100819.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100819.jpg <\/a> .<\/li>\r\n \t<li>User:\u017beglarz\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Prawa_burta_ORP_Iskra.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Prawa_burta_ORP_Iskra.JPG <\/a> .<\/li>\r\n \t<li>User:Kenyon\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:CamelBak_water_bottle.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:CamelBak_water_bottle.jpg <\/a> .<\/li>\r\n \t<li>Bram Van Damme (Flickr: Bramus!). <a href=\"http:\/\/www.flickr.com\/photos\/bramus\/3249196137\/\"> http:\/\/www.flickr.com\/photos\/bramus\/3249196137\/ <\/a> .<\/li>\r\n \t<li>User:Darrien\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Graduated_cylinder.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Graduated_cylinder.jpg <\/a> .<\/li>\r\n \t<li>Courtesy of NASA. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:151746main_s121e05215-lg.jpeg\"> http:\/\/commons.wikimedia.org\/wiki\/File:151746main_s121e05215-lg.jpeg <\/a> .<\/li>\r\n \t<li>Courtesy of US Drug Enforcement Administration. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Analytical_balance_mettler_ae-260.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Analytical_balance_mettler_ae-260.jpg <\/a> .<\/li>\r\n \t<li>User:Dlls\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Cat_public_domain_dedication_image_0002.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Cat_public_domain_dedication_image_0002.jpg <\/a> .<\/li>\r\n \t<li>John Collier. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:James_Prescott_Joule_by_John_Collier,_1882.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:James_Prescott_Joule_by_John_Collier,_1882.jpg <\/a> .<\/li>\r\n \t<li>Charcoal: Serge Melki; Snow: User:Haymanj\/Wikimedia Commons. Charcoal: http:\/\/www.flickr.com\/photos\/sergemelki\/3106924114\/; Snow: http:\/\/commons.wikimedia.org\/wiki\/File:Snow_Gum1.JPG .<\/li>\r\n \t<li>. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Fahrenheit_small.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Fahrenheit_small.jpg <\/a> .<\/li>\r\n \t<li>Olof Arenius. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Anders-Celsius-Head.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Anders-Celsius-Head.jpg <\/a> .<\/li>\r\n \t<li>. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Kelvin-1200-scale1000.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Kelvin-1200-scale1000.jpg <\/a> .<\/li>\r\n \t<li>Laura Guerin. CK-12 Foundation .<\/li>\r\n \t<li>Courtesy of the US Army. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Flickr_-_The_U.S._Army_-_Track_practice.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Flickr_-_The_U.S._Army_-_Track_practice.jpg <\/a> .<\/li>\r\n \t<li>User:Joegrimes\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Farmlandlysander.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Farmlandlysander.JPG <\/a> .<\/li>\r\n \t<li>CK-12 Foundation - Christopher Auyeung. .<\/li>\r\n \t<li>Tony Hisgett (Flickr:ahisgett). <a href=\"http:\/\/www.flickr.com\/photos\/hisgett\/220279395\/\"> http:\/\/www.flickr.com\/photos\/hisgett\/220279395\/ <\/a> .<\/li>\r\n \t<li>Daniel Arizpe. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:High_school_basketball_game.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:High_school_basketball_game.jpg <\/a> .<\/li>\r\n \t<li>CK-12 Foundation - Christopher Auyeung. .<\/li>\r\n \t<li>Image copyright zebrik, 2012. <a href=\"http:\/\/www.shutterstock.com\"> http:\/\/www.shutterstock.com <\/a> .<\/li>\r\n \t<li>Vald Kliper. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Resistencias_250W_5%25_sobre_papel_milimetrado.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Resistencias_250W_5%25_sobre_papel_milimetrado.JPG <\/a> .<\/li>\r\n \t<li>User:Riemann\/Da.Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Danish_police_arrest.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Danish_police_arrest.jpg <\/a> .<\/li>\r\n \t<li>CK-12 Foundation - Christopher Auyeung. .<\/li>\r\n \t<li>User:WhisperToMe\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:JacintoCitySignJacintoCityTexas.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:JacintoCitySignJacintoCityTexas.JPG <\/a> .<\/li>\r\n \t<li>CK-12 Foundation - Christopher Auyeung. .<\/li>\r\n \t<li>Nancy Heise. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Catching_salmon_in_the_ocean_off_Raspberry_Island.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Catching_salmon_in_the_ocean_off_Raspberry_Island.JPG <\/a> .<\/li>\r\n \t<li>Adrian Pingstone (Wikimedia: Arpingstone). <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Calculator.arp.600pix.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Calculator.arp.600pix.jpg <\/a> .<\/li>\r\n \t<li>User:Septagram\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Cfx400c.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Cfx400c.JPG <\/a> .<\/li>\r\n \t<li><em>Martha Marie Day, Ed.D., Anthony Carpi, Ph.D. \u201cTemperature\u201d Visionlearning Vol. SCI-1 (5), 2003. \u00a0<a href=\"http:\/\/www.visionlearning.com\/en\/library\/General-Science\/3\/Temperature\/48\">http:\/\/www.visionlearning.com\/en\/library\/General-Science\/3\/Temperature\/48<\/a>.<\/em><\/li>\r\n<\/ol>\r\n[\/hidden-answer]","rendered":"<h3>SI Base Units<\/h3>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-NTc1MmZmMGU2ZjgzMzM0MGQ5NGU0MjBiZDIxZGJkYTc.-rtj\">\n<li>Define the SI system of units.<\/li>\n<li>List the seven base units of measurement.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>How long is a yard?<\/h3>\n<p>It depends on whom you ask and when you asked the question. Today we have a standard definition of the yard, which you can see marked on every football field. If you move the ball ten yards, you get a first down and it doesn\u2019t matter whether you are playing in Los Angeles, Dallas, or Green Bay. But at one time that yard was arbitrarily defined as the distance from the tip of the king\u2019s nose to the end of his outstretched hand. Of course, the problem there is simple: new king, new distance (and then you have to remark all those football fields).<\/p>\n<\/div>\n<h3>SI Base Units<\/h3>\n<p id=\"x-ck12-YzUxZDA1OTk2MWM5ODQyNWVmMTRiZGNlYTViMjg5MDY.-sp2\">All measurements depend on the use of units that are well known and understood. The <strong> English system <\/strong> of measurement units (inches, feet, ounces, etc.) are not used in science because of the difficulty in converting from one unit to another. The <strong> metric system <\/strong> is used because all metric units are based on multiples of 10, making conversions very simple. The metric system was originally established in France in 1795. <strong> The International System of Units <\/strong> is a system of measurement based on the metric system. The acronym <strong> SI <\/strong> is commonly used to refer to this system and stands for the French term, <em> Le Syst\u00e8me International d\u2019Unit\u00e9s <\/em> . The SI was adopted by international agreement in 1960 and is composed of seven base units, as shown in <strong> Table <\/strong> below .<\/p>\n<table id=\"x-ck12-MjRjMzVmMWM5MzM5ODliYjM5MGE4ZWI3MjVlZWRhN2I.-t8j\" class=\"x-ck12-nofloat\">\n<caption>SI Base Units of Measurement<\/caption>\n<tbody>\n<tr>\n<td><strong> Quantity <\/strong><\/td>\n<td><strong> SI Base Unit <\/strong><\/td>\n<td><strong> Symbol <\/strong><\/td>\n<\/tr>\n<tr>\n<td>Length<\/td>\n<td>meter<\/td>\n<td>m<\/td>\n<\/tr>\n<tr>\n<td>Mass<\/td>\n<td>kilogram<\/td>\n<td>kg<\/td>\n<\/tr>\n<tr>\n<td>Temperature<\/td>\n<td>kelvin<\/td>\n<td>K<\/td>\n<\/tr>\n<tr>\n<td>Time<\/td>\n<td>second<\/td>\n<td>s<\/td>\n<\/tr>\n<tr>\n<td>Amount of a Substance<\/td>\n<td>mole<\/td>\n<td>mol<\/td>\n<\/tr>\n<tr>\n<td>Electric Current<\/td>\n<td>ampere<\/td>\n<td>A<\/td>\n<\/tr>\n<tr>\n<td>Luminous Intensity<\/td>\n<td>candela<\/td>\n<td>cd<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"x-ck12-MWEwN2I3YzI5YWRkNWFiNTg4ZmJhMTNmYzY2YjI5ZDQ.-m75\">\n<p id=\"x-ck12-ZDBlZGE5ZGU1ZGU2MTI4ZTQ5M2I5ZTdjMzlkN2VkMjY.-xjt\">The first five units are frequently encountered in chemistry. All other measurement quantities, such as volume, force, and energy, can be derived from these seven base units.<\/p>\n<div id=\"x-ck12-ZTcyOWI2Zjg2M2U1ZmQxZjc3NzFmY2FhZjU1YjAwMGE.-1ec\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-azi\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2NTk1OC0zMi04OS1JbWFnZS0tLTI5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210659\/20140811155029197942.jpeg\" alt=\"The meter standard\" longdesc=\"Meter%20standard.\" \/><\/p>\n<p><strong> Figure 3.1 <\/strong><\/p>\n<p id=\"x-ck12-NWRkYmEyZmFkMTdkODI3NDQ1Y2MyMWM4Mjk1OGNkZjA.-lkg\">Meter standard.<\/p>\n<\/div>\n<div id=\"x-ck12-NWYzOGU0MzI3NGVkOTM1ZjU2MmU1ZGQwY2YxZjQ0YmM.-wim\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-lky\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2NjAwMi02OC0zOC1JbWFnZS0tLTMw\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210700\/20140811155029328243.jpeg\" alt=\"The kilogram standard\" longdesc=\"Kilogram%20standard\" \/><\/p>\n<p><strong> Figure 3.2 <\/strong><\/p>\n<p id=\"x-ck12-NTExOTVjY2U3MTMxNThlYWQ2MDdkZDg1NjlkNGFiOTg.-cuk\">Kilogram standard<\/p>\n<\/div>\n<p id=\"x-ck12-MDM1ZDRjN2Y1N2YzYTc3YjcwZGE0OWVjNTM2OTI1NTI.-e3g\">\u00a0The map in <strong> Figure <\/strong> below shows the adoption of the SI units in countries around the world. The United States has legally adopted the metric system for measurements, but does not use it in everyday practice. Great Britain and much of Canada use a combination of metric and imperial units.<\/p>\n<\/div>\n<div id=\"x-ck12-NTYyMDljZTk5M2IxMWNmZTYzY2QzMjA4YmI2MjU0Zjk.-3td\">\n<div id=\"x-ck12-MzI1ZTY0NDI2NGU3ZWFjNmQ3MmU4YWI2YjkwMGRkYWM.-ovu\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<p id=\"x-ck12-3eu\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2NjA2MS03My0zMC1JbWFnZS0tLTMx\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210701\/20140811155029406394.png\" alt=\"Map of the world that uses the metric system\" longdesc=\"Areas%20of%20world%20using%20metric%20system.\" \/><\/p>\n<p><strong> Figure 3.3 <\/strong><\/p>\n<p id=\"x-ck12-MDViOTYzZjI5MDIwODA5YzhmOWFiNjI4NDg0NGFjMjU.-ea4\">Areas of world using metric system.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-OWVhN2RjYTQyZGIyZjc4OTE4N2JmNGYyZGRmZTlkZjM.-wv3\">\n<ul id=\"x-ck12-OWVhN2RjYTQyZGIyZjc4OTE4N2JmNGYyZGRmZTlkZjM.-e5j\">\n<li>The SI system is based on multiples of ten.<\/li>\n<li>There are seven basic units in the SI system.<\/li>\n<li>Five of these units are commonly used in chemistry.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-xwo\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-xwo\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jta\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-yfi\">\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-vls\">Use the link below to answer the following questions:<\/p>\n<\/div>\n<div id=\"x-ck12-NTA2NmM1Nzk5YWZhNmFlYzJiNmQwMTFkZWQ4MTVhOTg.-mqt\">\n<p id=\"x-ck12-NTA2NmM1Nzk5YWZhNmFlYzJiNmQwMTFkZWQ4MTVhOTg.-ftx\"><a href=\"http:\/\/physics.nist.gov\/cuu\/Units\/history.html\"> http:\/\/physics.nist.gov\/cuu\/Units\/history.html <\/a><\/p>\n<\/div>\n<div id=\"x-ck12-MTZhYzM0YjFhOGQ0ZWQyZWYwNDBmMDU0YzJjMTZmNWE.-wip\">\n<ol id=\"x-ck12-MTZhYzM0YjFhOGQ0ZWQyZWYwNDBmMDU0YzJjMTZmNWE.-jbp\">\n<li>When was the metric system created?<\/li>\n<li>What was deposited in the Archives de la R\u00e9publique in Paris?<\/li>\n<li>What was the CGS system based on?<\/li>\n<li>When was the name <em> International System of Units <\/em> ( <em> SI <\/em> ) assigned?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-wnz\">\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-wnz\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-hkl\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-YWNjZmQ2MjQzNjEyMjFhNGYwNWFhMzk3M2ZiOGYyNDU.-7li\">\n<ol id=\"x-ck12-YWNjZmQ2MjQzNjEyMjFhNGYwNWFhMzk3M2ZiOGYyNDU.-ywl\">\n<li>What does SI stand for?<\/li>\n<li>When was this system adopted by the international community?<\/li>\n<li>Which of the units are commonly used in chemistry?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div id=\"x-ck12-Yzk0MmYwMDU1NTk1Y2EwNjdmYmZjN2MwM2Q1MmE1NTA.-q61\" class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-Y2Y0YmNiM2VkMDFiZjEyZjk1NTk5NjYzZGIwYmQ3NTg.-026\">\n<li><strong>English system: <\/strong> A system of measurements based on feet inches, and other somewhat arbitrary units.<\/li>\n<li><strong> The International System of Units: <\/strong> Based on the metric system of measurements.<\/li>\n<li><strong> Metric system <\/strong> : Based on units of 10.<\/li>\n<li><strong> SI: <\/strong> The metric system and stands for the French term, <em> Le Syst\u00e8me International d\u2019Unit\u00e9s. <\/em><\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-TWV0cmljIFByZWZpeGVz\">Metric Prefixes<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>List common metric prefixes and their exponential values.<\/li>\n<li>Convert from one exponential factor to another for a given unit.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>What do Latin and Greek have to do with modern science?<\/h3>\n<p id=\"x-ck12-NDAxYTVlMGNhYjQ1ZGU3YmU4ZWI5YWFlNzhmZWY1NTE.-kav\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210702\/20140811155029529152.jpeg\" alt=\"Drawing of ancient scientist\" width=\"250\" \/><\/span><\/p>\n<p id=\"x-ck12-ZWFjMWZkMGRlNDQ0ZWRkODRlZTYyOWNjZmNhZjZhNzM.-x6i\">Isn\u2019t it hard enough to learn English terms? For hundreds of years, the languages of the educated class were Latin and Greek. In part, because the literature of philosophy was Latin and Greek. Even the medieval Bibles were written in those two languages \u2013 the first English translation was in the late 1380s. Using Latin and Greek allowed scholars from different countries to communicate more easily with one another. Today we still see many Latin phrases in legal communications (\u201cpro bono\u201d meaning to do something \u201cfor the good\u201d and not charge legal fees), scientific naming of biological species, and Latin is used for the annual student speech at Harvard University graduations. Not bad for a \u201cdead\u201d language.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Metric Prefixes <strong><br \/>\n<\/strong><\/h3>\n<p id=\"x-ck12-YTFhYTRlZmIzYzFlZDAxM2Q4YTZiZjM0ODNlNzkwZmQ.-y8h\">Conversions between metric system units are straightforward because the system is based on powers of ten. For example, meters, centimeters, and millimeters are all metric units of length. There are 10 millimeters in 1 centimeter and 100 centimeters in 1 meter. <strong> Metric prefixes <\/strong> are used to distinguish between units of different size. These prefixes all derive from either Latin or Greek terms. For example, <em> mega <\/em> comes from the Greek word <img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM3ODMxODg1OTc5MQ..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210704\/3632ee411a7fe20a46f5041dee4bbbd8.png\" alt=\"mu acute{varepsilon} gammaalphavarsigma\" width=\"49\" height=\"16\" \/> , meaning \u201cgreat\u201d<\/p>\n<p id=\"x-ck12-MWI1MzM5MTVlY2QzYTI1ZGQ0NGVmMzgxNGFlZDIxNjk.-txa\"><strong> Table <\/strong> below lists the most common metric prefixes and their relationship to the central unit that has no prefix. Length is used as an example to demonstrate the relative size of each prefixed unit.<\/p>\n<table id=\"x-ck12-YjY1MzI0NmRlMDU2Yjk4OTcyZDAwZDBiMDc3ZTc0NDk.-ye0\" class=\"x-ck12-nofloat\">\n<caption>SI Prefixes<\/caption>\n<tbody>\n<tr>\n<td><strong> Prefix <\/strong><\/td>\n<td><strong> Unit Abbrev. <\/strong><\/td>\n<td><strong> Meaning <\/strong><\/td>\n<td><strong> Example <\/strong><\/td>\n<\/tr>\n<tr>\n<td>giga<\/td>\n<td>G<\/td>\n<td>1,000,000,000<\/td>\n<td>1 gigameter (Gm) = 10 <sup> 9 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>mega<\/td>\n<td>M<\/td>\n<td>1,000,000<\/td>\n<td>1 megameter (Mm) = 10 <sup> 6 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>kilo<\/td>\n<td>k<\/td>\n<td>1000<\/td>\n<td>1 kilometer (km) = 1000 m<\/td>\n<\/tr>\n<tr>\n<td>hecto<\/td>\n<td>h<\/td>\n<td>100<\/td>\n<td>1 hectometer (hm) = 100 m<\/td>\n<\/tr>\n<tr>\n<td>deka<\/td>\n<td>da<\/td>\n<td>10<\/td>\n<td>1 dekameter (dam) = 10 m<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong> 1 <\/strong><\/td>\n<td><strong> 1 meter (m) <\/strong><\/td>\n<\/tr>\n<tr>\n<td>deci<\/td>\n<td>d<\/td>\n<td>1\/10<\/td>\n<td>1 decimeter (dm) = 0.1 m<\/td>\n<\/tr>\n<tr>\n<td>centi<\/td>\n<td>c<\/td>\n<td>1\/100<\/td>\n<td>1 centimeter (cm) = 0.01 m<\/td>\n<\/tr>\n<tr>\n<td>milli<\/td>\n<td>m<\/td>\n<td>1\/1000<\/td>\n<td>1 millimeter (mm) = 0.001 m<\/td>\n<\/tr>\n<tr>\n<td>micro<\/td>\n<td>\u03bc<\/td>\n<td>1\/1,000,000<\/td>\n<td>1 micrometer (\u03bcm) = 10 <sup> -6 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>nano<\/td>\n<td>n<\/td>\n<td>1\/1,000,000,000<\/td>\n<td>1 nanometer (nm) = 10 <sup> -9 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>pico<\/td>\n<td>p<\/td>\n<td>1\/1,000,000,000,000<\/td>\n<td>1 picometer (pm) = 10 <sup> -12 <\/sup> m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"x-ck12-NzY2ZTA4NmZlNDVmNGE2NTA2NGI3MGU0MzY4ZGM1NzI.-8o4\">\n<div class=\"textbox\">There are more prefixes &#8211; some of them rarely used. Have you ever heard of a zeptometer? You can learn more about prefixes at <a href=\"https:\/\/web.archive.org\/web\/20070310221329\/http:\/\/www.essex1.com\/people\/speer\/large.html\" target=\"_blank\" rel=\"noopener\"> http:\/\/www.essex1.com\/people\/speer\/large.html<\/a>.<\/div>\n<\/div>\n<div id=\"x-ck12-NGU0NGE1MjJkYjA5YzZkYTkwYTI1YzE3MWM3MzA4ZTc.-lle\">\n<p id=\"x-ck12-NGU0NGE1MjJkYjA5YzZkYTkwYTI1YzE3MWM3MzA4ZTc.