{"id":103,"date":"2015-12-11T05:30:23","date_gmt":"2015-12-11T05:30:23","guid":{"rendered":"https:\/\/courses.candelalearning.com\/chemistry111labs1x1xmaster\/?post_type=chapter&#038;p=103"},"modified":"2016-06-27T16:42:08","modified_gmt":"2016-06-27T16:42:08","slug":"lab-1-worksheet-fun-with-dimensional-analysis","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/chapter\/lab-1-worksheet-fun-with-dimensional-analysis\/","title":{"raw":"Lab 1 Introduction","rendered":"Lab 1 Introduction"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n\t<li>Convert numbers from regular notation to scientific notation.<\/li>\r\n\t<li>Perform calculations to the correct number of significant figures.<\/li>\r\n\t<li>Perform calculations using numbers with SI units.<\/li>\r\n\t<li>Convert between base units and units containing prefixes.<\/li>\r\n\t<li>Perform calculations using dimensional analysis.<\/li>\r\n\t<li>Become acclimated with common laboratory equipment<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Introduction<\/h2>\r\n<h3>Scientific Notation<\/h3>\r\nScientific notation is a way to express numbers. It is especially useful for numbers that are very large or very small. In addition, it uses only significant figures, which is helpful for understanding error (see below). In scientific notation, a number is presented containing two components: a coefficient and the number 10 raised to a power. The coefficient contains a single nonzero number to the left of the decimal\r\nspace.\r\n\r\nAs an example, consider the speed of light: 299,000,000 m\/s. We would write this as 2.99 x 10<sup>8<\/sup> m\/s in\u00a0scientific notation. The coefficient is 2.99 and must be a number greater than or equal to 1 and less than 10 (one non-zero number will be to the left of the decimal space). The power of 10 is raised to the exponent 8 because you would have to multiply 2.99 by 10<sup>8<\/sup> to get the correct number. You can also think about the 8 being from the number of spaces you moved the decimal space. There is an understood\u00a0decimal at the end of 299,000,000 that we need to move to the right of the number 2 (to allow only a single digit to the left of the decimal). The seven is a positive integer because the number is very large.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204508\/Screen-Shot-2015-12-10-at-11.44.21-PM.png\"><img class=\"size-thumbnail wp-image-104 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204508\/Screen-Shot-2015-12-10-at-11.44.21-PM-150x93.png\" alt=\"Screen Shot 2015-12-10 at 11.44.21 PM\" width=\"150\" height=\"93\" \/><\/a>\r\n\r\nAlternatively 0.000003 m is also difficult to express without scientific notation. In order to convert this\u00a0number to we move the decimal to behind the 3 (the first non-zero number) and add the power of 10 (here\u00a0we moved the decimal 6 times so the exponent is -6) 3 x 10<sup>6<\/sup>. Here the exponent is negative because\u00a0the numb1er is very small (less than 1). Scientific notation is sometimes referred to as exponential\u00a0notation.[footnote]Selection modified from: Boundless Scientific Notation 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/scientific-notation-187-3705\/ [\/footnote]\r\n<h3>Significant Figures<\/h3>\r\nSignificant figures are an indication of accuracy and precision within\u00a0a measurement. All calculations in lab should be done to the\u00a0appropriate number of significant figures. When measuring\u00a0something in lab, include all known numbers and one estimated\u00a0number. For example if the meniscus in lab falls halfway between\u00a0the 21.0 and 21.2 mL marks we know the digits 21 are known. We\u00a0have to estimate the decimal space because we only know it is\u00a0larger than 21.0 and smaller than 21.2. Therefore we could say the\u00a0estimated mark is at the .1 position giving a volume of 21.1 mL. This\u00a0gives us two numbers we know and one we have estimated or three\u00a0significant figures. We could not say it was 21.08 mL because that\u00a0would be two estimated digits instead of one. Numbers are\u00a0significant if they meet one of the following criteria.