-muw\">There are a couple of odd little practices with the use of metric abbreviations. Most abbreviations are lower-case. We use \u201cm\u201d for meter and not \u201cM\u201d. However, when it comes to volume, the base unit \u201cliter\u201d is abbreviated as \u201cL\u201d and not \u201cl\u201d. So we would write 3.5 milliliters as 3.5 mL.<\/p>\n<\/div>\n<div id=\"x-ck12-MTZiZTdhNTkwMWU3YjliMGUyNDQ2ZDVmMjQ0NmI3MzE.-ctc\">\n<p id=\"x-ck12-MTZiZTdhNTkwMWU3YjliMGUyNDQ2ZDVmMjQ0NmI3MzE.-sy3\">As a practical matter, whenever possible you should express the units in a small and manageable number. If you are measuring the weight of a material that weighs 6.5 kg, this is easier than saying it weighs 6500 g or 0.65 dag. All three are correct, but the kg units in this case make for a small and easily managed number. However, if a specific problem needs grams instead of kilograms, go with the grams for consistency.<\/p>\n<\/div>\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-a6q\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-ZTY2OWUzM2ZmYmQyMDc4ODRhYjFkZTFmNTBmY2RmYjM.-nyq\">\n<ul id=\"x-ck12-ZTY2OWUzM2ZmYmQyMDc4ODRhYjFkZTFmNTBmY2RmYjM.-anh\">\n<li>Metric prefixes derive from Latin or Greek terms.<\/li>\n<li>The prefixes are used to make the units manageable.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-f61\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-f61\">\n<p id=\"x-ck12-YzUwYWQ3ZDZhZTEyMTg1YTg5ZmVhMWQxNmU1YmNmM2E.-pqr\">Do the online metric system crossword puzzle at<\/p>\n<\/div>\n<div id=\"x-ck12-NGY4ZDEzMzEyNTQ4NzZiYTc2ZGRlZGMwYmE5Y2EwNDE.-soz\">\n<p id=\"x-ck12-NGY4ZDEzMzEyNTQ4NzZiYTc2ZGRlZGMwYmE5Y2EwNDE.-ydj\"><a href=\"http:\/\/education.jlab.org\/sciencecrossword\/index.html\"> http:\/\/education.jlab.org\/sciencecrossword\/index.html <\/a><\/p>\n<\/div>\n<div id=\"x-ck12-ZjA2MzhhNTg2NWJhZmU3ZWIyZWY2M2EzZWZlOGE3ODc.-2ya\">\n<p id=\"x-ck12-ZjA2MzhhNTg2NWJhZmU3ZWIyZWY2M2EzZWZlOGE3ODc.-vnk\">Click on \u201cmetric system\u201d to get to the puzzle<\/p>\n<\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-myj\"><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-myj\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ded\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-OWQ1MzVmYTJmMWJmOTBhYmRiYjU5YzBlMWVlMTA3NzI.-qwz\">\n<ol id=\"x-ck12-OWQ1MzVmYTJmMWJmOTBhYmRiYjU5YzBlMWVlMTA3NzI.-d7i\">\n<li>What is the prefix for \u201cthousand\u201d?<\/li>\n<li>What is the prefix for 0.01?<\/li>\n<li>How would you write 500 milliliters?<\/li>\n<li>How many decimeters in one meter?<\/li>\n<li>You have a mass that weighs 1.2 hectograms. How many grams does it weigh?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-NzRiZGJlNTIyM2ZkYjE4MjU3ZmE0OGE2NDE2YzI5NjU.-bh9\">\n<li><strong> metric prefixes: <\/strong> Prefixes used to distinguish between metric units of different sizes.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U2NpZW50aWZpYyBOb3RhdGlvbiBpbiBDaGVtaXN0cnk.\">Scientific Notation in Chemistry<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define scientific (exponential) notation.<\/li>\n<li>Use this notation to simplify very large or very small numbers.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-MmNhOWZkMTY2NmFlYjA4YWEwZWIxZjFkOWIyMDYzZjY.-3jk\">\n<li>\n<div class=\"textbox examples\">\n<h3>How far is the Sun from Earth?<\/h3>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<p id=\"x-ck12-MWNmYWViNWIyMmMxZTQ1NGUxM2VjODE0NDc4OWI2YTg.-s6k\"><span class=\"x-ck12-img-inline\"> <img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210704\/20140811155029702638.jpeg\" alt=\"A picture of the sun\" width=\"300\" \/><\/span><\/p>\n<p id=\"x-ck12-NWE4Y2Q4MjMzN2YzYjM1MWZmZGM0ZTFmNjg0NWEyYmQ.-sc3\">Astronomers are used to really big numbers.\u00a0 While the moon is only 406,697 km from earth at its maximum distance, the sun is much further away (150 million km).\u00a0 Proxima Centauri, the star nearest the earth, is 39, 900, 000, 000, 000 km away and we have just started on long distances.\u00a0 On the other end of the scale, some biologists deal with very small numbers: a typical fungus could be as small as 30 \u03bcmeters (0.000030 meters) in length and a virus might only be 0.03 \u03bcmeters (0.00000003 meters) long.<\/p>\n<\/div>\n<p>&nbsp;<\/li>\n<\/ul>\n<\/div>\n<h3>Scientific Notation<\/h3>\n<p id=\"x-ck12-NGQ2OWJiODQ5ZTFkN2M5Yzc1NDc1Y2I0ZDJlZDBiNDI.-nda\">Scientific notation is a way to express numbers as the product of two numbers: a coefficient and the number 10 raised to a power. It is a very useful tool for working with numbers that are either very large or very small. \u00a0As an example, the distance from Earth to the Sun is about 150,000,000,000 meters \u2013 a very large distance indeed.\u00a0 In scientific notation, the distance is written as 1.5\u00a0\u00d7 10 <sup> 11 <\/sup> m. The coefficient is the 1.5 and must be a number greater than or equal to 1 and less than 10.\u00a0 The power of 10, or exponent, is 11 because you would have to multiply 1.5 by 10 <sup> 11 <\/sup> to get the correct number.\u00a0 Scientific notation is sometimes referred to as exponential notation. A summary of SI units is given in <strong> Table <\/strong> below .<\/p>\n<div id=\"x-ck12-NDBhMThjZjYyOGFkNDIyOTM5MmIwZWIxZTZjNzA3YTU.-acv\">\n<table id=\"x-ck12-YTg4MjEwODcxYmM1YzljMGQ5YjQ2NTU5NDMxNDkxYmI.-4yo\" class=\"x-ck12-nofloat\">\n<caption>SI Prefixes<\/caption>\n<tbody>\n<tr>\n<td><strong> Prefix <\/strong><\/td>\n<td><strong> Unit Abbrev. <\/strong><\/td>\n<td><strong> Exponential Factor <\/strong><\/td>\n<td><strong> Meaning <\/strong><\/td>\n<td><strong> Example <\/strong><\/td>\n<\/tr>\n<tr>\n<td>giga<\/td>\n<td>G<\/td>\n<td>10 <sup> 9 <\/sup><\/td>\n<td>1,000,000,000<\/td>\n<td>1 gigameter (Gm) = 10 <sup> 9 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>mega<\/td>\n<td>M<\/td>\n<td>10 <sup> 6 <\/sup><\/td>\n<td>1,000,000<\/td>\n<td>1 megameter (Mm) = 10 <sup> 6 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>kilo<\/td>\n<td>k<\/td>\n<td>10 <sup> 3 <\/sup><\/td>\n<td>1000<\/td>\n<td>1 kilometer (km) = 1000 m<\/td>\n<\/tr>\n<tr>\n<td>hecto<\/td>\n<td>h<\/td>\n<td>10 <sup> 2 <\/sup><\/td>\n<td>100<\/td>\n<td>1 hectometer (hm) = 100 m<\/td>\n<\/tr>\n<tr>\n<td>deka<\/td>\n<td>da<\/td>\n<td>10 <sup> 1 <\/sup><\/td>\n<td>10<\/td>\n<td>1 dekameter (dam) = 10 m<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong> 10 <sup> 0 <\/sup><\/strong><\/td>\n<td><strong> 1 <\/strong><\/td>\n<td><strong> 1 meter (m) <\/strong><\/td>\n<\/tr>\n<tr>\n<td>deci<\/td>\n<td>d<\/td>\n<td>10 <sup> -1 <\/sup><\/td>\n<td>1\/10<\/td>\n<td>1 decimeter (dm) = 0.1 m<\/td>\n<\/tr>\n<tr>\n<td>centi<\/td>\n<td>c<\/td>\n<td>10 <sup> -2 <\/sup><\/td>\n<td>1\/100<\/td>\n<td>1 centimeter (cm) = 0.01 m<\/td>\n<\/tr>\n<tr>\n<td>milli<\/td>\n<td>m<\/td>\n<td>10 <sup> -3 <\/sup><\/td>\n<td>1\/1000<\/td>\n<td>1 millimeter (mm) = 0.001 m<\/td>\n<\/tr>\n<tr>\n<td>micro<\/td>\n<td>\u03bc<\/td>\n<td>10 <sup> -6 <\/sup><\/td>\n<td>1\/1,000,000<\/td>\n<td>1 micrometer (\u03bcm) = 10 <sup> -6 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>nano<\/td>\n<td>n<\/td>\n<td>10 <sup> -9 <\/sup><\/td>\n<td>1\/1,000,000,000<\/td>\n<td>1 nanometer (nm) = 10 <sup> -9 <\/sup> m<\/td>\n<\/tr>\n<tr>\n<td>pico<\/td>\n<td>p<\/td>\n<td>10 <sup> -12 <\/sup><\/td>\n<td>1\/1,000,000,000,000<\/td>\n<td>1 picometer (pm) = 10 <sup> -12 <\/sup> m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"x-ck12-NmIwM2E0NDJhNWViZDdiZjA2NGQ4NDkxZTE1ZjI1ODQ.-qjy\">When working with small numbers, we use a negative exponent.\u00a0 So 0.1 meters is\u00a01\u00a0\u00d7\u00a010 <sup> -1 <\/sup> meters, 0.01 is\u00a01\u00a0\u00d7\u00a010 <sup> -2 <\/sup> and so forth.\u00a0 <strong> Table <\/strong> above gives examples of smaller units.\u00a0 Note the use of the <strong> leading zero <\/strong> (the zero to the left of the decimal point). That digit is there to help you see the decimal point more clearly.\u00a0 The figure 0.01 is less likely to be misunderstood than .01 where you may not see the decimal.<\/p>\n<\/div>\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-6wj\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-ODA4OTM3ZjUyMGRiOWM4ZDk3YjZiYjMxOTY1NTUxMmY.-uqo\">\n<ul id=\"x-ck12-ODA4OTM3ZjUyMGRiOWM4ZDk3YjZiYjMxOTY1NTUxMmY.-s2t\">\n<li>Scientific notation allows us to express very large or very small numbers in a convenient way.<\/li>\n<li>This notation uses a coefficient (a number between 1 and 10) and a power of ten sufficient for the actual number.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-e5p\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-YTYxNmQ0OTgyYWU3ZmNlMWRkODA5Y2ZlMzM3YWY4NmQ.-rkj\">\n<p id=\"x-ck12-YTYxNmQ0OTgyYWU3ZmNlMWRkODA5Y2ZlMzM3YWY4NmQ.-fss\">Practice scientific notation using the link below:<\/p>\n<\/div>\n<div id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-ure\">\n<p id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-bq5\"><a href=\"http:\/\/www.mathsisfun.com\/numbers\/scientific-notation.html\"> http:\/\/www.mathsisfun.com\/numbers\/scientific-notation.html<\/a><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-YWY1NGE1ZjhhNGIwOTVkN2JiMTQyNjQ4OTY0ZWNmNzY.-ure\"><\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-qep\">\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-qep\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-6kt\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-MDUyYzU3NmZlNGJiYmRlM2FiYjQwYTcyNmMxOWQyMzE.-j4p\">\n<ol id=\"x-ck12-MDUyYzU3NmZlNGJiYmRlM2FiYjQwYTcyNmMxOWQyMzE.-jjz\">\n<li>What is scientific notation?<\/li>\n<li>What do we use scientific notation for?<\/li>\n<li>What is a leading zero?<\/li>\n<li>Express 150,000,000 in scientific notation.<\/li>\n<li>Express 0.000043 in scientific notation.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div id=\"x-ck12-ZjM2NTVkMWFhYWQyYmM0YWUwYjE3OTRkYTJkZGVmZGE.-iz0\" class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZjM2NTVkMWFhYWQyYmM0YWUwYjE3OTRkYTJkZGVmZGE.-9sl\">\n<li><strong> exponent: <\/strong> A number placed to the right and above another number, symbol, or expression to indicate the power to which the expression is raised.<\/li>\n<li><strong> leading zero: <\/strong> The zero to the left of the decimal point which is there to help you see the decimal point more clearly.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U0kgTGVuZ3RoIGFuZCBWb2x1bWUgVW5pdHM.\">SI Length and Volume Units<\/h1>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\n<li>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\n<li>Define length.<\/li>\n<li>Define volume.<\/li>\n<li>Describe standard measure of length and volume.<\/li>\n<\/ul>\n<\/div>\n<p id=\"x-ck12-OGM1M2EwY2M0OGNlMDBjMTQ3MWQyNzhlODg1OWRkOWU.-km6\">\n<\/div>\n<div class=\"textbox examples\">\n<h3>How were sailors able to measure the depths of seas?<\/h3>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-ZGNlMzZmMjc3NmVmZmVhYzdiMjQxMTVlZjUwNDkwZDI.-qtk\">\n<li><img decoding=\"async\" style=\"line-height: 1.5;\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210706\/20140811155029876586.jpeg\" alt=\"Ships used fathoms to measure depth\" width=\"500\" \/><\/li>\n<\/ul>\n<\/div>\n<h4 id=\"x-ck12-MDA0YjY5NDNjMjFiNzAzYjExNDAwMWUzZjZlMWQ1NWU.-uvc_3-tgf\">How were sailors able to measure the depths of seas?<\/h4>\n<p id=\"x-ck12-MWM5NTBlYjBkMmI0MDM0ZGExZGVkNzI2ZGEyODgxMDM.-3yz\">Back in the days before all the electronic gadgets for measuring depth and locating undersea objects existed, the &#8220;fathom&#8221; was the unit of measurement for depth. A rope was knotted every six feet and the end was dropped over the side of the ship. You could tell how deep the water was by how many knots went under the water before the rope hit bottom. Today we just turn on an instrument and read the depth to a high level of accuracy.<\/p>\n<\/div>\n<p>&nbsp;<\/li>\n<\/ul>\n<\/div>\n<h3>Length and Volume<\/h3>\n<p id=\"x-ck12-ZmZmYWZkNmE2NmZlZmZmMjg3MTFlNjg2NThjZGFjYzM.-bt9\"><strong> Length <\/strong> is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or linear measure, is the <strong> meter <\/strong> (m). All measurements of length may be made in meters, though the prefixes listed in various tables will often be more convenient. The width of a room may be expressed as about 5 meters (m), whereas a large distance, such as the distance between New York City and Chicago, is better expressed as 1150 kilometers (km). Very small distances can be expressed in units such as the millimeter or the micrometer. The width of a typical human hair is about 20 micrometers (\u03bcm).<\/p>\n<p id=\"x-ck12-MTM4OWY3NWE2MjczNWQ0ODdjOTg0NDM5ZWFiY2U4NDc.-7cy\"><strong> Volume <\/strong> is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length. The SI unit of volume is the cubic meter (m <sup> 3 <\/sup> ), which is the volume occupied by a cube that measures 1 m on each side. This very large volume is not very convenient for typical use in a chemistry laboratory. A liter (L) is the volume of a cube that measures 10 cm (1 dm) on each side. A liter is thus equal to both 1000\u00a0cm <sup> 3 <\/sup> (10\u00a0cm \u00d7 10\u00a0cm \u00d7 10\u00a0cm) and to 1 dm <sup> 3 <\/sup> . A smaller unit of volume that is commonly used is the milliliter (mL \u2013 note the capital L which is a standard practice). A milliliter is the volume of a cube that measures 1 cm on each side. Therefore, a milliliter is equal to a cubic centimeter (cm <sup> 3 <\/sup> ). There are 1000 mL in 1 L, which is the same as saying that there are 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> .<\/p>\n<div id=\"x-ck12-ZGVjOWFhNmRlY2NhOGVjZGE2ZTM5NmI0NjZiZWE0Yjk.-eoi\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-13b\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2OTYwNi00MS02MS1JbWFnZS0tLTM1\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210707\/20140811155030027703.jpeg\" alt=\"Picture of a water bottle\" longdesc=\"A%20typical%20water%20bottle%20is%201%20liter%20in%20volume\" \/><\/p>\n<p><strong> Figure 3.4 <\/strong><\/p>\n<p id=\"x-ck12-NjlmYjg2ZjJmODFmZGU2MGE1YmViYzNkODg4ZTcwNTY.-bfu\">A typical water bottle is 1 liter in volume<\/p>\n<\/div>\n<div id=\"x-ck12-ZTA1YTE1NTNiZjZkZDJkNmYxNDYzMTJjMWYxMzEyMGU.-lyu\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-5zm\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2OTY0Ni00OS00Mi1JbWFnZS0tLTM3\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210708\/20140811155030108980.jpeg\" alt=\"Picture of a Rubik's Cube\" longdesc=\"Rubik%E2%80%99s%20cube.%20This%20Rubik%E2%80%99s%20cube%20is%205.7%20cm%20on%20each%20side%20and%20has%20a%20volume%20of%20185.2%20cm%3Csup%3E3%3C%2Fsup%3E%20or%20185.2%20mL.\" \/><\/p>\n<p><strong> Figure 3.5 <\/strong><\/p>\n<p id=\"x-ck12-NjkyMjZhNDgwMzBiYTFjNTI2NmM4ZjU3NGI5ZjVhZDI.-56n\">Rubik\u2019s cube. This Rubik\u2019s cube is 5.7 cm on each side and has a volume of 185.2 cm <sup> 3 <\/sup> or 185.2 mL.<\/p>\n<\/div>\n<div id=\"x-ck12-NThiNTZmMmVjNTA1NTgzZWFjMTliMDBiZDVmYmUzMWQ.-ynh\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-jwr\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE2OTY4Ny05My0yMC1JbWFnZS0tLTM2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210708\/20140811155030192453.jpeg\" alt=\"A graduated cylinder is used to measure volume\" longdesc=\"Graduated%20cylinder.%20Volume%20in%20the%20laboratory%20is%20often%20measured%20with%20a%20graduated%20cylinder%2C%20which%20come%20in%20a%20variety%20of%20sizes.\" \/><\/p>\n<p><strong> Figure 3.6 <\/strong><\/p>\n<p id=\"x-ck12-NWFmMzU0M2RjZDAxNDhiODM1OTkwOGY2NTEyMTVkZDk.-keg\">Graduated cylinder. Volume in the laboratory is often measured with a graduated cylinder, which come in a variety of sizes.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-MmMxZjRlMGM3NTUzN2VhNmYzNjZhODBmNjAxMDU2Mjc.-ojn\">\n<li>Length is the measurement of the extent of something along its greatest dimension.<\/li>\n<li>Volume is the amount of space occupied by a sample of matter.<\/li>\n<li>Volume can be determined by knowing the length of each side of the item.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-atu\"><em> Questions <\/em><\/p>\n<p id=\"x-ck12-OTQzODgyNWNmMWIwNTM0OTIzOWYwNGYyM2VjMzE4ZmM.-zsu\"><a href=\"https:\/\/web.archive.org\/web\/20130306094916\/http:\/\/www.montgomerycollege.edu\/Departments\/biotp\/Metric.html\" target=\"_blank\" rel=\"noopener\">Read the section of length and volume in this link<\/a> and answer the following questions:<\/p>\n<ol id=\"x-ck12-NWE2N2E0NDVjN2ViNTU1YWQwMmQ1Mjk0ZGEyZWMyOWE.-vna\">\n<li>What are some units of length in the metric system?<\/li>\n<li>Do the first three length conversions.<\/li>\n<li>Where on the meniscus do you measure volume in a graduated cylinder?<\/li>\n<li>Do the first two conversion examples for volume.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-3ps\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-NmFjZjZiZTYwMmJiMDFiY2QyNDRkNTdkZWI4MDJjY2M.-chp\">\n<li>Define length.<\/li>\n<li>Define volume.<\/li>\n<li>An object measures <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210709\/808661f1aaa48dfb18454f12290d5df0.png\" alt=\"6.2 cm times 13.7 cm times 26.9 cm\" width=\"220\" height=\"14\" \/> . Which value is the length of the object?<\/li>\n<li>How big is a mL?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-NTgwNjQ2NzQ4ZjAxMGEzYTU5ODEyNWViOWI5ZmU5NDU.-jve\">\n<li><strong> length: <\/strong> The measurement of the extent of something along its greatest dimension<\/li>\n<li><strong> meter: <\/strong> The SI basic unit of length, or linear measure<\/li>\n<li><strong> volume: <\/strong> The amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width by its height. Since each of those is a linear measurement, we say that units of volume are derived from units of length<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U0kgTWFzcyBhbmQgV2VpZ2h0IFVuaXRz\">SI Mass and Weight Units<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Type your learning objectives here.<\/p>\n<ul>\n<li>Define mass.<\/li>\n<li>Define weight.<\/li>\n<li>Explain the difference between mass and weight.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How is he floating?<\/h3>\n<p id=\"x-ck12-ZDZjMDI3NWMxNWNhNWMzNTA5MjZhNTJiZmZlMmQ3MjA.-07p\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210710\/20140811155030340053.jpeg\" alt=\"An astronaut floating in space\" width=\"500\" \/><\/span><\/p>\n<p id=\"x-ck12-MjE5MjM5ZmVlMjEzNGE0OTYzNGE4ZDhlZmZmMzMwNTU.-rop\"><strong>\u00a0<\/strong><\/p>\n<p id=\"x-ck12-YTE2ODNhNDM0MWQxYTliZDcxYTQ0ZGQ4YjhhMDAyODU.-gtt\">One of the many interesting things about travel in outer space is the idea of weightlessness. If something is not fastened down, it will float in mid-air. Early astronauts learned that weightlessness had bad effects on bone structure. If there was no pressure on the legs, those bones would begin to lose mass. Weight provided by gravity is needed to maintain healthy bones. Specially designed equipment is now a part of every space mission so the astronauts can maintain good body fitness.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Mass and Weight<\/h3>\n<p id=\"x-ck12-MmU2NjU2Y2FjM2FhNTg3NDMyYjkwMWU5Y2E5NGQ2ODA.-igr\"><strong> Mass <\/strong> is a measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram. The kilogram was originally defined as the mass of 1 L of liquid water at 4\u00b0C (volume of a liquid changes slightly with temperature). In the laboratory, mass is measured with a balance ( <strong> Figure <\/strong> below ), which must be calibrated with a standard mass so that its measurements are accurate.<\/p>\n<div id=\"x-ck12-ZjQ2MjJmNDg5NDI3N2M2ZWVhNWQ1MDAxZDMzNTVhODI.-2qx\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-gix\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MDI2Mi0xNS03OC1JbWFnZS0tLTM5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210713\/20140811155030427294.jpeg\" alt=\"An analytical balance is used to precisely measure weight\" longdesc=\"An%20analytical%20balance%20makes%20very%20sensitive%20mass%20measurements%20in%20a%20laboratory%2C%20usually%20in%20grams.\" \/><\/p>\n<p><strong> Figure 3.7 <\/strong><\/p>\n<p id=\"x-ck12-Nzc1MjlkOGM5ZDUzMWY2MTFhODNkZTYzMGNiZDIxOTg.-ibf\">An analytical balance makes very sensitive mass measurements in a laboratory, usually in grams.<\/p>\n<\/div>\n<p id=\"x-ck12-ZmVkNzMxZjA3MDIxZDkzODMzNGU4OGYwNzY1MDE1YTY.-zut\">Other common units of mass are the gram and the milligram. A gram is 1\/1000th of a kilogram, meaning that there are 1000 g in 1 kg. A milligram is 1\/1000th of a gram, so there are 1000 mg in 1 g.<\/p>\n<p id=\"x-ck12-ZmI2ZGFjOTgxYjdkODZiNjJmMzFhNzQ1NTA1YWE0OWI.-evb\">Mass is often confused with the term weight. <strong> Weight <\/strong> is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the force due to <strong> gravity <\/strong> is about one sixth that of the gravitational force on Earth. Therefore, a given object will weigh six times more on Earth than it does on the moon. Since mass is dependent only on the amount of matter present in an object, mass does not change with location. Weight measurements are often made with a spring scale by reading the distance that a certain object pulls down and stretches a spring.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-M2JmZTM4MmZlYWVjZmY2ZDZiOWYzYWY4MTQxMjcyNzQ.-xow\">\n<li>Mass is a measure of the amount of matter that an object contains.<\/li>\n<li>Weight is a measure of force that is equal to the gravitational pull on an object.<\/li>\n<li>Mass is independent of location, while weight depends on location.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-qw9\"><em> Questions <\/em><\/p>\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-bom\">Use the link below to answer the following questions:<\/p>\n<p id=\"x-ck12-MmNmZWRjYmJhMWQ2N2RmNWU5MGQ3NTI3ZTliNjAyNzU.-vtq\"><a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/mass.html\"> http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/mass.html <\/a><\/p>\n<ol id=\"x-ck12-YzgxMmVkNjIzOTYzZjg5NzAzODVhNjYzNTdiNWNlZDY.-cyr\">\n<li>The mass of an object is a __________ measure of its inertia.<\/li>\n<li>What is the SI unit for mass?<\/li>\n<li>How is weight different from mass?<\/li>\n<li>What is the unit of weight in the United States?<\/li>\n<\/ol>\n<h4><\/h4>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3><span style=\"line-height: 1.5;\">Review<\/span><\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-bwf\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-ZWVmNmUwNDQwZjUzOGEzMWM5MmU5ZjVlOTdjNjkwNTQ.-oz8\">\n<li>Define mass.<\/li>\n<li>Define weight.<\/li>\n<li>If I weigh 180 pounds on Earth, what will I weigh on the moon?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-NGU2YWRiZDc4NTEyMGI0MDc1NzZlYmI1MGFkNzRjMWE.-ipt\">\n<li><strong> gravity: <\/strong> The force that causes two particles to pull towards each other<\/li>\n<li><strong> mass: <\/strong> A measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram.<\/li>\n<li><strong> weight: <\/strong> A measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U0kgS2luZXRpYyBFbmVyZ3kgVW5pdHM.\">SI Kinetic Energy Units<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Type your learning objectives here.<\/p>\n<ul>\n<li>Define kinetic energy.<\/li>\n<li>Define potential energy.<\/li>\n<li>Write the expression for calculating energy in joules.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>Have you ever watched a cat in action?<\/h3>\n<p id=\"x-ck12-MzVjYzMyOTY2MjBkNzU5ODQ3MzRkYWU5MDgzY2YyMjc.-9tg\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210714\/20140811155030561341.jpeg\" alt=\"A picture of a cat\" width=\"500\" \/><\/span><\/p>\n<p id=\"x-ck12-NzcxMzg3MWMwOTUxMWI0NzQ4MTY3MGNjZmI4MmMzODY.-ics\"><strong>\u00a0\u00a0<\/strong><\/p>\n<p id=\"x-ck12-MGFkNWNlNzAwNTg4NWI5NDNjN2YyMmM2ODFjNmUwOWU.-a2g\">When cats are chasing something, they move very fast. We may comment, \u201cThat cat has a lot of energy\u201d. In saying that, we are more correct than we realize. One form of energy is seen when an object is moving and this type of energy is the basis for many chemical processes.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>SI Kinetic Energy Units<\/h3>\n<p id=\"x-ck12-MDhkYzZmYjc3M2JjZWIzYzU1ZmQxNzU1MTRhYmNlZTk.-t4f\">An object\u2019s <strong> kinetic <\/strong> <strong> energy <\/strong> is the energy due to motion. Kinetic energy can be defined mathematically as<\/p>\n<p id=\"x-ck12-vyg\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210715\/4576a6e07a6c6f2907195af2aaa5c534.png\" alt=\"text{KE} = frac{1}{2} text{mv}^2\" width=\"99\" height=\"37\" \/><\/p>\n<p id=\"x-ck12-N2RlNTcxY2FlYjNjNWNmOGFmMTk2Mzg2NTNiOGY2ZTI.-tld\">where <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210716\/3d9d87196b2a6db0461bb9f77b72b047.png\" alt=\"text{KE} = text{kinetic energy}\" width=\"160\" height=\"16\" \/><\/p>\n<p id=\"x-ck12-NzQxMWNmZjI0MWFiMzZkOGRhYmQ3YmE3NGVlYTkyMmY.-dyk\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210717\/28a7eb890220fe9154fd452a3539274a.png\" alt=\"text{m} = text{mass}\" width=\"77\" height=\"9\" \/><\/p>\n<p id=\"x-ck12-M2E1MTA0ODMzNGY0NmU2ZDYyMTE2ZjVmZGYzZjU1YjQ.-9ja\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210717\/4484d6e0c4455f52264f1e0498e3b149.png\" alt=\"text{v} = text{velocity}\" width=\"94\" height=\"16\" \/><\/p>\n<p id=\"x-ck12-MDQ1YjM3OGZlNDc0ODAzZWE2ODgwNzc5MWU3ZjAwOTk.-gjp\"><strong> Energy <\/strong> is defined as the capacity to do work or to produce heat. As discussed previously, kinetic energy is one type of energy and is associated with motion. Another frequently encountered energy is <strong> potential energy <\/strong> , a type of energy that is stored in matter and released during a chemical reaction. The <strong> joule <\/strong> (J) is the SI unit of energy and is named after English physicist James Prescott Joule (1818-1889). If we go back to the equation for kinetic energy written above, we can put units in (kg for mass and m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> for velocity squared). Then, in terms of SI base units a joule is equal to a kilogram times meter squared divided by a second squared (kg\u00a0\u2022\u00a0m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> ). Another common unit of energy that is often used is the <strong> calorie <\/strong> (cal), which is equivalent to 4.184 J.<\/p>\n<div id=\"x-ck12-Mjc4Y2UwZmRlZTBhNzM1OTI2OWM5MWI1NmY3Mjk3MWY.-qv2\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-rbr\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MDcyNS0yNy0xOC1JbWFnZS0tLTQx\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210718\/20140811155030763669.jpeg\" alt=\"Picture of James Prescott Joule\" longdesc=\"James%20Prescott%20Joule.\" \/><\/p>\n<p><strong> Figure 3.8 <\/strong><\/p>\n<p id=\"x-ck12-ZDI1MzIxYzFhODRiMDgwMzM5NGE3NDdhN2Y1ZWRmZTY.-icf\">James Prescott Joule.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZTJiOWExYmViZjk4NTE1Y2UzOTFkNzIxZDI0M2RlNjc.-sle\">\n<li>Energy is the capacity to do work or to produce heat.<\/li>\n<li>Kinetic energy is the energy due to motion.<\/li>\n<li>Potential energy is energy stored in matter.<\/li>\n<li>The joule (J) is the SI unit of energy and equals kg\u00a0\u2022\u00a0m <sup> 2 <\/sup> \/s <sup> 2 <\/sup> .<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<h4><em> Questions <\/em><\/h4>\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-jia\">Read <a href=\"https:\/\/web.archive.org\/web\/20160114103204\/http:\/\/chemwiki.ucdavis.edu\/Physical_Chemistry\/Thermodynamics\/State_Functions\/Kinetic_Energy\" target=\"_blank\" rel=\"noopener\">Kinetic Energy<\/a> to answer the following questions:<\/p>\n<ol id=\"x-ck12-YzU3NGE4MzFmYTQ1ZDg2N2QzZDliMGM3YTgwYjE3NTE.-hh5\">\n<li>What is kinetic energy dependent upon?<\/li>\n<li>Do molecules at a higher temperature move faster or slower than molecules at a lower temperature?<\/li>\n<li>What happens when a chemical reaction releases energy?<\/li>\n<li>What happens when a chemical reaction absorbs energy?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<h4><em> Questions <\/em><\/h4>\n<ol id=\"x-ck12-MWRiZGZhNWEwYjIyMDkyNzdkZDJjZGU4N2RkZWIyMjE.-q9y\">\n<li>What is kinetic energy?<\/li>\n<li>What is the mathematical equation for kinetic energy?<\/li>\n<li>What is potential energy?<\/li>\n<li>What is the SI unit for energy?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-MTMyNDhmZmZmZWNlMmE1MjdkNjkxN2JmZGZmZGEzODA.-eqk\">\n<li><strong> calorie: <\/strong> common unit of energy, which is equal to 4.184 J.<\/li>\n<li><strong> energy: <\/strong> As the capacity to do work or to produce heat.<\/li>\n<li><strong> joule: <\/strong> The SI unit of energy and is named after English physicist James Prescott Joule (1818-1889).<\/li>\n<li><strong> kinetic energy: <\/strong> The energy due to motion.<\/li>\n<li><strong> potential energy: <\/strong> A type of energy that is stored in matter and released during a chemical reaction.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-VGVtcGVyYXR1cmUgYW5kIFRlbXBlcmF0dXJlIFNjYWxlcw..\">Temperature and Temperature Scales<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define temperature.<\/li>\n<li>Describe the Fahrenheit temperature scale.<\/li>\n<li>Describe the Celsius temperature scale.<\/li>\n<li>Describe the Kelvin temperature scale.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>Touch the top of the stove after it has been on and it feels hot. Hold an ice cube in your hand and it feels cold. Why? The particles of matter in a hot object are moving much faster than the particles of matter in a cold object. An object\u2019s <strong> kinetic energy <\/strong> is the energy due to motion. The particles of matter that make up the hot stove have a greater amount of kinetic energy than those in the ice cube.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Temperature and Temperature Scales<\/h3>\n<p id=\"x-ck12-ZWFmMzViZTRiODI5YTBiZjNkNzRhYzgyOTEzOTI5MTQ.-ead\"><strong> Temperature <\/strong> is a measure of the average kinetic energy of the particles in matter. In everyday usage, temperature indicates a measure of how hot or cold an object is. Temperature is an important parameter in chemistry. When a substance changes from solid to liquid, it is because there was an increase in the temperature of the material. Chemical reactions usually proceed faster if the temperature is increased. Many unstable materials (such as enzymes) will be viable longer at lower temperatures.<\/p>\n<div id=\"x-ck12-MWUzODc2ZWU3NjI3ODlkMGI3ZWFmMzQyZGE5Njc1NTY.-csy\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<p id=\"x-ck12-s4h\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MTE4Mi0xMy04OS1JbWFnZS0tLTQy\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210719\/20140811155030968001.png\" alt=\"Charcoal and snow have two very different temperatures\" longdesc=\"The%20glowing%20charcoal%20on%20the%20left%20represents%20high%20kinetic%20energy%2C%20while%20the%20snow%20and%20ice%20on%20the%20right%20are%20of%20much%20lower%20kinetic%20energy.\" \/><\/p>\n<p><strong> Figure 3.9 <\/strong><\/p>\n<p id=\"x-ck12-ZTdkYTgzMzgxNzQ3YmZkNGU2M2E5NWMxMWE2ZjhkNTA.-v3u\">The glowing charcoal on the left represents high kinetic energy, while the snow and ice on the right are of much lower kinetic energy.<\/p>\n<\/div>\n<h4>Temperature Scales <strong><br \/>\n<\/strong><\/h4>\n<p id=\"x-ck12-ZTBmOTZiMzExMjU4Y2MwZjk0YzMwNTEzNDM1YTQwMDM.-ank\">The first thermometers were glass and contained alcohol, which expanded and contracted as the temperature changed. The German scientist, Daniel Gabriel Fahrenheit used mercury in the tube, an idea put forth by Ismael Boulliau. The Fahrenheit scale was first developed in 1724 and tinkered with for some time after that. The main problem with this scale is the arbitrary definitions of temperature. The freezing point of water was defined as 32\u00b0F and the boiling point as 212\u00b0F. The Fahrenheit scale is typically not used for scientific purposes.<\/p>\n<div id=\"x-ck12-NGY2MzQxZjkwZjk5MmJmNDc4MWUyM2VhMTc4OTdhOTU.-duv\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-gbh\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MTIxNy0zMS00MC1JbWFnZS0tLTQz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210720\/20140811155031131280.jpeg\" alt=\"Portrait of Daniel Gabriel Fahrenheit\" longdesc=\"Daniel%20Gabriel%20Fahrenheit.\" \/><\/p>\n<p><strong> Figure 3.10 <\/strong><\/p>\n<p id=\"x-ck12-MWIyY2UzNjJhZDU5YjUzY2ZiZTAwN2M3MGMwYmNmNzc.-gbe\">Daniel Gabriel Fahrenheit.<\/p>\n<\/div>\n<p id=\"x-ck12-MjAyZjMzNTMwOTM1NTQ2N2ViZTM5ZGJmNWQyNzdhYTM.-vom\">The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius (1701-1744). The Celsius scale sets the freezing point and boiling point of water at 0\u00b0C and 100\u00b0C respectively. The distance between those two points is divided into 100 equal intervals, each of which is one degree. Another term sometimes used for the Celsius scale is \u201ccentigrade\u201d because there are 100 degrees between the freezing and boiling points of water on this scale. However, the preferred term is \u201cCelsius.\u201d<\/p>\n<div id=\"x-ck12-NjAxNmI3MmY2YzE2YzNkN2NjMDE2ZjA0ZThhZDkxY2Q.-xiz\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-wg9\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MTI4OC0yNC00Ny1JbWFnZS0tLTQ0\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210721\/20140811155031266060.jpeg\" alt=\"Portrait of Andres Celsius\" longdesc=\"Anders%20Celsius.\" \/><\/p>\n<p><strong> Figure 3.11 <\/strong><\/p>\n<p id=\"x-ck12-MTM5ZjU5MzQyM2Q3NmVjNTRjMjhlYWJhN2MzNTNjZTk.-8s0\">Anders Celsius.<\/p>\n<\/div>\n<p id=\"x-ck12-YTI3MGFkN2Y3MTRlMmYzNTIxMDMwZDkxYTYzYTE2ZmM.-qkc\">The Kelvin temperature scale is named after Scottish physicist and mathematician Lord Kelvin (1824-1907). It is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases. The freezing point of water on the Kelvin scale is 273.15 K, while the boiling point is 373.15 K. Notice that here is no \u201cdegree\u201d used in the temperature designation. Unlike the Fahrenheit and Celsius scales where temperatures are referred to as \u201cdegrees F\u201d or \u201cdegrees C,\u201d we simply designated temperatures in the Kelvin scale as kelvins.<\/p>\n<div id=\"x-ck12-YmI5MWQ0YmFiNTk4MmYyNWYyZDc0M2MxOTJlMjJiYTY.-3el\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-h9i\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3MTMyOS0wNS03LUltYWdlLS0tNDU.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210721\/20140811155031349933.jpeg\" alt=\"Portrait of Lord Kelvin\" longdesc=\"Lord%20Kelvin.\" \/><\/p>\n<p><strong> Figure 3.12 <\/strong><\/p>\n<p id=\"x-ck12-YmFjZTdmMDVjOGY1NDE0ODE4YzA1MmI0NDEwOWM5OWU.-cic\">Lord Kelvin.<\/p>\n<\/div>\n<p id=\"x-ck12-YjNhZmJmNzJhNzQ2NTcxNTdlODA2N2U1YWI4OGY2YzM.-zsl\">As can be seen by the 100 kelvin difference between the two, a change of one degree on the Celsius scale is equivalent to the change of one kelvin on the Kelvin scale. Converting from the Kelvin scale to the Celsius scale or vice versa is easy, as you simply add or subtract 273.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"x-ck12-ZWQ1MmNiNzA3Y2ZlNmYwNWQ5OTkwOTc4MjkzN2JhYzk.-gyl\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/24175829\/3-Temperature-Scales-K-C-F1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2765\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/24175829\/3-Temperature-Scales-K-C-F1-300x269.jpg\" alt=\"3 Temperature Scales K-C-F\" width=\"300\" height=\"269\" \/><\/a><\/p>\n<p><strong>Figure 3.13 <\/strong><\/p>\n<p id=\"x-ck12-MDE4OGRkZTYyYTdkY2NkNDc4ZTUxZGQ1NDVkNzgzMTg.-afq\">Comparing the three different\u00a0temperature scales.