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204510\/Screen-Shot-2015-12-11-at-12.03.10-AM.png\"><img class=\"wp-image-106 size-full alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204510\/Screen-Shot-2015-12-11-at-12.03.10-AM.png\" alt=\"Screen Shot 2015-12-11 at 12.03.10 AM\" width=\"203\" height=\"262\" \/><\/a>\r\n<ul>\r\n\t<li>All non-zero numbers are significant. For example, 87 has\u00a0two significant figures, while 642.45 has five significant\u00a0figures.<\/li>\r\n\t<li>Zeros sandwiched between two non-zero numbers are significant. Example: 608.5 has four\u00a0significant figures.<\/li>\r\n\t<li>Leading zeros (zeros at the beginning of very small numbers (numbers &lt; 1) are not significant. For\u00a0example, 0.038 has two significant figures.<\/li>\r\n\t<li>Trailing zeros are only significant in a number with a decimal. For example 100 has only 1\u00a0significant figure. 100.0 has 4 significant figures. 0.01 has one significant figure because there\u00a0are no trailing zeros after the 1, but 0.010 has 2 significant figures.[footnote]Selection modified from: Boundless Significant Figures 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/significant-figures-188-7529\/ [\/footnote]<\/li>\r\n<\/ul>\r\n<h3>Significant Figures in Calculations<\/h3>\r\n<ul>\r\n\t<li>When multiplying or dividing, your answer should have the same number of significant figures as the\u00a0number in the calculation with the FEWEST.<\/li>\r\n\t<li>When adding or subtracting, your answer should go to number of decimal spaces as the one in the\u00a0calculation with the FEWEST number of decimal spaces.<\/li>\r\n<\/ul>\r\n<h3>A Guide to Solving Dimensional Analysis Problems<\/h3>\r\nThe following summary can be used as a guide for doing DA. While not all steps listed below will be\u00a0necessary to solve all problems, any problem can be solved using the following. Do not memorize the\u00a0sequence of steps, but rather complete practice until you understand how to solve these problems.\u00a0Dimensional analysis is a fundamental part of chemistry and will be applied all semester. It is imperative\u00a0you gain an understanding of how to perform calculations using dimensional analysis.\r\n\r\n1. Determine what you<strong> want<\/strong> to know. Read the problem and identify what you're being asked to\u00a0figure out, e.g. \"how many milliliters are in 1 liter of solution.\"\r\n<p style=\"padding-left: 30px;\">a. Find starting and ending units:<\/p>\r\n<p style=\"padding-left: 30px;\">We are looking for mg in L which means we begin with L and end with mL. You may\u00a0want to draw out the step(s) you will need for this conversion.<\/p>\r\n<p style=\"text-align: center; padding-left: 30px;\">L\u2192mL<\/p>\r\n2. Determine what you already<strong> know<\/strong>.\r\n<p style=\"padding-left: 30px;\">a. What are you<strong> given<\/strong> by the problem, if anything? In this example, we know we have 1 liter of\u00a0solution.<\/p>\r\n<p style=\"padding-left: 30px;\">b. Determine<strong> conversion factors<\/strong> that may be needed and write them in a form you can use,\u00a0such as \"60 min\/1 hour.\"<\/p>\r\n<p style=\"padding-left: 30px;\">Here we would need 1 L = 1000 mL Which we can write as a fraction<\/p>\r\n<p style=\"padding-left: 30px; text-align: center;\">[latex]\\displaystyle\\frac{1\\text{ L}}{1000\\text{ mL}}\\\\[\/latex] or\u00a0[latex]\\displaystyle\\frac{1000\\text{ mL}}{1\\text{ L}}\\\\[\/latex]<\/p>\r\n<strong>3. Setup<\/strong> the problem using only what you need to know.