<\/p>\n<p>Converting between the Celsius and Fahrenheit temperature scales is a little bit trickier but still not too difficult. \u00a0To convert from Fahrenheit to Celsius, first multiply the temperature in Celsius (T<sub>C<\/sub>) by 1.8 and then add 32, in that order.<\/p>\n<p>T<sub>F<\/sub> = 1.8 X T<sub>C<\/sub> + 32<\/p>\n<\/div>\n<p>To convert from Celsius to Farenheit, first subtract 32 from the temperature in Farenheit then divide by 1.8, in that order.<\/p>\n<p>T<sub>C<\/sub> = (T<sub>F<\/sub> &#8211; 32)\/1.8<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZjJkZjE2Yzk5NTc4M2E0OGY0NGFlNzc0NDk1ZDg2MWQ.-cf7\">\n<li>Temperature is a measure of the average kinetic energy of the particles in matter.<\/li>\n<li>The Fahrenheit scale defines the freezing point of water as 32\u00b0F and the boiling point as 212\u00b0F.<\/li>\n<li>The Celsius scale sets the freezing point and boiling point of water at 0\u00b0C and 100\u00b0C respectively.<\/li>\n<li>The Kelvin scale is based on molecular motion, with the temperature of 0 K, also known as absolute zero, being the point where all molecular motion ceases.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-cby\"><em> Questions <\/em><\/p>\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-avl\">Use the link below to answer the following questions:<\/p>\n<p id=\"x-ck12-ZDk1OTZhNTE2ZmRlZTM3NzA5NmE1N2MxN2E4YTNhNjM.-7tp\"><a href=\"http:\/\/www.visionlearning.com\/library\/module_viewer.php?mid=48\"> http:\/\/www.visionlearning.com\/library\/module_viewer.php?mid=48 <\/a><\/p>\n<ol id=\"x-ck12-OGQwYWJlMmFjNzg2YTVlZGUwZWMwNDI5MTc0MDlhYmI.-huq\">\n<li>What mixture did Fahrenheit use to set his thermometer at zero degrees?<\/li>\n<li>Why is the Celsius scale preferred in scientific work over the Fahrenheit scale?<\/li>\n<li>What was the idea behind the establishment of the Kelvin temperature scale?<\/li>\n<li>What is the advantage of using the Kelvin scale at low temperatures?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-x6q\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-NjU2ZWRiYjNmMmRkZTYxYTExYzRlMTNjODhjYzlmNjQ.-xjs\">\n<li>What is absolute zero on the Celsius temperature scale?<\/li>\n<li>What are the freezing and boiling points of water in the Celsius scale?<\/li>\n<li>Convert the following Kelvin temperatures to degrees Celsius.\n<ol id=\"x-ck12-YjJkOTJlM2UwOWQyYzJhMGU2Mzc4NjI1ZjIwYzgwOTE.-psu\">\n<li>188 K<\/li>\n<li>631 K<\/li>\n<\/ol>\n<\/li>\n<li>Temperature in degrees Fahrenheit can be converted to Celsius by first subtracting 32, then dividing by 1.8. What is the Celsius temperature outside on a warm day (88\u00b0F)?<\/li>\n<li>Why is the Celsius scale sometimes called \u201ccentigrade\u201d?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZWYwMWEyNWJmZDQwODM2NDY3ODM4NWE3YzlhYTc1ZTU.-7me\">\n<li><strong> kinetic energy: <\/strong> The energy due to motion<\/li>\n<li><strong> temperature: <\/strong> A measure of the average kinetic energy of the particles in matter. In everyday usage, temperature is how hot or cold an object is<\/li>\n<li><strong> temperature scale: <\/strong> A way of measuring temperature quantitatively. There are three major scales used today.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U2NpZW50aWZpYyBEaW1lbnNpb25hbCBBbmFseXNpcw..\">Scientific Dimensional Analysis<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define dimensional analysis.<\/li>\n<li>Use dimensional analysis in solving problems.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<h3>Conversion Factors<\/h3>\n<p id=\"x-ck12-MDMwNDY1ODhmZDQ5MzI0MmJjOWNkNThlYmNkMTg2Yzk.-1cw\" class=\"x-ck12-math\">Many quantities can be expressed in several different ways. The English system measurement of 4 cups is also equal to 2 pints, 1 quart, and \u00bc of a gallon.<\/p>\n<p id=\"x-ck12-YjNhYTdkMWZmNjYxOGE3YzFkOWZmYThkMjEwZmE0NmY.-co9\" class=\"x-ck12-indent\">4 cups = 2 pints = 1 quart = 0.25 gallon<\/p>\n<p id=\"x-ck12-MjEzYmI4NmZiNGI0YzdkNzg3MGU4NjQ4ZGE1NjM3N2Y.-l0e\">Notice that the numerical component of each quantity is different, while the actual amount of material that it represents is the same. That is because the units are different. We can establish the same set of equalities for the metric system:<\/p>\n<p id=\"x-ck12-ZTMyYzBjNTJmNDAxYjllODExMWZmMDVmNTRkMmQxZjc.-lyx\" class=\"x-ck12-indent\">1 meter = 10 decimeters = 100 centimeters = 100 millimeters<\/p>\n<p id=\"x-ck12-ZmZkMmE4ZDJkMzJjNzVlNTg1YzMwNmRhYTcwY2Y3MDI.-kl0\">The metric system\u2019s use of powers of 10 for all conversions makes this quite simple.<\/p>\n<p id=\"x-ck12-YzMxZWRjZGM1Y2E2MDUwNTEzNmVjMWI1OGE1ZWI5MDY.-mij\">Whenever two quantities are equal, a ratio can be written that is numerically equal to 1. Using the metric examples above:<\/p>\n<p id=\"x-ck12-4fp\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210722\/ae4352c20b2cfe66c4c7529e5ce63449.png\" alt=\"frac{1 text{m}}{100 text{cm}}=frac{100 text{cm}}{100 text{cm}}=frac{1 text{m}}{1 text{m}}=1\" width=\"196\" height=\"24\" \/><\/p>\n<p id=\"x-ck12-MzJjZjVkNmE2NDJjZGI3NjI4NjE1NDI1NzNjNGI5ODI.-kwf\">The <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210723\/2c0a32e16a39f8df5841a8fdcd09c6e8.png\" alt=\"frac{1 text{m}}{100 text{cm}}\" width=\"42\" height=\"24\" \/> is called a <strong> conversion factor <\/strong> . A conversion factor is a ratio of equivalent measurements. Because both 1 m and 100 cm represent the exact same length, the value of the conversion factor is 1. The conversion factor is read as \u201c1 meter per 100 centimeters\u201d. Other conversion factors from the cup measurement example can be:<\/p>\n<p id=\"x-ck12-u8p\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210724\/08fa91bb7883a50f0d8c8a89c6b0ac51.png\" alt=\"frac{4 text{cups}}{2 text{pints}}=frac{2 text{pints}}{1 text{quart}}=frac{1 text{quart}}{0.25 text{gallon}}=1\" width=\"235\" height=\"27\" \/><\/p>\n<p id=\"x-ck12-M2ZhOTRhMWQwNmMwMWRhNWNkZDk2MGQ5MDk2YTRkY2I.-kwh\">Since the numerator and denominator represent equal quantities in each case, all are valid conversion factors.<\/p>\n<h3>Scientific Dimensional Analysis<\/h3>\n<p id=\"x-ck12-OTRhMWE0MjJkYTg5MzU1ZGRmNmQzZWJiNmVhM2EzODM.-prt\">Conversion factors are used in solving problems in which a certain measurement must be expressed with different units. When a given measurement is multiplied by an appropriate conversion factor, the numerical value changes, but the actual size of the quantity measured remains the same. <strong> Dimensional analysis <\/strong> is a technique that uses the units (dimensions) of the measurement in order to correctly solve problems. Dimensional analysis is best illustrated with an example.<\/p>\n<h4>Sample Problem: Dimensional Analysis<\/h4>\n<p id=\"x-ck12-ZjBhNTRmMWJlZDQxNDU0Njg5MDU2NzQxZTdkOTBlNWI.-tem\">How many seconds are in a day?<\/p>\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-pvz\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-qeu\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-OWE4ZjcyM2U4NjVhYTJkM2QxOTI2OGI3OGZlMzAzMmQ.-h7e\">\n<li>1 day = 24 hours<\/li>\n<li>1 hour = 60 minutes<\/li>\n<li>1 minute = 60 seconds<\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-xvj\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-MDI0ZThjOTExMjJiMDkxNjFmODk0OGU5NjBkYTJiZmU.-fqr\">\n<li>1 day = ? seconds<\/li>\n<\/ul>\n<p id=\"x-ck12-YzQ4ZGRjZDY4M2FiODZhMjczYTRmZWVmNmEzMDQ0YWE.-dr6\">The known quantities above represent the conversion factors that we will use. The first conversion factor will have day in the denominator so that the \u201cday\u201d unit will cancel. The second conversion factor will then have hours in the denominator, while the third conversion factor will have minutes in the denominator. As a result, the unit of the last numerator will be seconds and that will be the units for the answer.<\/p>\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-uk8\"><em> Step 2: Calculate <\/em><\/p>\n<p id=\"x-ck12-g3l\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210725\/9e11e5a18ed11ef727045fd9a63c4ed7.png\" alt=\"1 text{d} times frac{24 text{h}}{1 text{d}} times frac{60 text{min}}{1 text{h}} times frac{60 text{s}}{1 text{min}}=86, 400 text{s}\" width=\"323\" height=\"39\" \/><\/p>\n<p id=\"x-ck12-ZjlmNWE5ZGNjY2U4OTc3MWU3NDkxZWJmMjllOGU4YWY.-hsp\">Applying the first conversion factor, the \u201cd\u201d unit cancels and 1\u00a0\u00d7\u00a024\u00a0=\u00a024. Applying the second conversion factor, the \u201ch\u201d unit cancels and 24\u00a0\u00d7 60 = 1440. Applying the third conversion factor, the \u201cmin\u201d unit cancels and 1440\u00a0\u00d7\u00a060\u00a0=\u00a086,400. The unit that remains is \u201cs\u201d for seconds.<\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-2b4\"><em> Step 3: Think about your result. <\/em><\/p>\n<p id=\"x-ck12-NGFmYjM2ZGJhNzc0MjFlNTNiM2VlYjlmMWM3ZGVlOWM.-8bk\">Seconds is a much smaller unit of time than a day, so it makes sense that there are a very large number of seconds in one day.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-N2Y4ZWYyMjhjMTFlZjg3OWRhOGY2MzM4ZTAyM2QyMTk.-pwu\">\n<li>A conversion factor is a ratio of equivalent measurements.<\/li>\n<li>Dimensional analysis is a technique that uses the units (dimensions) of the measurement in order to correctly solve problems.<\/li>\n<\/ul>\n<h4><\/h4>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3><span style=\"line-height: 1.5;\">Practice<\/span><\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ddg\"><em> Questions <\/em><\/p>\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-cut\">Use the link below to answer the following questions:<\/p>\n<p><a href=\"http:\/\/www.felderbooks.com\/papers\/units.html\" target=\"_blank\" rel=\"noopener\">http:\/\/www.felderbooks.com\/papers\/units.html<\/a><\/p>\n<ol id=\"x-ck12-NjkyYWZmZGVjMDJlNzU3NTM1MDZiMTFiM2IyMzE4NWI.-wv9\">\n<li>What do we always need to express measurements correctly?<\/li>\n<li>What does dimensional analysis tell you?<\/li>\n<li>How do you know that you have set the problem up incorrectly?<\/li>\n<li>How do you know that you have set the problem up correctly?<\/li>\n<\/ol>\n<h4><\/h4>\n<\/div>\n<div class=\"textbox exercises\">\n<h3><strong>Review<\/strong><\/h3>\n<p><em>Questions <\/em><\/p>\n<ol id=\"x-ck12-ZTIyM2ZhYTQ5NTA3MWQ4ODEwMDc0MmVjZmVmYWUzOTI.-d1m\">\n<li>What is a conversion factor?<\/li>\n<li>What is dimensional analysis?<\/li>\n<li>How many meters are in 3.7 km?<\/li>\n<li>How many kg in 12980 g?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-YTcyZWU5NzBlNjk1YWUwOTI3MTIzMWMxYjRlMGFmZmE.-axc\">\n<li><strong> conversion factor: <\/strong> A ratio of equivalent measurements.<\/li>\n<li><strong> dimensional analysis: <\/strong> A technique that uses the units (dimensions) of the measurement in order to correctly solve problems.<\/li>\n<\/ul>\n<\/div>\n<h1>Metric Unit Conversions<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Use dimensional analysis to carry out metric unit conversions.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How can a number of track laps be converted to a distance in meters?<\/h3>\n<p id=\"x-ck12-N2Q2OTgzYTNjNTBiMmYyY2MwZDk4YTVhNDZmNDJjNDI.-rve\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210727\/20140811155031590883.jpeg\" alt=\"Runners on a track\" width=\"250\" \/><\/span><\/p>\n<h4 id=\"x-ck12-ZDE4MzczNjhkMDY2MDY2OWFmZGI2ZDhlZWY3ZGI1YmU.-3hf_8-mwf\"><\/h4>\n<p id=\"x-ck12-ZDZkNDI0NDQzOThiZGIzYzM3NDUyMDAyYzJlNzVjNmQ.-a8h\">You are training for a 10-kilometer run by doing laps on a 400-meter track. You ask yourself \u201cHow many times do I need to run around this track in order to cover ten kilometers?\u201d (more than you realize). By using dimensional analysis, you can easily determine the number of laps needed to cover the 10 k distance.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Metric Unit Conversions<\/h3>\n<p id=\"x-ck12-MTgyNzdiZTQyMDU3MWUzMWJhYmYxYjE2MWMyYzNhNjU.-je9\">The metric system\u2019s many prefixes allow quantities to be expressed in many different units. Dimensional analysis is useful to convert from one metric system unit to another.<\/p>\n<p id=\"x-ck12-YTY3MzE3MzhlY2I0ZDYzZTJkNTZlYTExOTRiY2NlZmI.-enf\"><strong> Sample Problem: Metric Unit Conversions <\/strong><\/p>\n<p id=\"x-ck12-Zjc2ZjBlYzc4ZTYzNzQxZTcwZmQzZTkzOTJkY2JkMGY.-qbt\">A particular experiment requires 120 mL of a solution. The teacher knows that he will need to make enough solution for 40 experiments to be performed throughout the day. How many liters of solution should he prepare?<\/p>\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-prq\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-kcd\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-OGZlNjNjMmYxMmI3ZDQ0NjFmNzdlZjU0MzVjNjdmMTE.-pst\">\n<li>1 exp requires 120 mL<\/li>\n<li>1 L = 1000 mL<\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-d1i\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-ZTk1MTU5YmU4MmZlZWQwNGFiNjY4Y2JiYmJhMjE0MTQ.-wdk\">\n<li>L of solution for 40 exp<\/li>\n<\/ul>\n<p id=\"x-ck12-YmVkNDRiNDZiOTRmYWQxNmIyMjgzOGVmMGE3ZWNjYzI.-6me\">Since each experiment requires 120 ml of solution and the teacher needs to prepare enough for 40 experiments, multiply 120 by 40 to get 4800 mL of solution needed. Now you must convert ml to L by using a conversion factor.<\/p>\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-ycs\"><em> Step 2: Calculate <\/em><\/p>\n<p id=\"x-ck12-dxg\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210728\/f1f58c6c9d42b60d0cb77e8f1f28fa5a.png\" alt=\"4800 text{mL} times frac{1 text{L}}{1000 text{mL}}=4.8 text{L}\" width=\"226\" height=\"39\" \/><\/p>\n<p id=\"x-ck12-ZjE0MzM2ZDFiMTU1YzUzMmMzZmY1MmM5OTFmYTQxZjA.-aej\">Note that conversion factor is arranged so that the mL unit is in the denominator and thus cancels out, leaving L as the remaining unit in the answer.<\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-ydr\"><em> Step 3: Think about your result. <\/em><\/p>\n<p id=\"x-ck12-YTYxZDk5NGRiYjFiZmRkMDljOGFjYjJkZmEwMjljMGY.-fzh\">A liter is much larger than a milliliter, so it makes sense that the number of liters required is less than the number of milliliters.<\/p>\n<h4>Two-Step Metric Unit Conversions<\/h4>\n<p id=\"x-ck12-MmE0ZmE2MDZkZWE4NDkyOGE4YTFhM2FjMDg3NmRmYWI.-j2l\">Some metric conversion problems are most easily solved by breaking them down into more than one step. When both the given unit and the desired unit have prefixes, one can first convert to the simple (unprefixed) unit, followed by a conversion to the desired unit. An example will illustrate this method.<\/p>\n<p id=\"x-ck12-YmVhOTVhZmE5NDg2YjA2NzI3Yzc1NzZkMjQ4MTVkMjk.-tug\"><strong> <em> Sample Problem 3.3: Two-Step Metric Conversion <\/em> <\/strong><\/p>\n<p id=\"x-ck12-OWI0MDVmZmJjOTJkOTVhY2VjOGNiMWVjNTEwMTVmMTk.-kei\">Convert 4.3 cm to \u03bcm.<\/p>\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-s6x\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-ina\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-NmEwMWJmNmQxYjY3MjA3MTBmMWQxYTBkMTkzNjgwMGM.-9ba\">\n<li>1 m = 100 cm<\/li>\n<li>1 m = 10 <sup> 6 <\/sup> \u03bcm<\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-8sm\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-NDg1MGQ5NTUwZDI4MmU0ZmQ5MjA5NzIxYjQ0ODIxNGQ.-o5k\">\n<li>4.3 cm = ?\u00a0\u03bcm<\/li>\n<\/ul>\n<p id=\"x-ck12-YThmNzE5MWI1N2Y1YWE0ZDMxNzgwZTJhZjhlODAyYWU.-6dz\">You may need to consult a table for the multiplication factor represented by each metric prefix. First convert cm to m, followed by a conversion of m to \u03bcm.<\/p>\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-4zp\"><em> Step 2: Calculate <\/em><\/p>\n<p id=\"x-ck12-fv8\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210729\/0ec8d310fedb14f0af22dd4a8d0d93a9.png\" alt=\"4.3 text{cm} times frac{1 text{m}}{100 text{cm}} times frac{10^6 mu text{m}}{1 text{m}}=43, 000 mu text{m}\" width=\"325\" height=\"42\" \/><\/p>\n<p id=\"x-ck12-NmJjMjMzZDgzOGI1MmJmZmI0NTMxMzZhNzEwZjRhMTk.-kan\">Each conversion factor is written so that unit of the denominator cancels with the unit of the numerator of the previous factor.<\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-urj\"><em> Step 3: Think about your result. <\/em><\/p>\n<p id=\"x-ck12-NjExZThmM2UyMGFhMGRhN2MyYmNhYmQyOGIzMTFiMTQ.-qdl\">A micrometer is a smaller unit of length than a centimeter, so the answer in micrometers is larger than the number of centimeters given.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-MTVlZTllZmY4ZGJhYTAwNTMyMjlkZDJhZmM3ZTU0Y2I.-jkw\">\n<li>Dimensional analysis can be used to carry out metric unit conversions.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-mld\"><em> Questions <\/em><\/p>\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-k5n\">Use the link below to answer the following questions:<\/p>\n<p id=\"x-ck12-YTk2MTBiODcyNDI4YTY4MmQ0MjBlZjdkMzMxM2MzZjc.-c5d\"><a href=\"http:\/\/www.purplemath.com\/modules\/metric.htm\"> http:\/\/www.purplemath.com\/modules\/metric.htm <\/a><\/p>\n<ol id=\"x-ck12-NzRhMTQ4OTExYzg1ZTFiZGU5NDQ0YTU1M2NjY2Q5ZGQ.-e5k\">\n<li>Why are metric units nice to work with?<\/li>\n<li>What are the basic metric units?<\/li>\n<li>To move to a smaller unit, which direction do you move the decimal?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ybc\"><em> Question <\/em><\/p>\n<ol id=\"x-ck12-MDkyYTI4MTA2MmJjNzBlZGE1OWIzNGUzMjhiMDQ4NjA.-vu0\">\n<li>Perform the following conversions.\n<ol id=\"x-ck12-YmYyNTIwYTQwNWU4NmU1NDg3ZDBlMTc3MzQ0Y2I1YzM.-rzi\">\n<li>0.074 km to m<\/li>\n<li>24,600 \u03bcg to g<\/li>\n<li>4.9 \u00d7 10 <sup> 7 <\/sup> \u00a0\u03bcg to kg<\/li>\n<li>84 dm to mm<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-YTBiOWFmODk5ZjVlNjU3NTY5N2NkZTQ4MzljNDE4MTQ.-ryc\">\n<li><strong> unit conversion: <\/strong> Conversion factors between different units of measurement for the same quantity.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-RGVyaXZlZCBVbml0cw..\">Derived Units<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define derived unit.<\/li>\n<li>Carry out unit conversions using derived units.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How has farming evolved?<\/h3>\n<p id=\"x-ck12-MTQ0M2I0N2Y3M2Y4OTdiZDNlNWVlNGM0OTcyODkzMWM.-ge9\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210731\/20140811155031753897.jpeg\" alt=\"Picture of a farm\" width=\"450\" \/><\/span><\/p>\n<h4>How has farming evolved?<\/h4>\n<p id=\"x-ck12-YjUzMmY5ZWY2NzgxZTIxNTRmY2ZjMzQ3ZWQwYTcyNWM.-pjg\">As farming becomes more expensive and less profitable (at least for small farms), many families will sell the land to builders who want to erect either commercial or residential properties. In order to sell, an accurate property tile is needed. The dimensions of the farm must be determined and the acreage calculated from those dimensions.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Dimensional Analysis and Derived Units<\/h2>\n<p id=\"x-ck12-ZDE5MjQ2OTEzNzJiNjM2YTk2N2QxY2Y5OTM2OTFmMGY.-bny\">Some units are combinations of SI base units. A <strong> derived unit <\/strong> is a unit that results from a mathematical combination of SI base units. We have already discussed volume and energy as two examples of derived units.\u00a0 Some others are listed in the <strong> Table <\/strong> below :<\/p>\n<div id=\"x-ck12-MzEyY2ZkNzliN2YwY2E5MzM5NWY2ZWNmYWI5YmI2Mjk.-qoc\">\n<table id=\"x-ck12-NWI0ZGM3NDVlYzQ2ZDg4ZDljYmM3NDMwZmZhOWMyNTQ.-gld\" class=\"x-ck12-nofloat\">\n<caption>Derived SI Units<\/caption>\n<tbody>\n<tr>\n<td><strong> Quantity <\/strong><\/td>\n<td><strong> Symbol <\/strong><\/td>\n<td><strong> Unit <\/strong><\/td>\n<td><strong> Unit Abbreviation <\/strong><\/td>\n<td><strong> Derivation <\/strong><\/td>\n<\/tr>\n<tr>\n<td>Area<\/td>\n<td>A<\/td>\n<td>square meter<\/td>\n<td>m <sup> 2 <\/sup><\/td>\n<td>length \u00d7 width<\/td>\n<\/tr>\n<tr>\n<td>Volume<\/td>\n<td>V<\/td>\n<td>cubic meter<\/td>\n<td>m <sup> 3 <\/sup><\/td>\n<td>length \u00d7 width \u00d7 height<\/td>\n<\/tr>\n<tr>\n<td>Density<\/td>\n<td>D<\/td>\n<td>kilograms\/cubic meter<\/td>\n<td>kg\/m <sup> 3 <\/sup><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/9ede8d0e286966a5308df7c6c1b6dfe7.png\" alt=\"frac{text{mass}}{text{volume}}\" width=\"41\" height=\"21\" \/><\/td>\n<\/tr>\n<tr>\n<td>Concentration<\/td>\n<td>c<\/td>\n<td>moles\/liter<\/td>\n<td>mol\/L<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/79546fcbac576cbd074ab94e37430eae.png\" alt=\"frac{text{amount}}{text{volume}}\" width=\"43\" height=\"24\" \/><\/td>\n<\/tr>\n<tr>\n<td>Speed (velocity)<\/td>\n<td>v<\/td>\n<td>meters\/second<\/td>\n<td>m\/s<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210732\/abb6627e8b97fb49ee7a4785b2487278.png\" alt=\"frac{text{length}}{text{time}}\" width=\"36\" height=\"26\" \/><\/td>\n<\/tr>\n<tr>\n<td>Acceleration<\/td>\n<td>a<\/td>\n<td>meters\/second\/second<\/td>\n<td>m\/s <sup> 2 <\/sup><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210733\/19947f47ee444e653f80065eec57bf2e.png\" alt=\"frac{text{speed}}{text{time}}\" width=\"32\" height=\"26\" \/><\/td>\n<\/tr>\n<tr>\n<td>Force<\/td>\n<td>F<\/td>\n<td>newton<\/td>\n<td>N<\/td>\n<td>mass \u00d7 acceleration<\/td>\n<\/tr>\n<tr>\n<td>Energy<\/td>\n<td>E<\/td>\n<td>joule<\/td>\n<td>J<\/td>\n<td>force \u00d7 length<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"x-ck12-MWRiZTRjNTA5NDAyNTJhZmI3MzM5MDA3MTUyNWUzZmY.-flg\">Using dimensional analysis with derived units requires special care. When units are squared or cubed as with area or volume, the conversion factors themselves must also be squared. Shown below is the conversion factor for cubic centimeters and cubic meters.<\/p>\n<p id=\"x-ck12-6af\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210733\/01413b2a3f5bef18cc62ebe66feeee74.png\" alt=\"left(frac{1 text{m}}{100 text{cm}}right)^3=frac{1 text{m}^3}{10^6 text{cm}^3}=1\" width=\"176\" height=\"27\" \/><\/p>\n<\/div>\n<div id=\"x-ck12-ZThmYzM2YjRlYWM2NGU5NjljZjdhYzhiMWY4OTM0MTY.-wpy\">\n<p id=\"x-ck12-ZThmYzM2YjRlYWM2NGU5NjljZjdhYzhiMWY4OTM0MTY.-kp3\">Because a cube has 3 sides, each side is subject to the conversion of 1 m to 100 cm. Since 100 cubed is equal to 1 million (10 <sup> 6 <\/sup> ), there are 10 <sup> 6 <\/sup> cm <sup> 3 <\/sup> in 1 m <sup> 3 <\/sup> . Two convenient volume units are the liter, which is equal to a cubic decimeter, and the milliliter, which is equal to a cubic centimeter. The conversion factor would be:<\/p>\n<p id=\"x-ck12-bqk\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210734\/2199e3a669a1868fe67664a976fa947f.png\" alt=\"left(frac{1 text{dm}}{10 text{cm}}right)^3 = frac{1 text{dm}^3}{1000 text{cm}^3}=1\" width=\"176\" height=\"27\" \/><\/p>\n<\/div>\n<div id=\"x-ck12-Mzk2NmE0MTI5NzE2ZWIyMmUyMmFhNmQ1ZGY3MzMwMzI.-hft\">\n<p id=\"x-ck12-Mzk2NmE0MTI5NzE2ZWIyMmUyMmFhNmQ1ZGY3MzMwMzI.-qce\">There are thus 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> , which is the same thing as saying there are 1000 mL in 1 L<\/p>\n<\/div>\n<div id=\"x-ck12-ZjA1ZDQ0YzYwMzlkMmQxYjZkNjQ1OTMwZjJkOTU0YjM.-t4s\">\n<div id=\"x-ck12-YWEwNWYzYTkyNDM1YzFjNDBmNWY5ZjVkZGI3OWI2YzU.-ff1\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<p id=\"x-ck12-mxt\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzE3NDAzNi0zNy04Ni1JbWFnZS0tLTQ5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210734\/20140811155031845423.png\" alt=\"1000\u00a0milliliter cubes are in\u00a0a\u00a0liter cube\" longdesc=\"There%20are%201000%20cm%3Csup%3E3%3C\/sup%3E%20in%201%20dm%3Csup%3E3%3C\/sup%3E.%20Since%20a%20cm%3Csup%3E3%3C\/sup%3E%20is%20equal%20to%20a%20mL%20and%20a%20dm%3Csup%3E3%3C\/sup%3E%20is%20equal%20to%20a%20L%2C%20we%20can%20say%20that%20there%20are%201000%20mL%20in%201%20L.\" \/><\/p>\n<p><strong> Figure 3.14 <\/strong><\/p>\n<p id=\"x-ck12-NDg4NWQ0NWVkMjFiOGQ3ODI1ZTY2ODY5MmQxZDU5NzM.-ob1\">There are 1000 cm <sup> 3 <\/sup> in 1 dm <sup> 3 <\/sup> . Since a cm <sup> 3 <\/sup> is equal to a mL and a dm <sup> 3 <\/sup> is equal to a L, we can say that there are 1000 mL in 1 L.<\/p>\n<\/div>\n<p id=\"x-ck12-YmVjYTM1ZWMwMjEyZDQzZmMzMGY1YmVjMzYyOTY3MzY.-os3\"><strong> <em> Sample Problem:\u00a0 <\/em> <\/strong> <strong> <em> Derived Unit Conversion <\/em> <\/strong><\/p>\n<\/div>\n<div id=\"x-ck12-MTcyYzhlNjhjMDJhN2MxYTg5MWFkNTkxODVlOWRkNDM.-ef8\">\n<p id=\"x-ck12-MTcyYzhlNjhjMDJhN2MxYTg5MWFkNTkxODVlOWRkNDM.-vch\">Convert 3.6 \u00d7 10 <sup> 8 <\/sup> mm <sup> 3 <\/sup> to mL.<\/p>\n<\/div>\n<div id=\"x-ck12-ZjNlNGYwZmFiMDA2MzFhMmViM2Y1ZjhkMTEyOTgxNWY.-c6r\">\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-qxu\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-qfy\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-YzI1YWQyOTEwNDAyYWYzMjRhNzNkZDc2MDRjZTZjZWE.-wpn\">\n<li>1 m = 1000 mm<\/li>\n<li>1 ml = 1 cm <sup> 3 <\/sup><\/li>\n<li>1 m = 100 cm<\/li>\n<\/ul>\n<p id=\"x-ck12-vpw\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-ZGFhNzgwZWU3M2YwMjVhZjEwNzBiYTQwMWQ2ZWZlZWM.-tfl\">\n<li>3.6 mm <sup> 3 <\/sup> = ? mL<\/li>\n<\/ul>\n<\/div>\n<div id=\"x-ck12-YjZiMjJlZWExMzFkZTIxZGU3YmVjZDJiMmI3YTdiNTE.-mg9\">\n<p id=\"x-ck12-YjZiMjJlZWExMzFkZTIxZGU3YmVjZDJiMmI3YTdiNTE.-yog\">This problem requires multiple steps and the technique for converting with derived units.\u00a0 Simply proceed one step at a time: mm <sup> 3 <\/sup> to m <sup> 3 <\/sup> to cm <sup> 3 <\/sup> = mL.<\/p>\n<\/div>\n<div id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-xdi\">\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-nb3\"><em> Step 2: Calculate <\/em><\/p>\n<p id=\"x-ck12-znq\" class=\"x-ck12-indent\"><em> <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210736\/6ba3d5895e340e0946e87dc89590ce6f.png\" alt=\"3.6 text{mm}^3 times left(frac{1 text{m}}{1000 text{mm}}right)^3 times left(frac{100 text{cm}}{1 text{m}}right)^3 times frac{1 text{mL}}{1 text{cm}^3}=0.0036 text{mL}\" width=\"490\" height=\"49\" \/><\/em><\/p>\n<\/div>\n<div id=\"x-ck12-OTcxNjFmYjk5YzBiMGNlNjk3MDU5ZWZkZjhhMWMxMjc.-m6y\">\n<p id=\"x-ck12-OTcxNjFmYjk5YzBiMGNlNjk3MDU5ZWZkZjhhMWMxMjc.-ki3\">Numerically, the steps are to divide 3.6 by 10 <sup> 9 <\/sup> , followed by multiplying by 10 <sup> 6 <\/sup> .\u00a0 You may find that you can shorten the problem by a step by first determining the conversion factor from mm to cm and using that instead of first converting to m. There are 10 mm in 1 cm.<\/p>\n<p id=\"x-ck12-qew\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210737\/11806a72633f700675cc5cf0a50a915e.png\" alt=\"3.6 text{mm}^3 times left(frac{1 text{cm}}{10 text{mm}}right)^3 times frac{1 text{mL}}{1 text{cm}^3}=0.0036 text{mL}\" width=\"323\" height=\"27\" \/><\/p>\n<\/div>\n<div id=\"x-ck12-MDk2NjVlMWZjZmVhYTEwMTQxNWZlMzE5ODQ0Nzg1ZDA.-koy\">\n<p id=\"x-ck12-MDk2NjVlMWZjZmVhYTEwMTQxNWZlMzE5ODQ0Nzg1ZDA.-twp\">In this case 3.6 \/ 1000 gives the same result of 0.0036.<\/p>\n<\/div>\n<div id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-jxf\">\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-xad\"><em> Step 3: Think about your result. <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-NTlkOTQ3N2YxMGRmNjA0ZDJlOTA2NmE4NGVlMWRiODY.-uyd\">\n<p id=\"x-ck12-NTlkOTQ3N2YxMGRmNjA0ZDJlOTA2NmE4NGVlMWRiODY.-cgt\">Cubic millimeters are much smaller than cubic centimeters, so the final answer is much less than the original number of mm <sup> 3 <\/sup> .<\/p>\n<\/div>\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-xld\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-YmIxYTAzNTIzYzFmYmY0YjhmNGMwMGE1MDg4M2VlMDM.-3c2\">\n<ul id=\"x-ck12-YmIxYTAzNTIzYzFmYmY0YjhmNGMwMGE1MDg4M2VlMDM.-ech\">\n<li>A derived unit is a unit that results from a mathematical combination of SI base units.<\/li>\n<li>Calculations involving derived units follow the same principles as other unit conversion calculations.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-qxf\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-qxf\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-atw\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-zay\">\n<p id=\"x-ck12-Y2JlMjQ5M2YzMTNmNmRjMzNmZTI0MTMzYzcwM2IzZmY.-rvr\">Use the link below to answer the following questions:<\/p>\n<\/div>\n<div id=\"x-ck12-MDdiNGIzM2I4ZjBmNTU2YjZlZmIwNWY5Zjg3ZGY3ZTE.-7mj\">\n<p id=\"x-ck12-MDdiNGIzM2I4ZjBmNTU2YjZlZmIwNWY5Zjg3ZGY3ZTE.-bk9\"><a href=\"http:\/\/www.unc.edu\/~rowlett\/units\/siderive.html\"> http:\/\/www.unc.edu\/~rowlett\/units\/siderive.html <\/a><\/p>\n<\/div>\n<div id=\"x-ck12-OGQxNTVkOTE0OGU4Nzc2YjMxMGNkZGIyMTc3NTJmMWY.-hru\">\n<ol id=\"x-ck12-OGQxNTVkOTE0OGU4Nzc2YjMxMGNkZGIyMTc3NTJmMWY.-nsj\">\n<li>How many derived units are there?<\/li>\n<li>Who established these units?<\/li>\n<li>What derived unit gives rise to the definition of the watt?<\/li>\n<li>What derived units are defined by the newton?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-2vi\">\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-2vi\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-tu3\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-ZDk5ZmJiYTBjODk4ZWEzNjlhZTNhZDYxZDJmZmFlNmY.-ibh\">\n<ol id=\"x-ck12-NzdlYTgzZDM3ZTU1MTJlZGM5ODdlMzI4YTIxZDc0ZTk.-nmd\">\n<li>What is a derived unit?<\/li>\n<li>Convert 0.00722 km <sup> 2 <\/sup> to m <sup> 2 <\/sup><\/li>\n<li>Convert 129 cm <sup> 3 <\/sup> to L<\/li>\n<li>Convert 4.9 \u00d7 10 <sup> 5 <\/sup> \u03bcm <sup> 3 <\/sup> to mm <sup> 3 <\/sup> .<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZTdkMWEwZGU1OTE5YTlmNGU5ZmUwOGY2ODFkNjU3YzA.-njq\">\n<li><strong>derived unit: <\/strong> A unit that results from a mathematical combination of SI base units.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-RGVuc2l0eQ..\">Density<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define density.<\/li>\n<li>Use physical measurements to calculate density.<\/li>\n<li>Use density values to calculate mass or volume.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox examples\">\n<h3>How do logs stay afloat in water?<\/h3>\n<p id=\"x-ck12-NzI5ZTI5ZmQzMDA3MzFiNTc4MGRiYjhiMGVjMTBiNDE.-lxy\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210739\/20140811155031985542.jpeg\" alt=\"Logs floating in a river\" width=\"200\" \/><\/span><\/p>\n<h4 id=\"x-ck12-NTc2ZWY0MzA3ZTdhMjFkYjYzNGE4NWU4ODc4Nzc2MjQ.-j85_10-rtq\">How do logs stay afloat in water?<\/h4>\n<p id=\"x-ck12-NTc2ZWY0MzA3ZTdhMjFkYjYzNGE4NWU4ODc4Nzc2MjQ.-3cl\">After trees are cut, logging companies often move these materials down a river to a sawmill where they can be shaped into building materials or other products.\u00a0 The logs float on the water because they are less dense than the water they are in.\u00a0 Knowledge of density is important in the characterization and separation of materials.\u00a0 Information about density allows us to make predictions about the behavior of matter.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Density<\/h3>\n<p id=\"x-ck12-MGZiOTIxODQ3ZDI3YjJiY2NiZmIxNWVmMDI1MTQ2NGU.-cfk\">A golf ball and a table tennis ball are about the same size. However, the golf ball is much heavier than the table tennis ball. Now imagine a similar size ball made out of lead. That would be very heavy indeed! What are we comparing? By comparing the mass of an object relative to its size, we are studying a property called <strong> density. <\/strong> Density is the ratio of the mass of an object to its volume.<\/p>\n<p id=\"x-ck12-olz\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODQ5NjkzNg..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210740\/09fef6cb6260d14ca9756d1b69d3b68c.png\" alt=\"text{Density} = frac{text{mass}}{text{volume}}\" width=\"141\" height=\"34\" \/><\/p>\n<p id=\"x-ck12-MWZjYmJmNDRlNzgwOTgwZmU4YzFlMzAyYjYzMGNlMzQ.-ual\">Density is an intensive property, meaning that it does not depend on the amount of material present in the sample. Water has a density of 1.0 g\/mL. That density is the same whether you have a small glass of water or a swimming pool full of water. Density is a property that is constant for the particular identity of the matter being studied.<\/p>\n<p id=\"x-ck12-YWUwM2ZhMTUzNGZjOThiYzE1YzY4OTQ0YzE4ZDM0OTA.-xha\">The SI units of density are kilograms per cubic meter (kg\/m <sup> 3 <\/sup> ), since the kg and the m are the SI units for mass and length respectively. In everyday usage in a laboratory, this unit is awkwardly large. Most solids and liquids have densities that are conveniently expressed in grams per cubic centimeter\u00a0(g\/cm <sup> 3 <\/sup> ). Since a cubic centimeter is equal to a milliliter, density units can also be expressed as g\/mL. Gases are much less dense than solids and liquids, so their densities are often reported in g\/L. Densities of some common substances at 20\u00b0C are listed in the <strong> Table <\/strong> below.<\/p>\n<table id=\"x-ck12-Njc3MmU1NjYzZTFjMDM5NTAwNjZjNGMxYTZjZjc0MDQ.-lec\" class=\"x-ck12-nofloat\">\n<caption>Densities of Some Common Substances<\/caption>\n<tbody>\n<tr>\n<td><strong> Liquids and Solids <\/strong><\/td>\n<td><strong> Density at 20\u00b0C (g\/ml) <\/strong><\/td>\n<td><strong> Gases <\/strong><\/td>\n<td><strong> Density at 20\u00b0C (g\/L) <\/strong><\/td>\n<\/tr>\n<tr>\n<td>Ethanol<\/td>\n<td>0.79<\/td>\n<td>Hydrogen<\/td>\n<td>0.084<\/td>\n<\/tr>\n<tr>\n<td>Ice (0\u00b0C)<\/td>\n<td>0.917<\/td>\n<td>Helium<\/td>\n<td>0.166<\/td>\n<\/tr>\n<tr>\n<td>Corn oil<\/td>\n<td>0.922<\/td>\n<td>Air<\/td>\n<td>1.20<\/td>\n<\/tr>\n<tr>\n<td>Water<\/td>\n<td>0.998<\/td>\n<td>Oxygen<\/td>\n<td>1.33<\/td>\n<\/tr>\n<tr>\n<td>Water (4\u00b0C)<\/td>\n<td>1.000<\/td>\n<td>Carbon dioxide<\/td>\n<td>1.83<\/td>\n<\/tr>\n<tr>\n<td>Corn syrup<\/td>\n<td>1.36<\/td>\n<td>Radon<\/td>\n<td>9.23<\/td>\n<\/tr>\n<tr>\n<td>Aluminum<\/td>\n<td>2.70<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Copper<\/td>\n<td>8.92<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Lead<\/td>\n<td>11.35<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Mercury<\/td>\n<td>13.6<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Gold<\/td>\n<td>19.3<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"x-ck12-YjMxMzk2ODU2OTIwZWVlMmRiYTU4N2NiZGM0YTdjN2M.-mr8\">Since most materials expand as temperature increases, the density of a substance is temperature dependent and usually decreases as temperature increases.<\/p>\n<p id=\"x-ck12-MWMxNjI3NWRlZTY5NDM0YmZiMTdmZmRhMjhlN2U3NjU.-hoh\">You know that ice floats in water and it can be seen from the table that ice is less dense. Alternatively, corn syrup, being denser, would sink if placed into water.<\/p>\n<h4>Sample Problem: Density Calculations<\/h4>\n<p id=\"x-ck12-NTZhZTYzODIwY2JiMTU2M2ViODQwOGRlOTdkMmYwY2U.-xbi\">An 18.2 g sample of zinc metal has a volume of 2.55 cm <sup> 3 <\/sup> . Calculate the density of zinc.<\/p>\n<p id=\"x-ck12-OGU2YWEyYzY0NzAwMDUxZjI4NjFjY2E4MjYyNmNhN2I.-qvm\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-7bk\"><span class=\"x-ck12-underline\"> Known <em><br \/>\n<\/em> <\/span><\/p>\n<ul id=\"x-ck12-YzdlMjI3Nzk3NGQwZDAxYWQwYmRiNjliM2ViMGE5YTk.-ck8\">\n<li>mass = 18.2 g<\/li>\n<li>volume = 2.55 cm <sup> 3 <\/sup><\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-o7p\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-ZmYwMGQ4Yjc0N2JiMWZlMzU5NmVjNTM4NzBmYmI5YzM.-n8p\">\n<li>density =\u00a0? g\/cm <sup> 3 <\/sup><\/li>\n<\/ul>\n<p id=\"x-ck12-NzgyMjc2ZWJiYzM3YTJlNWIwOTE0OWFhYmU1MDgzZTc.-dop\">Use the equation for density, <img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODQ5NjkzNw..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/6a010143d9bbda127ddf0081214df314.png\" alt=\"D = frac{m}{V}\" width=\"53\" height=\"20\" \/> , to solve the problem.<\/p>\n<p id=\"x-ck12-YjlmZWM1OTI2ZTA2NThkOTk4OGE4NWE0N2EyOWY0OWE.