\r\n<p style=\"padding-left: 30px;\">a. Pick a<strong> starting factor<\/strong>.\u00a0If possible, pick what is given, but make sure it is in the appropriate location (top or\u00a0bottom depending on the final units you want).<\/p>\r\n<p style=\"padding-left: 30px;\">b. Set up the problem with all units and making sure conversion factors allow units to cancel.\u00a0Set up the problem to cancel unwanted units.\u00a0Our plan is to go to from L\u2192mL using 1 L = 1000 mL<\/p>\r\n<p style=\"padding-left: 30px;\">c. If you can't get to what you want, try picking a different starting factor, or checking for a\u00a0needed conversion factor.<\/p>\r\n<strong>4. Solve<\/strong>: make sure all the units other than the answer units cancel out, and then do the math.\r\n<p style=\"padding-left: 30px;\">a. Simplify the numbers by cancellation.\r\nb. Multiply all the top numbers together, then divide into that number all the bottom numbers.\r\nc. Double check to make sure you didn't press a wrong calculator key by dividing the first top number by the first bottom number, alternating until finished, then comparing the answer to the first one. Miskeying is a significant source of error, so always double check.\r\nd. Round off the calculated answer. Make sure you use the appropriate number of significant figures.\r\ne. Add labels (the answer unit) to the appropriately rounded number to get your answer. Compare units in answer to answer units recorded from first step.<\/p>\r\n<p style=\"padding-left: 30px; text-align: center;\">[latex]\\displaystyle1\\cancel{\\text{ L}}\\Bigg|\\frac{1000\\text{ mL}}{1\\cancel{\\text{ L}}}\\Bigg|=1000\\text{ mL}\\\\[\/latex]<\/p>\r\n5. Take a few seconds and ask yourself if the answer you came up with makes sense. If it\u00a0doesn't, start over.[footnote]Selection modified from: Mrs. Patton 2014 CC-BY-SA Dimensional Analysis with Samples http:\/\/math- mrspatton.wikispaces.com\/file\/links\/Dimensional+Analysis+with+Samples.doc [\/footnote]\r\n<h2>Guides<\/h2>\r\n<h3>Significant Figures \u2013 Rules<\/h3>\r\nSignificant figures are critical when reporting scientific data because they give the reader an idea of\u00a0how well you could actually measure\/report your data. Before looking at a few examples, let\u2019s\u00a0summarize the rules for significant figures.\r\n<p style=\"padding-left: 30px;\">1) ALL non-zero numbers (1, 2, 3, 4, 5, 6 ,7, 8, 9) are ALWAYS significant.\r\n2) ALL zeroes between non-zero numbers are ALWAYS significant.\r\n3) ALL zeros which are SIMULTANEOUSLY to the right of the decimal point AND at the\u00a0end of the number are ALWAYS significant.\r\n4) ALL zeros which are to the left of a written decimal point and are in a number &gt; 1 are\u00a0ALWAYS significant.<\/p>\r\nA helpful way to check rules 3 &amp; 4 is to write the number in scientific notation. If you can\/must get rid of the zeros, then they are NOT significant.\r\n<table style=\"height: 249px;\" width=\"282\">\r\n<tbody>\r\n<tr>\r\n<td>Number<\/td>\r\n<td># Significant Figures<\/td>\r\n<td>Rule(s)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>49,923<\/td>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3,967<\/td>\r\n<td>4<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>900.06<\/td>\r\n<td>5<\/td>\r\n<td>1, 2, 4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0.004 (=4 E<sup>-4<\/sup>)<\/td>\r\n<td>1<\/td>\r\n<td>1, 4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>8.1000<\/td>\r\n<td>5<\/td>\r\n<td>1, 3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>501.040<\/td>\r\n<td>6<\/td>\r\n<td>1, 2, 3, 4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3,000,000 (=3 E<sup>+6<\/sup>)<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>10.0 (=1.00 E<sup>+1<\/sup>)<\/td>\r\n<td>3<\/td>\r\n<td>1, 3, 4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204516\/Screen-Shot-2015-12-11-at-8.51.14-AM.png\"><img class=\"alignnone wp-image-113 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204516\/Screen-Shot-2015-12-11-at-8.51.14-AM.png\" alt=\"Screen Shot 2015-12-11 at 8.51.14 AM\" width=\"632\" height=\"396\" \/><\/a>\r\n\r\n&nbsp;\r\n<div>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Prefix<\/strong><\/td>\r\n<td><strong>Root Abbreviation<\/strong><\/td>\r\n<td><strong>Decimal (1 with prefix=___ base)<\/strong><\/td>\r\n<td><strong>Power of Ten<\/strong><\/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>10<sup>6<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilo<\/td>\r\n<td>k<\/td>\r\n<td>1 000<\/td>\r\n<td>10<sup>3<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>hecto<\/td>\r\n<td>h<\/td>\r\n<td>1 00<\/td>\r\n<td>10<sup>2<\/sup><\/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>10<sup>1<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>METER (base unit)<\/td>\r\n<td>m<\/td>\r\n<td>1<\/td>\r\n<td>10<sup>0<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>LITER (base unit)<\/td>\r\n<td>L<\/td>\r\n<td>1<\/td>\r\n<td>10<sup>0<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>GRAM (base unit)<\/td>\r\n<td>g<\/td>\r\n<td>1<\/td>\r\n<td>10<sup>0<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>deci<\/td>\r\n<td>d<\/td>\r\n<td>0.1<\/td>\r\n<td>10<sup>-1<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centi<\/td>\r\n<td>c<\/td>\r\n<td>0.01<\/td>\r\n<td>10<sup>-2<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>milli<\/td>\r\n<td>m<\/td>\r\n<td>0.001<\/td>\r\n<td>10<sup>-3<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>micro<\/td>\r\n<td>\u03bc<\/td>\r\n<td>0.000.001<\/td>\r\n<td>10<sup>-6<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<h2>Metric Steps Conversion<img class=\"alignnone wp-image-120 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204520\/Screen-Shot-2015-12-11-at-3.16.35-PM.png\" alt=\"Metric steps showing the units like steps up stairs. It begins with micro, then takes three steps up to milli, then centi, deci, the base units (m, L, g), then deka, hecto, kilo, three steps and then Mega.\" width=\"629\" height=\"260\" \/><\/h2>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Convert numbers from regular notation to scientific notation.<\/li>\n<li>Perform calculations to the correct number of significant figures.<\/li>\n<li>Perform calculations using numbers with SI units.<\/li>\n<li>Convert between base units and units containing prefixes.<\/li>\n<li>Perform calculations using dimensional analysis.<\/li>\n<li>Become acclimated with common laboratory equipment<\/li>\n<\/ul>\n<\/div>\n<h2>Introduction<\/h2>\n<h3>Scientific Notation<\/h3>\n<p>Scientific notation is a way to express numbers. It is especially useful for numbers that are very large or very small. In addition, it uses only significant figures, which is helpful for understanding error (see below). In scientific notation, a number is presented containing two components: a coefficient and the number 10 raised to a power. The coefficient contains a single nonzero number to the left of the decimal<br \/>\nspace.<\/p>\n<p>As an example, consider the speed of light: 299,000,000 m\/s. We would write this as 2.99 x 10<sup>8<\/sup> m\/s in\u00a0scientific notation. The coefficient is 2.99 and must be a number greater than or equal to 1 and less than 10 (one non-zero number will be to the left of the decimal space). The power of 10 is raised to the exponent 8 because you would have to multiply 2.99 by 10<sup>8<\/sup> to get the correct number. You can also think about the 8 being from the number of spaces you moved the decimal space. There is an understood\u00a0decimal at the end of 299,000,000 that we need to move to the right of the number 2 (to allow only a single digit to the left of the decimal). The seven is a positive integer because the number is very large.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204508\/Screen-Shot-2015-12-10-at-11.44.21-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-thumbnail wp-image-104 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204508\/Screen-Shot-2015-12-10-at-11.44.21-PM-150x93.png\" alt=\"Screen Shot 2015-12-10 at 11.44.21 PM\" width=\"150\" height=\"93\" \/><\/a><\/p>\n<p>Alternatively 0.000003 m is also difficult to express without scientific notation. In order to convert this\u00a0number to we move the decimal to behind the 3 (the first non-zero number) and add the power of 10 (here\u00a0we moved the decimal 6 times so the exponent is -6) 3 x 10<sup>6<\/sup>. Here the exponent is negative because\u00a0the numb1er is very small (less than 1). Scientific notation is sometimes referred to as exponential\u00a0notation.<a class=\"footnote\" title=\"Selection modified from: Boundless Scientific Notation 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/scientific-notation-187-3705\/\" id=\"return-footnote-103-1\" href=\"#footnote-103-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<h3>Significant Figures<\/h3>\n<p>Significant figures are an indication of accuracy and precision within\u00a0a measurement. All calculations in lab should be done to the\u00a0appropriate number of significant figures. When measuring\u00a0something in lab, include all known numbers and one estimated\u00a0number. For example if the meniscus in lab falls halfway between\u00a0the 21.0 and 21.2 mL marks we know the digits 21 are known. We\u00a0have to estimate the decimal space because we only know it is\u00a0larger than 21.0 and smaller than 21.2. Therefore we could say the\u00a0estimated mark is at the .1 position giving a volume of 21.1 mL. This\u00a0gives us two numbers we know and one we have estimated or three\u00a0significant figures. We could not say it was 21.08 mL because that\u00a0would be two estimated digits instead of one. Numbers are\u00a0significant if they meet one of the following criteria.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204510\/Screen-Shot-2015-12-11-at-12.03.10-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-106 size-full alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204510\/Screen-Shot-2015-12-11-at-12.03.10-AM.png\" alt=\"Screen Shot 2015-12-11 at 12.03.10 AM\" width=\"203\" height=\"262\" \/><\/a><\/p>\n<ul>\n<li>All non-zero numbers are significant. For example, 87 has\u00a0two significant figures, while 642.45 has five significant\u00a0figures.<\/li>\n<li>Zeros sandwiched between two non-zero numbers are significant. Example: 608.5 has four\u00a0significant figures.<\/li>\n<li>Leading zeros (zeros at the beginning of very small numbers (numbers &lt; 1) are not significant. For\u00a0example, 0.038 has two significant figures.<\/li>\n<li>Trailing zeros are only significant in a number with a decimal. For example 100 has only 1\u00a0significant figure. 100.0 has 4 significant figures. 0.01 has one significant figure because there\u00a0are no trailing zeros after the 1, but 0.010 has 2 significant figures.<a class=\"footnote\" title=\"Selection modified from: Boundless Significant Figures 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/significant-figures-188-7529\/\" id=\"return-footnote-103-2\" href=\"#footnote-103-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/li>\n<\/ul>\n<h3>Significant Figures in Calculations<\/h3>\n<ul>\n<li>When multiplying or dividing, your answer should have the same number of significant figures as the\u00a0number in the calculation with the FEWEST.