-9ay\"><em> Step 2: Calculate <\/em><\/p>\n<p id=\"x-ck12-vqa\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/55158119dd4315ab0dd90b8ec2cba188.png\" alt=\"D=frac{m}{V}=frac{18.2 text{g}}{2.55 text{cm}^3}=7.14 text{g}\/text{cm}^3\" width=\"243\" height=\"24\" \/><\/p>\n<p id=\"x-ck12-ZGJmYWE4NWM0YmIyZGJiOTdhZTZmY2NmYmJmYjM1MjI.-pk3\"><em> Step 3: Think about your result. <\/em><\/p>\n<p id=\"x-ck12-ZTNhY2IzNWMwZGIxMzU0M2MzMmIzNDM3ODEyZmNjY2Q.-nq6\">If 1 cm <sup> 3 <\/sup> of zinc has a mass of about 7 grams, then 2 and a half cm <sup> 3 <\/sup> will have a mass about 2 and a half times as great. Metals are expected to have a density greater than that of water and zinc\u2019s density falls within the range of the other metals listed above<\/p>\n<p id=\"x-ck12-NGFhNDcyMGNkNjYxMjEzNDFiOWYwZGYyMTM1YjQ3NDY.-sqe\">Since density values are known for many substances, density can be used to determine an unknown mass or an unknown volume. Dimensional analysis will be used to ensure that units cancel appropriately.<\/p>\n<h4>Sample Problem: Using Density to Determine Mass and Volume<\/h4>\n<ol id=\"x-ck12-MGFhNWYwNWFjZTk5YzEyYzkzNzQ5MzJiODBjNGIzNWE.-ngn\">\n<li>What is the mass of 2.49 cm <sup> 3 <\/sup> of aluminum?<\/li>\n<li>What is the volume of 50.0 g of aluminum?<\/li>\n<\/ol>\n<p id=\"x-ck12-OGU2YWEyYzY0NzAwMDUxZjI4NjFjY2E4MjYyNmNhN2I.-ezv\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-piw\"><span class=\"x-ck12-underline\"> Known <\/span> <em><br \/>\n<\/em><\/p>\n<ul id=\"x-ck12-MjUyMjRiNDQ1MjExNzhhMmI2NzgxMTEzZWQyNTJmZDA.-qnh\">\n<li>density = 2.70 g\/cm <sup> 3 <\/sup><\/li>\n<li>1. volume = 2.49 cm <sup> 3 <\/sup><\/li>\n<li>2. mass = 50.0 g<\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-j1l\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-ZGE2NGM5ZDI5NzJmMDNjYjM4YjM1NDAyZDgzM2MyNDc.-0nc\">\n<li>1. mass =\u00a0? g<\/li>\n<li>2. volume =\u00a0? cm <sup> 3 <\/sup><\/li>\n<\/ul>\n<p id=\"x-ck12-ZDMyMDcxMDg2OWM2MzAxNzRiZGU5Y2I3NjJiNTNiNTE.-cyh\">Use the equation for density, <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210741\/6a010143d9bbda127ddf0081214df314.png\" alt=\"D = frac{m}{V}\" width=\"53\" height=\"20\" \/> , and dimensional analysis to solve each problem.<\/p>\n<p id=\"x-ck12-YjlmZWM1OTI2ZTA2NThkOTk4OGE4NWE0N2EyOWY0OWE.-dle\"><em> Step 2: Calculate <\/em><\/p>\n<ol id=\"x-ck12-vnb\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210742\/bcc345b6877bcde5c3928c4c72797269.png\" alt=\"2.49 text{cm}^3 times frac{2.70 text{g}}{1 text{cm}^3}=6.72 text{g}\" width=\"200\" height=\"25\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210743\/8127a940e36a3a22c6d08e57a1863520.png\" alt=\"50.0 text{g} times frac{1 text{cm}^3}{2.70 text{g}}=18.5 text{cm}^3\" width=\"199\" height=\"27\" \/><\/li>\n<\/ol>\n<p id=\"x-ck12-YzFhOWFhYjZlMmEzZjA4Mzg5Nzk3N2E5NjI1Y2EwNjY.-cfh\">In problem 1, the mass is equal to the density multiplied by the volume. In problem 2, the volume is equal to the mass divided by the density.<\/p>\n<p id=\"x-ck12-NWI4MjExZjgzODRhNTExMjdjNTVlYWMwNmQ1MTRmYjM.-m0k\"><em> Step 3: Think about your results. <\/em><\/p>\n<p id=\"x-ck12-N2ZhNjcyMGZiMzI5M2U2MWUzYjExNjFkNjcyNDBlMGY.-3kb\">Because a mass of 1 cm <sup> 3 <\/sup> of aluminum is 2.70 g, the mass of about 2.5 cm <sup> 3 <\/sup> should be about 2.5 times larger. The 50 g of aluminum is substantially more than its density, so that amount should occupy a relatively large volume.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-MDU3MTg2MzA2ZTU0MTI3MWU3MzlhMmIyZWQ1MTBiMzY.-jfk\">\n<li>Density is the ratio of the mass of an object to its volume.<\/li>\n<li>Gases are less dense that either solids or liquids<\/li>\n<li>Both liquid and solid materials can have a variety of densities<\/li>\n<li>For liquids and gases, the temperature will affect the density to some extent.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-ODJhYjQ2NzVkOWE0NWI2MTAwY2UxZjIxNTJhMjhkYTI.-fuh\">You can perform a density experiment to identify a mystery object online. Find this simulation at\u00a0<a href=\"https:\/\/phet.colorado.edu\/en\/simulation\/density\" target=\"_blank\" rel=\"noopener\">https:\/\/phet.colorado.edu\/en\/simulation\/density<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-woj\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-NWI3NmUyMGI2NzdjYWRhNjFhYzFhMTM2YWM2NTIwNjk.-8lt\">\n<li>Define \u201cdensity.\u201d<\/li>\n<li>Are gases more or less dense that liquids or solids at room temperature?<\/li>\n<li>How does temperature affect the density of a material?<\/li>\n<li>A certain liquid sample has a volume of 14.7 mL and a mass of 22.8 grams. Calculate the density.<\/li>\n<li>A material with a density of 2.7 grams\/mL occupies 35.6 mL. How many grams of the material are there?<\/li>\n<li>A certain material has a density of 19.3 g\/mL. What is the material?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-MDI1MWE5NzEyMmUxMmFlN2ZjMWZjN2RlZjI2YjE3NDM.-g80\">\n<li><strong>density: <\/strong> The ratio of the mass of an object to its volume. <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210744\/539a0d1b39b487f97368ee471ac72aa9.png\" alt=\"text{Density} = frac{text{mass}}{text{volume}}\" width=\"127\" height=\"21\" \/> . Density is an intensive property, meaning that it does not depend on the amount of material present in the sample.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-QWNjdXJhY3kgYW5kIFByZWNpc2lvbg..\">Accuracy and Precision<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define accuracy.<\/li>\n<li>Define precision.<\/li>\n<li>Describe situations with varying levels of accuracy and precision.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How do professional basketball players improve their shooting accuracy?<\/h3>\n<p id=\"x-ck12-YTdhNDZhYjEwYmU1NDQxMjI1ZmQ2OTc2ZjRhYWU3Y2I.-e1v\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210744\/20140811155032103310.jpeg\" alt=\"A basketball game requires shooting accuracy\" width=\"400\" \/><\/span><\/p>\n<h4 id=\"x-ck12-ODA2NzE4YmQ2M2FmOGIzNjY2N2RkYjBlYTEzZWQ5OTM.-9fc_11-pyl\">How do professional basketball players improve their shooting accuracy?<\/h4>\n<p id=\"x-ck12-ODA2NzE4YmQ2M2FmOGIzNjY2N2RkYjBlYTEzZWQ5OTM.-c4p\">Basketball is one of those sports where you need to hit the target.\u00a0 A football field goal kicker might have room for some deviation from a straight line \u2013 for college and pro football there is an 18 foot 6 inch space for the ball to go through.\u00a0 In basketball, the basket is only 18 inches across and the ball is a little less than 10 inches across \u2013 not much room for error.\u00a0 The ball has to be on target in order to go into the basket and score.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Accuracy and Precision<\/h3>\n<p id=\"x-ck12-N2MxNDcwODhiYzQ1ZGNhOWE2OTA1ODkxZmRmMDQ5MzY.-cfe\">In everyday speech, the terms <strong> accuracy <\/strong> and <strong> precision <\/strong> are frequently used interchangeably.\u00a0 However, their scientific meanings are quite different.\u00a0 Accuracy is a measure of how close a measurement is to the correct or accepted value of the quantity being measured.\u00a0 Precision is a measure of how close a series of measurements are to one another. \u00a0Precise measurements are highly reproducible, even if the measurements are not near the correct value.<\/p>\n<p id=\"x-ck12-ZTEwZGEzMzY0NDM0NWIzYThkYWIzYmJhZTEwNWQ2ZGU.-nui\">Darts thrown at a dartboard are helpful in illustrating accuracy and precision<\/p>\n<div id=\"x-ck12-NDU2ZGJhMDFlYjI0YjFjMjgzNDI4NWU0Y2EwYzU0NDY.-ekm\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<p id=\"x-ck12-sn8\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzI0Mzc5OS01NC0yNS1JbWFnZS0tLTUy\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210746\/20140811155032248757.png\" alt=\"A basketball game requires shooting accuracy\" longdesc=\"The%20distribution%20of%20darts%20on%20a%20dartboard%20shows%20the%20difference%20between%20accuracy%20and%20precision.\" \/><\/p>\n<p><strong> Figure 3.15 <\/strong><\/p>\n<p id=\"x-ck12-NTcxMGJhODJmMWQxOGVmMzk3MWRhZDhiYTczYzZjZjk.-bhg\">The distribution of darts on a dartboard shows the difference between accuracy and precision.<\/p>\n<\/div>\n<p id=\"x-ck12-NWY1MzU0YTAxYWQxY2UzMmFiZDZlMTc5YmY1OWY3MWQ.-da4\">Assume that three darts are thrown at the dartboard, with the bulls-eye representing the true, or accepted, value of what is being measured.\u00a0 A dart that hits the bulls-eye is highly accurate, whereas a dart that lands far away from the bulls-eye displays poor accuracy.\u00a0 The <strong> Figure <\/strong> above demonstrates four possible outcomes.<\/p>\n<ol id=\"x-ck12-ZDc5M2IwMWE1YzlkMzVmMjAxNDI1MzUyYmUzMGJmNDY.-gn9\" class=\"x-ck12-lower-alpha\">\n<li>The darts have landed far from each other and far from the bulls-eye.\u00a0 This grouping demonstrates measurements that are neither accurate, nor precise.<\/li>\n<li>The darts are close to one another, but far from the bulls-eye.\u00a0 This grouping demonstrates measurements that are precise, but not accurate.\u00a0 In a laboratory situation, high precision with low accuracy often results from a systematic error.\u00a0 Either the measurer makes the same mistake repeatedly or the measuring tool is somehow flawed.\u00a0 A poorly calibrated balance may give the same mass reading every time, but it will be far from the true mass of the object.<\/li>\n<li>The darts are not grouped very near to each other, but are generally centered around the bulls-eye.\u00a0 This demonstrates poor precision, but fairly high accuracy.\u00a0 This situation is not desirable in a lab situation because the \u201chigh\u201d accuracy may simply be random chance and not a true indicator of good measuring skill.<\/li>\n<li>The darts are grouped together and have hit the bulls-eye.\u00a0 This demonstrates high precision and high accuracy.\u00a0 Scientists always strive to maximize both in their measurements.<\/li>\n<\/ol>\n<div id=\"x-ck12-Mzc5NDc2NTIxNzJkMzNjNzY4ZTQwY2JiNmM1NTQ2MjQ.-bls\" class=\"x-ck12-img-postcard x-ck12-nofloat\">\n<p id=\"x-ck12-vaz\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzI0Mzg5OC01Ny01MS1JbWFnZS0tLTUz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210747\/20140811155032366639.jpeg\" alt=\"Students in a lab using volumetric flasks\" longdesc=\"Students%20in%20a%20chemistry%20lab%20are%20making%20careful%20measurements%20with%20a%20series%20of%20volumetric%20flasks.%20Accuracy%20and%20precision%20are%20critical%20in%20every%20experiment.\" \/><\/p>\n<p><strong> Figure 3.16 <\/strong><\/p>\n<p>Students in a chemistry lab are making careful measurements with a series of volumetric flasks. Accuracy and precision are critical in every experiment.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-N2M1MmZhOWQwNjgxMmMyYmVhOWNlNDkzZmIxMDhkZDA.-bqy\">\n<li>Accuracy is a measure of how close a measurement is to the correct or accepted value of the quantity being measured.<\/li>\n<li>Precision is a measure of how close a series of measurements are to one another.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NDI4ZWZlYjIzODA1Zjg1YmYwNjkxYzZhZDc1MDgxNTA.-lra\">Take the quiz at the link below:<\/p>\n<p id=\"x-ck12-MzQ0YzA4Zjg4OGI1YmFjMzM2MTUzNTFjYWJkMTEzMmM.-cqm\"><a href=\"http:\/\/www.quia.com\/quiz\/1863743.html?AP_rand=980502951\"> http:\/\/www.quia.com\/quiz\/1863743.html?AP_rand=980502951<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-m8s\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-NTRkMWI2NWUzN2Q3NGUwZGYwNThmMWNjMWQ1MzZhZTE.-l6p\">\n<li>Define accuracy.<\/li>\n<li>Define precision.<\/li>\n<li>What can be said about the reproducibility of precise values?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-YzQ3MGMyMGRkNjMzZDM1NTc0Y2U1NThhNTJlZjhlNjk.-i9k\">\n<li><strong>accuracy: <\/strong> A measure of how close a measurement is to the correct or accepted value of the quantity being measured<\/li>\n<li><strong> precision: <\/strong> A measure of how close a series of measurements are to one another. Precise measurements are highly reproducible, even if the measurements are not near the correct value.<\/li>\n<\/ul>\n<\/div>\n<h1>Percent Error<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define accepted value.<\/li>\n<li>Define experimental value.<\/li>\n<li>Define error and calculate the error given appropriate data.<\/li>\n<li>Define percent error and calculate the error given appropriate data.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How does an electrical circuit work?<\/h3>\n<p id=\"x-ck12-ODA0NTRjMDNlOTliZWI2YjY4NGExNzdkMmQ2NzdiNTY.-okf\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210749\/20140811155032515994.jpeg\" alt=\"Resistors have a percent error indicated by a colored band\" width=\"450\" \/><\/span><\/p>\n<h4 id=\"x-ck12-ZjVjNzI5NThkY2NkMGM2NWFmZTUyZmQ1ZDBiNTkwNTg.-vjk_12-r3d\">How does an electrical circuit work?<\/h4>\n<p id=\"x-ck12-ZjVjNzI5NThkY2NkMGM2NWFmZTUyZmQ1ZDBiNTkwNTg.-94f\">A complicated piece of electronics equipment may contain several resistors whose role is to control the voltage and current in the electrical circuit.\u00a0 Too much current and the apparatus malfunctions.\u00a0 Too little current and the system simply does not perform.\u00a0 The resistors values are always given with an error range.\u00a0 A resistor may have a stated value of 200 ohms, but a 10% error range, meaning the resistance could be anywhere between 195-205 ohms.\u00a0 By knowing these values, an electronics person can design and service the equipment to make sure it functions properly.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Percent Error<\/h3>\n<p id=\"x-ck12-MjMyNjI3YWZmZjdkZGZmZjYzZDkwNDI1NDE5YWM0YjY.-1mx\">An individual measurement may be accurate or inaccurate, depending on how close it is to the true value.\u00a0 Suppose that you are doing an experiment to determine the density of a sample of aluminum metal.\u00a0 The <strong> accepted value <\/strong> of a measurement is the true or correct value based on general agreement with a reliable reference.\u00a0 For aluminum the accepted density is 2.70 g\/cm <sup> 3 <\/sup> .\u00a0 The <strong> experimental value <\/strong> of a measurement is the value that is measured during the experiment.\u00a0 Suppose that in your experiment you determine an experimental value for the aluminum density to be 2.42 g\/cm <sup> 3 <\/sup> .\u00a0 The <strong> error <\/strong> of an experiment is the difference between the experimental and accepted values.<\/p>\n<p id=\"x-ck12-lvc\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODUxNTAyMw..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210750\/b61ee1e78e24ac187558913c39c54f89.png\" alt=\"text{Error}=text{experimental value}-text{accepted value}\" width=\"349\" height=\"17\" \/><\/p>\n<p id=\"x-ck12-NDkwNjZhYzRhNTBhYjhiMGQ1MjQxY2QzMDg2NDg0ZTU.-csx\">If the experimental value is less than the accepted value, the error is negative.\u00a0 If the experimental value is larger than the accepted value, the error is positive.\u00a0 Often, error is reported as the absolute value of the difference in order to avoid the confusion of a negative error.\u00a0 The <strong> percent error <\/strong> is the absolute value of the error divided by the accepted value and multiplied by 100%.<\/p>\n<p id=\"x-ck12-ih5\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODUxNTAyNA..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210751\/3168e89be27137f5d2fc86683460c77b.png\" alt=\"% text{Error}=frac{|text{experimental value}-text{accepted value}|}{text{accepted value}} times 100 %\" width=\"447\" height=\"43\" \/><\/p>\n<p id=\"x-ck12-ZmJlZDk4ZGEwOGI2NGFhMTE1ODc3MDE5MDk4NmZkM2Q.-csm\">To calculate the percent error for the aluminum density measurement, we can substitute the given values of 2.45 g\/cm <sup> 3 <\/sup> for the experimental value and 2.70 g\/cm <sup> 3 <\/sup> for the accepted value.<\/p>\n<p id=\"x-ck12-ja5\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210753\/0f40e186c0d644f76be7d3103d772f83.png\" alt=\"% text{Error}=frac{|2.45 text{g}\/text{cm}^3-2.70 text{g}\/text{cm}^3|}{2.70 text{g}\/text{cm}^3} times 100 % = 9.26 %\" width=\"428\" height=\"46\" \/><\/p>\n<p id=\"x-ck12-YmJiNGI1ZGI1M2IyYTViYmU5MDY5MGY0NDJjMzFiODE.-bqm\">If the experimental value is equal to the accepted value, the percent error is equal to 0.\u00a0 As the accuracy of a measurement decreases, the percent error of that measurement rises.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-Mzk0YjgyMTFhNGY5MDRhMTJhYmJiY2M4NjlkYzZhYjc.-pze\">\n<li>Definitions of accepted value and experimental value are given.<\/li>\n<li>Calculations of error and percent error are demonstrated.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-ZDBiNTFhODU4YWM5NDVlNjI5Yjk5NzkxZTU4NDcxZTY.-nyw\">Read the material at the link below and then do \u201cYour Turn\u201d questions to see how well you did.<\/p>\n<p id=\"x-ck12-MTUxYjM5YTZkZjUyNmVhNGVkNmFhNzY0ZTI2MTA5MjU.-sav\"><a href=\"http:\/\/www.mathsisfun.com\/numbers\/percentage-error.html\"> http:\/\/www.mathsisfun.com\/numbers\/percentage-error.html<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-7wt\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-NzlkNGMwZDUxNWFkNTZhZWVkOTNhYWRmMzE4ODcyOTc.-2mi\">\n<li>Define accepted value.<\/li>\n<li>Define experimental value<\/li>\n<li>What happens as the accuracy of the measurement decreases?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-Y2RjYjg0NDNlOGUxYTI4YWZhNzUzZDIzY2U1NDc3NDM.-2hz\">\n<li><strong> accepted value: <\/strong> \u00a0The true or correct value based on general agreement with a reliable reference.<\/li>\n<li><strong> error: <\/strong> \u00a0The difference between the experimental and accepted values.<\/li>\n<li><strong> experimental value: <\/strong> \u00a0The value that is measured during the experiment.<\/li>\n<li><strong> percent error: <\/strong> The absolute value of the error divided by the accepted value and multiplied by 100%.