<\/li>\n<li>When adding or subtracting, your answer should go to number of decimal spaces as the one in the\u00a0calculation with the FEWEST number of decimal spaces.<\/li>\n<\/ul>\n<h3>A Guide to Solving Dimensional Analysis Problems<\/h3>\n<p>The following summary can be used as a guide for doing DA. While not all steps listed below will be\u00a0necessary to solve all problems, any problem can be solved using the following. Do not memorize the\u00a0sequence of steps, but rather complete practice until you understand how to solve these problems.\u00a0Dimensional analysis is a fundamental part of chemistry and will be applied all semester. It is imperative\u00a0you gain an understanding of how to perform calculations using dimensional analysis.<\/p>\n<p>1. Determine what you<strong> want<\/strong> to know. Read the problem and identify what you&#8217;re being asked to\u00a0figure out, e.g. &#8220;how many milliliters are in 1 liter of solution.&#8221;<\/p>\n<p style=\"padding-left: 30px;\">a. Find starting and ending units:<\/p>\n<p style=\"padding-left: 30px;\">We are looking for mg in L which means we begin with L and end with mL. You may\u00a0want to draw out the step(s) you will need for this conversion.<\/p>\n<p style=\"text-align: center; padding-left: 30px;\">L\u2192mL<\/p>\n<p>2. Determine what you already<strong> know<\/strong>.<\/p>\n<p style=\"padding-left: 30px;\">a. What are you<strong> given<\/strong> by the problem, if anything? In this example, we know we have 1 liter of\u00a0solution.<\/p>\n<p style=\"padding-left: 30px;\">b. Determine<strong> conversion factors<\/strong> that may be needed and write them in a form you can use,\u00a0such as &#8220;60 min\/1 hour.&#8221;<\/p>\n<p style=\"padding-left: 30px;\">Here we would need 1 L = 1000 mL Which we can write as a fraction<\/p>\n<p style=\"padding-left: 30px; text-align: center;\">[latex]\\displaystyle\\frac{1\\text{ L}}{1000\\text{ mL}}\\\\[\/latex] or\u00a0[latex]\\displaystyle\\frac{1000\\text{ mL}}{1\\text{ L}}\\\\[\/latex]<\/p>\n<p><strong>3. Setup<\/strong> the problem using only what you need to know.<\/p>\n<p style=\"padding-left: 30px;\">a. Pick a<strong> starting factor<\/strong>.\u00a0If possible, pick what is given, but make sure it is in the appropriate location (top or\u00a0bottom depending on the final units you want).<\/p>\n<p style=\"padding-left: 30px;\">b. Set up the problem with all units and making sure conversion factors allow units to cancel.\u00a0Set up the problem to cancel unwanted units.\u00a0Our plan is to go to from L\u2192mL using 1 L = 1000 mL<\/p>\n<p style=\"padding-left: 30px;\">c. If you can&#8217;t get to what you want, try picking a different starting factor, or checking for a\u00a0needed conversion factor.<\/p>\n<p><strong>4. Solve<\/strong>: make sure all the units other than the answer units cancel out, and then do the math.<\/p>\n<p style=\"padding-left: 30px;\">a. Simplify the numbers by cancellation.<br \/>\nb. Multiply all the top numbers together, then divide into that number all the bottom numbers.<br \/>\nc. Double check to make sure you didn&#8217;t press a wrong calculator key by dividing the first top number by the first bottom number, alternating until finished, then comparing the answer to the first one. Miskeying is a significant source of error, so always double check.<br \/>\nd. Round off the calculated answer. Make sure you use the appropriate number of significant figures.<br \/>\ne. Add labels (the answer unit) to the appropriately rounded number to get your answer. Compare units in answer to answer units recorded from first step.