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-TWVhc3VyZW1lbnQgVW5jZXJ0YWludHk.\">Measurement Uncertainty<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Describe uncertainty in measurements.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How do police officers identify criminals?<\/h3>\n<p id=\"x-ck12-MzVmYTE4MzRlMzhiMmM1YmYyYjI0MWM5ODYxZmZlN2I.-gis\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210755\/20140811155032812983.jpeg\" alt=\"Police arresting man\" width=\"450\" \/><\/span><\/p>\n<h4 id=\"x-ck12-OTRjNzM0ZGZlNjAzOWQzNzQzYzZlNzBhMjlhNzlmMzc.-sd6_13-evq\">How do police officers identify criminals?<\/h4>\n<p id=\"x-ck12-OWY5NTA1NjQ2YmM1NTllNWIxN2UwZDhiMjEwYzc3NmY.-x6r\">After a bank robbery has been committed, police will ask witnesses to describe the robbers. They will usually get some answer such as \u201cmedium height.\u201d Others may say \u201cbetween 5 foot 8 inches and 5 foot 10 inches.\u201d In both cases, there is a significant amount of uncertainty about the height of the criminals.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Measurement Uncertainty<\/h2>\n<p id=\"x-ck12-MzVmYTE4MzRlMzhiMmM1YmYyYjI0MWM5ODYxZmZlN2I.-gis\">Some error or <strong> uncertainty <\/strong> always exists in any measurement. The amount of uncertainty depends both upon the skill of the measurer and upon the quality of the measuring tool. While some balances are capable of measuring masses only to the nearest 0.1 g, other highly sensitive balances are capable of measuring to the nearest 0.001 g or even better. Many measuring tools such as rulers and graduated cylinders have small lines which need to be carefully read in order to make a measurement. The figure below shows two rulers making the same measurement of an object (indicated by the blue arrow).<\/p>\n<div id=\"x-ck12-YTA4MjdkNWMyMTY0Y2YxZWUxZjdjYTc3OWEyMWViMjg.-2k1\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-mlk\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzI0NDg0Ny0yMy02Mi1JbWFnZS0tLTU2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210757\/20140811155032979963.png\" alt=\"Uncertainty in measurement on a ruler\" longdesc=\"Uncertainty%20in%20measurement.\" \/><\/p>\n<p><strong> Figure 3.17 <\/strong><\/p>\n<p id=\"x-ck12-MWQ4ZDI0N2U5MGVjM2Y2ZGZiZDYyZGZiN2ZjY2JkYmE.-twk\">Uncertainty in measurement.<\/p>\n<\/div>\n<p id=\"x-ck12-OGI1OGMxNTdhM2QwNTQ0N2MwZTI5MzI4YWMxMjEzMjE.-z76\">With either ruler, it is clear that the length of the object is between 2 and 3 cm. The bottom ruler contains no millimeter markings. With that ruler, the tenths digit can be estimated and the length may be reported as 2.5 cm.\u00a0 However, another person may judge that the measurement is 2.4 cm or perhaps 2.6 cm. While the 2 is known for certain, the value of the tenths digit is uncertain.<\/p>\n<p id=\"x-ck12-OTJiYTU4ODYyNDcyNTBmN2NmYzczMWZmOTczN2IzNTg.-arw\">The top ruler contains marks for tenths of a centimeter (millimeters). Now the same object may be measured as 2.55 cm. The measurer is capable of estimating the hundredths digit because he can be certain that the tenths digit is a 5. Again, another measurer may report the length to be 2.54 cm or 2.56 cm. In this case, there are two certain digits (the 2 and the 5), with the hundredths digit being uncertain. Clearly, the top ruler is a superior ruler for measuring lengths as precisely as possible.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZTVmNDE3Y2RlOGQ4Y2EzMmU4MWRiNGVmZTU4NDcxMzk.-wls\">\n<li>Uncertainty exists in all measurements.<\/li>\n<li>The degree of uncertainty is affected in part by the quality of the measuring tool.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-NGMwYzQ1ODU1ODE4MDU5MmY0OTY1YzBmYjczNjc1Yjk.-qmm\">Read the material at the link below and answer the questions on the web site:<\/p>\n<p id=\"x-ck12-OGRmNGYxNDMzYTYyMTJjYzg3ZjllODM5MzhjZDViYzI.-u1i\"><a href=\"http:\/\/www2.southeastern.edu\/Academics\/Faculty\/rallain\/plab194\/error.html\"> http:\/\/www2.southeastern.edu\/Academics\/Faculty\/rallain\/plab194\/error.html<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-med\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-Mzc0MDMyMjc5YzYyMzE4Yzg3ZmYyZjE1NDk2YmI1YzY.-efj\">\n<li>What is uncertainty in measurements?<\/li>\n<li>Why is the top ruler more reliable in measuring length than the bottom ruler?<\/li>\n<li>How could the top ruler be made more accurate?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Glossary<\/h2>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZmExNjAyMjVmMDMwYWQ4MGJlZmYzNTA0YzMxNzY5NjE.-gce\">\n<li><strong>uncertainty: <\/strong> lack of sureness about something.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-U2lnbmlmaWNhbnQgRmlndXJlcw..\">Significant Figures<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Define significant figures.<\/li>\n<li>Use significant figure rules to express numerical values correctly.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>How fast do you drive?<\/h3>\n<p id=\"x-ck12-MDExNGQ4ODM0Y2E5YTRiZjI0ZDA1NTc5OTRiZGU0OTk.-7xs\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210758\/20140811155033084790.jpeg\" alt=\"Speed limits have uncertainty built into it\" width=\"400\" \/><\/span><\/p>\n<h4 id=\"x-ck12-YTg5YzcyY2YwMjVhMTQ3OTNhYTUxYzIzZGIwYzdmNmU.-e5a_14-7qx\">How fast do you drive?<\/h4>\n<p id=\"x-ck12-NmJjYzNjMGE1MjQ4Y2NhMWFmYWM0YTRjZjQyODY2MWM.-bx8\">As you enter the town of Jacinto City, Texas, the sign below tells you that the speed limit is 30 miles per hour. But what if you happen to be driving 31 miles an hour? Are you in trouble? Probably not, because there is a certain amount of leeway built into enforcing the regulation. Most speedometers do not measure the vehicle speed very accurately and could easily be off by a mile or so (on the other hand, radar measurements are much more accurate). So, a couple of miles\/hour difference won\u2019t matter that much. Just don\u2019t try to stretch the limits any further unless you want a traffic ticket.<\/p>\n<\/div>\n<h2>Significant Figure<\/h2>\n<p id=\"x-ck12-MDExNGQ4ODM0Y2E5YTRiZjI0ZDA1NTc5OTRiZGU0OTk.-7xs\"><span style=\"line-height: 1.5;\">\u00a0<\/span><\/p>\n<p id=\"x-ck12-NDU3YmJmMGMzNmExYjIwZmU2NjBlZDgxZWI2MjQ1MzI.-s0m\">The <strong> significant figures <\/strong> in a measurement consist of all the certain digits in that measurement plus one uncertain or estimated digit. In the ruler illustration below, the bottom ruler gave a length with 2 significant figures, while the top ruler gave a length with 3 significant figures. In a correctly reported measurement, the final digit is significant but not certain. Insignificant digits are not reported. With either ruler, it would not be possible to report the length as 2.553 cm as there is no possible way that the thousandths digit could be estimated. The 3 is not significant and would not be reported.<\/p>\n<div id=\"x-ck12-ZmQ1YTcxYjM5OWE1NmY4NTE0YTAyNGUxODM5OWY5M2I.-c9z\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<p id=\"x-ck12-nkr\"><img decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2MzI0NTIyOC02Mi00LUltYWdlLS0tNTg.\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210759\/20140811155033245807.png\" alt=\"Uncertainty in measurement on a ruler\" longdesc=\"Measurement%20with%20two%20different%20rulers.\" \/><\/p>\n<p><strong> Figure 3.18 <\/strong><\/p>\n<p id=\"x-ck12-MDdmODRlNzQ2MzYxNjU2OGI1NjRiYTkxNzRiNDEyYjQ.-jy2\">Measurement with two different rulers.<\/p>\n<\/div>\n<p id=\"x-ck12-YWY1M2FiY2NkN2QwMGEzZWI1ZjZjMTExMTZiN2VhNjE.-yph\">When you look at a reported measurement, it is necessary to be able to count the number of significant figures.\u00a0 The <strong> Table <\/strong> below details the rules for determining the number of significant figures in a reported measurement. For the examples in the table,\u00a0assume that the quantities are correctly reported values of a measured quantity.<\/p>\n<div id=\"x-ck12-N2ExOWRhYTcwMTJlNjJkMDBkNjM3NzE2NTZkNDBlYzY.-c1f\">\n<table id=\"x-ck12-NmQ3ZjhlNWIxZjBjYmQxYzY2ZjQyNGMwZGRmMGE1Njg.-oqf\" class=\"x-ck12-nofloat\">\n<caption>Significant Figure Rules<\/caption>\n<tbody>\n<tr>\n<td><strong> Rule <\/strong><\/td>\n<td><strong> Examples <\/strong><\/td>\n<\/tr>\n<tr>\n<td>1. All nonzero digits in a measurement are significant<\/td>\n<td>\n<p id=\"x-ck12-MTViODUwNTQ3OTBhZmUzYTRiZDU1OTFkYzkyNjczMzY.-k0h\">A. 237 has three significant figures.<\/p>\n<p id=\"x-ck12-NzBiNzJhYmVhZmI5ZTJjMmYwNjdhOGZlMTgzNjExOTY.-2et\">B. 1.897 has four significant figures.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>2. Zeros that appear between other nonzero digits are always significant.<\/td>\n<td>\n<p id=\"x-ck12-MmZiOGQwZjkzMTNjNGI5NzFlZDdiMDNhOTQ0ZmQ4NmE.-ih3\">A. 39,004 has five significant figures.<\/p>\n<p id=\"x-ck12-YmM3Mzc0NjVkZTM5M2ZiNGM3OTk2OGJiYzFmYzEzZmQ.-lb9\">B. 5.02 has three significant figures<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>3. Zeros that appear in front of all of the nonzero digits are called left-end zeros.\u00a0 Left-end zeros are never significant<\/td>\n<td>\n<p id=\"x-ck12-NmE3NWM4ZmJjMGUyYTQxOWZkNjBkZjU5MGMyMDY1Yjc.-ik6\">A. 0.008 has one significant figure.<\/p>\n<p id=\"x-ck12-OGYxYmZlYzNlYWZlMDE3M2VhZWYwZGEzNGJhYTBkYjA.-ueb\">B. 0.000416 has three significant figures.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>4. Zeros that appear after all nonzero digits are called right-end zeros.\u00a0 Right-end zeros in a number that lacks a decimal point are not significant.<\/td>\n<td>\n<p id=\"x-ck12-NjEzYjI3NDExM2Y1ZDQ4MGM5NWFiODg4NzQxNzA1ZWI.-1cx\">A. 140 has two significant figures.<\/p>\n<p id=\"x-ck12-MDEwNzZiMjA3MzNkNmExMTkzNzA5NjljYmY1NjQxMGE.-aq1\">B. 75,210 has four significant figures.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>5. Right-end zeros in a number with a decimal point are significant.\u00a0 This is true whether the zeros occur before or after the decimal point.<\/td>\n<td>\n<p id=\"x-ck12-MGM5ZTJkODcxMDhkMDhlYmY0Yzc0ZGJjNzdmYzIwNGE.-qga\">A. 620.0 has four significant figures.<\/p>\n<p id=\"x-ck12-NGQxOTlhNjRlMTYzMzdiMWNhNzAyODFiYjcxYTYyYmY.-vne\">B. 19.000 has five significant figures<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"x-ck12-ZTg0YzJlMGE3ZTE2NGMwMjMzNzVmYzgyZDBlNjAyMGE.-cpa\">It needs to be emphasized that to say a certain digit is not significant does not mean that it is not important or can be left out. Though the zero in a measurement of 140 may not be significant, the value cannot simply be reported as 14. An insignificant zero functions as a placeholder for the decimal point. When numbers are written in scientific notation, this becomes more apparent. The measurement 140 can be written as 1.4 \u00d7 10 <sup> 2 <\/sup> with two significant figures in the coefficient. For a number with left-end zeros, such as 0.000416, it can be written as 4.16 \u00d7 10 <sup> \u22124 <\/sup> with 3 significant figures. In some cases, scientific notation is the only way to correctly indicate the correct number of significant figures. In order to report a value of 15,000,000 with four significant figures, it would need to be written as 1.500 \u00d7 10 <sup> 7 <\/sup> . The right-end zeros after the 5 are significant. The original number of 15,000,000 only has two significant figures.<\/p>\n<\/div>\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-x1k\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-MGU0YTdlY2ZmYWZmOWEwMTBkN2UxZWFmZWNmNWE0NWQ.-kat\">\n<ul id=\"x-ck12-MGU0YTdlY2ZmYWZmOWEwMTBkN2UxZWFmZWNmNWE0NWQ.-36i\">\n<li>Significant figures give an indication of the certainty of a measurement.<\/li>\n<li>Rules allow decisions to be made about how many digits to use in any given situation.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-u6w\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-NzQ5MTA5ZWE5NTI3MzhkYmNiNTFiNmQzN2IxNGZlMmI.-8ot\">\n<p id=\"x-ck12-NzQ5MTA5ZWE5NTI3MzhkYmNiNTFiNmQzN2IxNGZlMmI.-djy\">Take a quiz at the link below:<\/p>\n<\/div>\n<div id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-nz2\">\n<p id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-bpw\"><a href=\"http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/sigfigs.htm\"> http:\/\/www.sciencegeek.net\/APchemistry\/APtaters\/sigfigs.htm<\/a><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-Yzk1MWEyMmQ1YTliZjY5MGM0OGQyNTA1MmQ1ZWY2MTY.-nz2\"><\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-1zi\">\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-1zi\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jsg\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-ZDc4NGNkNDc5NTI0NTg5Y2E0ZGNiNTk4MTFjNGE5YmM.-xuc\">\n<ol id=\"x-ck12-ZDc4NGNkNDc5NTI0NTg5Y2E0ZGNiNTk4MTFjNGE5YmM.-e1m\">\n<li>What does a significant figure tell us?<\/li>\n<li>What is a left-end zero?<\/li>\n<li>What is a right-end zero?<\/li>\n<li>What does an insignificant zero do?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-YTc2NjMyZDkzNzQ5OWYzNWUwZGUwYTIzYjAzY2Y5YjY.-2s3\">\n<li><strong> significant figures: <\/strong> All the certain digits in that measurement plus one uncertain or estimated digit.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-Um91bmRpbmc.\">Rounding<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Learn and apply rules for rounding numbers.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>Have you ever been fishing?<\/h3>\n<p id=\"x-ck12-NTNiNjgxNzM3OTRiYjc1ZTMzZGIxOTE0NDE5OTU3YWQ.-8ts\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210800\/20140811155033332051.jpeg\" alt=\"People fishing\" width=\"450\" \/><\/span><\/p>\n<h4 id=\"x-ck12-NDcxMWIzZDk2ODA5OWYyZjVhMjQ0MTU3NTQyOTBmZWU.-mj1_15-gam\">Have you ever been fishing?<\/h4>\n<p id=\"x-ck12-YjM2MDA1MWIzZWY0YjJlMzQ0ZWZlZjgxNjdlNzMzNmI.-cz4\">People who fish often are a little unreliable when it comes to describing what they caught and how much it weighed. It\u2019s easier to say your fish weighed ten pounds than it is to accurately describe the weight of 8 pounds 11 ounces. Ten pounds is \u201cclose enough\u201d when you are talking about your catch.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Rounding <strong><br \/>\n<\/strong><\/h3>\n<p id=\"x-ck12-ZDAyYjAxZmQ2NTNhNzMyN2I5MTIxY2NhYzU3YmQzOTY.-ax1\">Before dealing with the specifics of the rules for determining the significant figures in a calculated result, we need to be able to round numbers correctly. To <strong> round <\/strong> a number, first decide how many significant figures the number should have. Once you know that, round to that many digits, starting from the left. If the number immediately to the right of the last significant digit is less than 5, it is dropped and the value of the last significant digit remains the same. If the number immediately to the right of the last significant digit is greater than or equal to 5, the last significant digit is increased by 1.<\/p>\n<p id=\"x-ck12-MDQwNzRmODQzNzNhYWM3NTY4ZmVlM2RhNDUwZTk2MDY.-pi4\">Consider the measurement 207.518 m. Right now, the measurement contains six significant figures. How would we successively round it to fewer and fewer significant figures? Follow the process as outlined in <strong> Table <\/strong> below .<\/p>\n<div id=\"x-ck12-ODA4MWJlNDNkMTE4Y2IyMDUxMDBjMGRjYTdlZDhjYWU.-kps\">\n<table id=\"x-ck12-ZjU5NTAzMDc4YjYyOGJmZDA3ZTNhNDk2ODVjMmIyZTU.-xtq\" class=\"x-ck12-nofloat\">\n<tbody>\n<tr>\n<td><strong> Number of Significant Figures <\/strong><\/td>\n<td><strong> Rounded Value <\/strong><\/td>\n<td><strong> Reasoning <\/strong><\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>207.518<\/td>\n<td>All digits are significant<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>207.52<\/td>\n<td>8 rounds the 1 up to 2<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>207.5<\/td>\n<td>2 is dropped<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>208<\/td>\n<td>5 rounds the 7 up to 8<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>210<\/td>\n<td>8 is replaced by a 0 and rounds the 0 upto 1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>200<\/td>\n<td>1 is replaced by a 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"x-ck12-ZmE5ZjkzMjFhMzJmNzA4M2NkNmNhZTAyMTFiZDk2YzQ.-5xh\">Notice that the more rounding is done, the less reliable to figure is. An approximate value may be sufficient for some purposes, but scientific work requires a much higher level of detail.<\/p>\n<\/div>\n<div id=\"x-ck12-MjkwNjEyMTk5ODYxYzMxZDEwMzZiMTg1YjRlNjliNzU.-kx7\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<div id=\"x-ck12-NTFjNTE1YTI4OWUxMDUwMDE2MTQxYTM0Yjk2ODcyMTI.-jaz\">\n<ul id=\"x-ck12-NTFjNTE1YTI4OWUxMDUwMDE2MTQxYTM0Yjk2ODcyMTI.-iff\">\n<li>Rounding involves the adjustment of a value to account for the proper number of significant digits.<\/li>\n<li>Rules exist for rounding of numbers.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-2nv\">\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<div id=\"x-ck12-OGMwMDRkN2UzYjhhNWE4NTBhYjI0NTljM2FmYzJmNTc.-2nv\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-lte\">Practice rounding numbers using the following link:<\/p>\n<\/div>\n<div id=\"x-ck12-YjEwZjVjYzkxZWM2NWZmNmJjNDdiZGRiZDhmY2JkZTY.-g0z\">\n<p id=\"x-ck12-YmFiZDNhNGEwZDg0ODAyMDg4ZDk4MmFlYWQ4ZGZmM2E.-n4g\"><a href=\"http:\/\/www.mathscore.com\/math\/practice\/Rounding%20Numbers\/\" target=\"_blank\" rel=\"noopener\">http:\/\/www.mathscore.com\/math\/practice\/Rounding%20Numbers\/<\/a><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-tlb\">\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<div id=\"x-ck12-NDU3ZGQ1NTE4NGZhZWRiNzg4NWFmZDQwMDlkNzAxNjM.-tlb\">\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-ut8\"><em> Questions <\/em><\/p>\n<\/div>\n<div id=\"x-ck12-MzJiMjFjYThjOTdlNTk2OGY1OTZhMjJkMzM4YTMxNDQ.-hoy\">\n<ol id=\"x-ck12-MzJiMjFjYThjOTdlNTk2OGY1OTZhMjJkMzM4YTMxNDQ.-sg6\">\n<li>Why do we round numbers?<\/li>\n<li>What do we need to know before we round a number?<\/li>\n<li>What is \u201crounding up\u201d?<\/li>\n<li>What is \u201crounding down\u201d?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"x-ck12-data-problem-set\">\n<h2>Glossary<\/h2>\n<\/div>\n<div id=\"x-ck12-ZWIzMjM1MzFiOGViOGVmODExNjk5NTBhOTgxYTVlOTU.-kuj\" class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZWIzMjM1MzFiOGViOGVmODExNjk5NTBhOTgxYTVlOTU.-sfv\">\n<li><strong>round: <\/strong> Adjust a value to reflect the actual number of significant figures.<\/li>\n<li><strong> rounding down: <\/strong> Adjusting a value to less than the original value.<\/li>\n<li><strong> rounding up: <\/strong> Adjusting a value to more than the original value.<\/li>\n<\/ul>\n<\/div>\n<h1 id=\"x-ck12-VW5jZXJ0YWludHkgaW4gTXVsdGlwbGljYXRpb24gYW5kIERpdmlzaW9u\">Uncertainty in Multiplication and Division<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>State the rule for rounding values obtained by multiplication or division.<\/li>\n<li>Apply the rule to appropriate problems.<\/li>\n<\/ul>\n<\/div>\n<div class=\"x-ck12-data-objectives\"><\/div>\n<div class=\"textbox examples\">\n<h3>Who should report the number &#8211; you or your calculator?<\/h3>\n<p id=\"x-ck12-MzFmZTBmODRlOGI3MDFkODhkNmRlYTQyMjA3NGE1MmQ.-tqt\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210802\/20140811155033473901.jpeg\" alt=\"Calculators do not keep track of significant figures\" width=\"300\" \/><\/span><\/p>\n<h4 id=\"x-ck12-ODQzOTVkMzlhYWU2NjQ0ODM0ZDU2ZTg3ZmM1NGIyNmI.-ozy_16-c5w\">Who should report the numbers &#8211; you or your calculator?<\/h4>\n<p id=\"x-ck12-ODQzOTVkMzlhYWU2NjQ0ODM0ZDU2ZTg3ZmM1NGIyNmI.-byi\">Calculators do just what you ask of them, no more and no less.\u00a0 However, they sometimes can get a little out of hand.\u00a0 If I multiply 2.48 times 6.3, I get an answer of 15.687, a value that ignores the number of significant figures in either number.\u00a0 Division with a calculator is even worse. When I divide 12.2 by 1.7, the answer I obtain is\u00a0 7.176470588.\u00a0 Neither piece of data is accurate to nine decimal places, but the calculator doesn\u2019t know that.\u00a0 The human being operating the instrument has to make the decision about how many places to report.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Uncertainty in Multiplication and Division<\/h3>\n<p id=\"x-ck12-MzA3YTdiMzVkYmY5ODVlYzA2OTA5Nzg4ZmFiNmIxZmU.-vcp\">The density of a certain object is calculated by dividing the mass by the volume.\u00a0 Suppose that a mass of 37.46 g is divided by a volume of 12.7 cm <sup> 3 <\/sup> .\u00a0 The result on a calculator would be:<\/p>\n<p id=\"x-ck12-fgj\" class=\"x-ck12-indent\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODU3Njk1Mw..\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210803\/2ec47941246b37af7b95030a4e61e163.png\" alt=\"D=frac{m}{V}=frac{37.46 text{g}}{12.7 text{cm}^3}=2.949606299 text{g}\/text{cm}^3\" width=\"325\" height=\"39\" \/><\/p>\n<p id=\"x-ck12-OWU0MTEzMDE3MTZiZTIzZTJhNzE5NTU3ODYyNGJhZGE.-ymt\">The value of the mass measurement has four significant figures, while the value of the volume measurement has only three significant figures.\u00a0 For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.\u00a0 Applying this rule results in a density of 2.95 g\/cm <sup> 3 <\/sup> , for three significant figures \u2013 the same as the volume measurement.<\/p>\n<h4>Sample Problem:\u00a0 Significant Figures in Calculations<\/h4>\n<p id=\"x-ck12-OWI5MTc0YmU2Y2ZjOTY2NGNjZDU0YTc2ZDk3YTE1MjU.-5l0\">Perform the following calculations, rounding the answers to the appropriate number of significant figures.<\/p>\n<ol id=\"x-ck12-ff4\" class=\"x-ck12-upper-alpha\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210804\/9f8361320e1e8d6f294697e451567dab.png\" alt=\"0.048 text{m} times 32.97 text{m}\" width=\"146\" height=\"14\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM5NjU4ODU3Njk1NA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210805\/b04417fd0bca3bf75738436e1bced6fd.png\" alt=\"14,570 text{kg} div 5.81 text{L}\" width=\"147\" height=\"17\" \/><\/li>\n<\/ol>\n<p id=\"x-ck12-M2ZkZjY4NDZkODRkNWJlNjEwM2JlZjVhOWQwZGFlMTU.-xau\"><em> Step 1:\u00a0 Plan the problem. <\/em><\/p>\n<p id=\"x-ck12-NjcxYWI2ZGUxODZlMDZhZjA2N2E5Y2RiODFkZmJmNzI.-zko\">Analyze each of the measured values to determine how many significant figures should be in the result.\u00a0 Perform the calculation and round appropriately.\u00a0 Apply the correct units to the answer. When multiplying or dividing, the units are also multiplied or divided.<\/p>\n<p id=\"x-ck12-YWQ0ODVjMzM3ODc2OTlmZGQ5MDJmNDg4ZDM1YzU3Mzc.-04n\"><em> Step 2:\u00a0 Calculate <\/em><\/p>\n<ol id=\"x-ck12-MmFmNDE4ZmM4ODk1YTA1MTZkNzE4ODFlZmYxMjk3OGM.-65y\" class=\"x-ck12-upper-alpha\">\n<li><sup><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210806\/566dd18a8eb080a8f60e472c4e2efddc.png\" alt=\"0.048 text{m} times 32.97 text{m} = 1.6 text{m}^2\" width=\"219\" height=\"16\" \/> \u00a0 <\/sup> Round to two significant figures because 0.048 has two.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210807\/a3ad0272ba73f28950d5452c88fa5f55.png\" alt=\"14,570 text{kg} div 5.81 text{L} = 2510 text{kg}\/ text{L}\" width=\"252\" height=\"18\" \/> \u00a0Round to three significant figures because 5.81 has three.<\/li>\n<\/ol>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-OWM0NTNmMWY1ZjVjMzRkNTRiNDA3N2M3NjJkZDZlN2M.-mpv\">\n<li>For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-MDBhNjIzYzY5MDM2MGM4NWY4NzMyMzJmODYyMDdkYWM.-lty\"><a href=\"https:\/\/web.archive.org\/web\/20150316195329\/http:\/\/sigfigscalculator.appspot.com\/tutorial\/multiply_and_divide\" target=\"_blank\" rel=\"noopener\">Read the information and work on the problems on this web site.<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-z8k\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-ZjBlYzFlMDdmZTM0MzM4OTE4YjRkNDExN2JkODE3ODQ.-dyr\">\n<li>What is the basic principle involved in working with multiplication and division?<\/li>\n<li>What happens to units in multiplication and division problems?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"x-ck12-data-problem-set\"><\/div>\n<div class=\"x-ck12-data-vocabulary\"><\/div>\n<h1 id=\"x-ck12-VW5jZXJ0YWludHkgaW4gQWRkaXRpb24gYW5kIFN1YnRyYWN0aW9u\">Uncertainty in Addition and Subtraction<\/h1>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>&nbsp;<\/p>\n<ul>\n<li>State the rule for rounding values obtained by addition or subtraction.<\/li>\n<li>Apply the rule to appropriate problems.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox examples\">\n<h3>How old do you think this calculator?<\/h3>\n<p id=\"x-ck12-NDY1ZjU5YjczYjg0NDk4ZDFkNjI1ODc5NjczYTk0YjE.-jhr\"><span class=\"x-ck12-img-inline\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19210808\/20140811155033588269.jpeg\" alt=\"Watch calculator\" width=\"300\" \/><\/span><\/p>\n<h4 id=\"x-ck12-NDAzYzllNDBkODFjN2JkYTQ1OTQ2YjcwYzFlOTZjNmY.-d3u_17-axc\">How old do you think this calculator is?<\/h4>\n<p id=\"x-ck12-M2VkNjEzMmEwNmRmNjRmZDg1MjEwZDQyYzAxMzkxZmM.-q5d\">Calculators are great devices. Their invention has allowed for quick computation at work, school, or other places where manipulation of numbers needs to be done rapidly and accurately. But they are only as good as the numbers put into them. The calculator cannot determine how accurate each of a set of numbers is and the answer given on the screen must be assessed by the user for reliability.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Uncertainty in Addition and Subtraction<\/h2>\n<p id=\"x-ck12-NTQyYjI5MTIxZWE0NWE2YjY4ZmM0MjY3NjQ1ODhkZjk.-2jv\">Consider two separate mass measurements: 16.7 g and 5.24 g. The first mass measurement (16.7 g) is known only to the tenths place or to one digit after the decimal point. There is no information about its hundredths place and so that digit cannot be assumed to be zero. The second measurement (5.24 g) is known to the hundredths place or to two digits after the decimal point.<\/p>\n<p id=\"x-ck12-OGFkYjc4NGEwZDhlODdhNmYwYjQzM2Q5Y2E5NmExZTg.-evp\">When these masses are added together, the result on a calculator is 16.7 + 5.24 = 21.94 g. Reporting the answer as 21.94 g suggests that the sum is known all the way to the hundredths place. However that cannot be true because the hundredths place of the first mass was completely unknown. The calculated answer needs to be rounded in such a way as to reflect the certainty of each of the measured values that contributed to it. For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places. The sum of the above masses would be properly rounded to a result of 21.9 g.<\/p>\n<p id=\"x-ck12-MWE5NmE0YzU2NmRmODUxYzNkMmE3NGFkZGEwMjE3Yjg.-yqc\">When working with whole numbers, pay attention to the last significant digit that is to the left of the decimal point and round your answer to that same point. For example, consider the subtraction: 78,500 m \u2013 362 m. The calculated result is 78,138 m. However, the first measurement is known only to the hundreds place, as the 5 is the last significant digit. Rounding the result to that same point means that the correct result is 78,100 m.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZWFmOGVkOGYwZTE3ODJmNWM5YmMzMjRjMjM4YTliNzA.-jwv\">\n<li>For addition and subtraction problems, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-MDBhNjIzYzY5MDM2MGM4NWY4NzMyMzJmODYyMDdkYWM.-1vm\"><a href=\"https:\/\/web.archive.org\/web\/20150316175012\/http:\/\/sigfigscalculator.appspot.com\/tutorial\/add_and_subtract\" target=\"_blank\" rel=\"noopener\">Read the information and work on the problems at this web site.<\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<p id=\"x-ck12-NmNlM2JkYzM5ZTU0NDcyNTAzOGUwZTg3Yjc3MWRiMWU.-jxp\"><em> Questions <\/em><\/p>\n<ol id=\"x-ck12-OWU2ZDQ3OTU3MTA5ZmViYTJhNjM3ZWI3MTBlMDkxZDc.-rog\">\n<li>What is the basic principle to use in working with addition and subtraction?<\/li>\n<li>What do you pay attention to when working with whole numbers?<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q836080\">Show References<\/span><\/p>\n<div id=\"q836080\" class=\"hidden-answer\" style=\"display: none\">\n<h2>References<\/h2>\n<ol>\n<li>Courtesy of US Department of Commerce. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:US_National_Length_Meter.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:US_National_Length_Meter.JPG <\/a> .<\/li>\n<li>Courtesy of National Institute of Standards and Technology . <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Standard_kilogram,_2.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Standard_kilogram,_2.jpg <\/a> .<\/li>\n<li>User:Canuckguy\/Wikipedia and User:AzaToth\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Metric_system_adoption_map.svg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Metric_system_adoption_map.svg <\/a> .<\/li>\n<li>Joseph Wright of Derby. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:JosephWright-Alchemist.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:JosephWright-Alchemist.jpg <\/a> .<\/li>\n<li>Courtesy of NASA. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100819.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:The_Sun_by_the_Atmospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100819.jpg <\/a> .<\/li>\n<li>User:\u017beglarz\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Prawa_burta_ORP_Iskra.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Prawa_burta_ORP_Iskra.JPG <\/a> .<\/li>\n<li>User:Kenyon\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:CamelBak_water_bottle.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:CamelBak_water_bottle.jpg <\/a> .<\/li>\n<li>Bram Van Damme (Flickr: Bramus!). <a href=\"http:\/\/www.flickr.com\/photos\/bramus\/3249196137\/\"> http:\/\/www.flickr.com\/photos\/bramus\/3249196137\/ <\/a> .<\/li>\n<li>User:Darrien\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Graduated_cylinder.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Graduated_cylinder.jpg <\/a> .<\/li>\n<li>Courtesy of NASA. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:151746main_s121e05215-lg.jpeg\"> http:\/\/commons.wikimedia.org\/wiki\/File:151746main_s121e05215-lg.jpeg <\/a> .<\/li>\n<li>Courtesy of US Drug Enforcement Administration. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Analytical_balance_mettler_ae-260.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Analytical_balance_mettler_ae-260.jpg <\/a> .<\/li>\n<li>User:Dlls\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Cat_public_domain_dedication_image_0002.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Cat_public_domain_dedication_image_0002.jpg <\/a> .<\/li>\n<li>John Collier. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:James_Prescott_Joule_by_John_Collier,_1882.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:James_Prescott_Joule_by_John_Collier,_1882.jpg <\/a> .<\/li>\n<li>Charcoal: Serge Melki; Snow: User:Haymanj\/Wikimedia Commons. Charcoal: http:\/\/www.flickr.com\/photos\/sergemelki\/3106924114\/; Snow: http:\/\/commons.wikimedia.org\/wiki\/File:Snow_Gum1.JPG .<\/li>\n<li>. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Fahrenheit_small.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Fahrenheit_small.jpg <\/a> .<\/li>\n<li>Olof Arenius. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Anders-Celsius-Head.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Anders-Celsius-Head.jpg <\/a> .<\/li>\n<li>. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Kelvin-1200-scale1000.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Kelvin-1200-scale1000.jpg <\/a> .<\/li>\n<li>Laura Guerin. CK-12 Foundation .<\/li>\n<li>Courtesy of the US Army. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Flickr_-_The_U.S._Army_-_Track_practice.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Flickr_-_The_U.S._Army_-_Track_practice.jpg <\/a> .<\/li>\n<li>User:Joegrimes\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Farmlandlysander.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Farmlandlysander.JPG <\/a> .<\/li>\n<li>CK-12 Foundation &#8211; Christopher Auyeung. .<\/li>\n<li>Tony Hisgett (Flickr:ahisgett). <a href=\"http:\/\/www.flickr.com\/photos\/hisgett\/220279395\/\"> http:\/\/www.flickr.com\/photos\/hisgett\/220279395\/ <\/a> .<\/li>\n<li>Daniel Arizpe. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:High_school_basketball_game.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:High_school_basketball_game.jpg <\/a> .<\/li>\n<li>CK-12 Foundation &#8211; Christopher Auyeung. .<\/li>\n<li>Image copyright zebrik, 2012. <a href=\"http:\/\/www.shutterstock.com\"> http:\/\/www.shutterstock.com <\/a> .<\/li>\n<li>Vald Kliper. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Resistencias_250W_5%25_sobre_papel_milimetrado.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Resistencias_250W_5%25_sobre_papel_milimetrado.JPG <\/a> .<\/li>\n<li>User:Riemann\/Da.Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Danish_police_arrest.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Danish_police_arrest.jpg <\/a> .<\/li>\n<li>CK-12 Foundation &#8211; Christopher Auyeung. .<\/li>\n<li>User:WhisperToMe\/Wikimedia Commons. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:JacintoCitySignJacintoCityTexas.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:JacintoCitySignJacintoCityTexas.JPG <\/a> .<\/li>\n<li>CK-12 Foundation &#8211; Christopher Auyeung. .<\/li>\n<li>Nancy Heise. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Catching_salmon_in_the_ocean_off_Raspberry_Island.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Catching_salmon_in_the_ocean_off_Raspberry_Island.JPG <\/a> .<\/li>\n<li>Adrian Pingstone (Wikimedia: Arpingstone). <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Calculator.arp.600pix.jpg\"> http:\/\/commons.wikimedia.org\/wiki\/File:Calculator.arp.600pix.jpg <\/a> .<\/li>\n<li>User:Septagram\/Wikipedia. <a href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Cfx400c.JPG\"> http:\/\/commons.wikimedia.org\/wiki\/File:Cfx400c.JPG <\/a> .<\/li>\n<li><em>Martha Marie Day, Ed.D., Anthony Carpi, Ph.D. \u201cTemperature\u201d Visionlearning Vol. SCI-1 (5), 2003. \u00a0<a href=\"http:\/\/www.visionlearning.com\/en\/library\/General-Science\/3\/Temperature\/48\">http:\/\/www.visionlearning.com\/en\/library\/General-Science\/3\/Temperature\/48<\/a>.<\/em><\/li>\n<\/ol>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-170\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry Concepts Intermediate. <strong>Authored by<\/strong>: Calbreath, Baxter, et al.. <strong>Provided by<\/strong>: CK12.org. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\">http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":1507,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry Concepts Intermediate\",\"author\":\"Calbreath, Baxter, et al.\",\"organization\":\"CK12.org\",\"url\":\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-170","chapter","type-chapter","status-publish","hentry"],"part":2325,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/170","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/users\/1507"}],"version-history":[{"count":26,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/170\/revisions"}],"predecessor-version":[{"id":3578,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/170\/revisions\/3578"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/parts\/2325"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/170\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=170"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=170"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=170"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}