<\/p>\n<p style=\"padding-left: 30px; text-align: center;\">[latex]\\displaystyle1\\cancel{\\text{ L}}\\Bigg|\\frac{1000\\text{ mL}}{1\\cancel{\\text{ L}}}\\Bigg|=1000\\text{ mL}\\\\[\/latex]<\/p>\n<p>5. Take a few seconds and ask yourself if the answer you came up with makes sense. If it\u00a0doesn&#8217;t, start over.<a class=\"footnote\" title=\"Selection modified from: Mrs. Patton 2014 CC-BY-SA Dimensional Analysis with Samples http:\/\/math- mrspatton.wikispaces.com\/file\/links\/Dimensional+Analysis+with+Samples.doc\" id=\"return-footnote-103-3\" href=\"#footnote-103-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/p>\n<h2>Guides<\/h2>\n<h3>Significant Figures \u2013 Rules<\/h3>\n<p>Significant figures are critical when reporting scientific data because they give the reader an idea of\u00a0how well you could actually measure\/report your data. Before looking at a few examples, let\u2019s\u00a0summarize the rules for significant figures.<\/p>\n<p style=\"padding-left: 30px;\">1) ALL non-zero numbers (1, 2, 3, 4, 5, 6 ,7, 8, 9) are ALWAYS significant.<br \/>\n2) ALL zeroes between non-zero numbers are ALWAYS significant.<br \/>\n3) ALL zeros which are SIMULTANEOUSLY to the right of the decimal point AND at the\u00a0end of the number are ALWAYS significant.<br \/>\n4) ALL zeros which are to the left of a written decimal point and are in a number &gt; 1 are\u00a0ALWAYS significant.<\/p>\n<p>A helpful way to check rules 3 &amp; 4 is to write the number in scientific notation. If you can\/must get rid of the zeros, then they are NOT significant.<\/p>\n<table style=\"height: 249px; width: 282px;\">\n<tbody>\n<tr>\n<td>Number<\/td>\n<td># Significant Figures<\/td>\n<td>Rule(s)<\/td>\n<\/tr>\n<tr>\n<td>49,923<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>3,967<\/td>\n<td>4<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>900.06<\/td>\n<td>5<\/td>\n<td>1, 2, 4<\/td>\n<\/tr>\n<tr>\n<td>0.004 (=4 E<sup>-4<\/sup>)<\/td>\n<td>1<\/td>\n<td>1, 4<\/td>\n<\/tr>\n<tr>\n<td>8.1000<\/td>\n<td>5<\/td>\n<td>1, 3<\/td>\n<\/tr>\n<tr>\n<td>501.040<\/td>\n<td>6<\/td>\n<td>1, 2, 3, 4<\/td>\n<\/tr>\n<tr>\n<td>3,000,000 (=3 E<sup>+6<\/sup>)<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>10.0 (=1.00 E<sup>+1<\/sup>)<\/td>\n<td>3<\/td>\n<td>1, 3, 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204516\/Screen-Shot-2015-12-11-at-8.51.14-AM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-113 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204516\/Screen-Shot-2015-12-11-at-8.51.14-AM.png\" alt=\"Screen Shot 2015-12-11 at 8.51.14 AM\" width=\"632\" height=\"396\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td><strong>Prefix<\/strong><\/td>\n<td><strong>Root Abbreviation<\/strong><\/td>\n<td><strong>Decimal (1 with prefix=___ base)<\/strong><\/td>\n<td><strong>Power of Ten<\/strong><\/td>\n<\/tr>\n<tr>\n<td>mega<\/td>\n<td>M<\/td>\n<td>1 000 000<\/td>\n<td>10<sup>6<\/sup><\/td>\n<\/tr>\n<tr>\n<td>kilo<\/td>\n<td>k<\/td>\n<td>1 000<\/td>\n<td>10<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>hecto<\/td>\n<td>h<\/td>\n<td>1 00<\/td>\n<td>10<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>deka<\/td>\n<td>da<\/td>\n<td>10<\/td>\n<td>10<sup>1<\/sup><\/td>\n<\/tr>\n<tr>\n<td>METER (base unit)<\/td>\n<td>m<\/td>\n<td>1<\/td>\n<td>10<sup>0<\/sup><\/td>\n<\/tr>\n<tr>\n<td>LITER (base unit)<\/td>\n<td>L<\/td>\n<td>1<\/td>\n<td>10<sup>0<\/sup><\/td>\n<\/tr>\n<tr>\n<td>GRAM (base unit)<\/td>\n<td>g<\/td>\n<td>1<\/td>\n<td>10<sup>0<\/sup><\/td>\n<\/tr>\n<tr>\n<td>deci<\/td>\n<td>d<\/td>\n<td>0.1<\/td>\n<td>10<sup>-1<\/sup><\/td>\n<\/tr>\n<tr>\n<td>centi<\/td>\n<td>c<\/td>\n<td>0.01<\/td>\n<td>10<sup>-2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>milli<\/td>\n<td>m<\/td>\n<td>0.001<\/td>\n<td>10<sup>-3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>micro<\/td>\n<td>\u03bc<\/td>\n<td>0.000.001<\/td>\n<td>10<sup>-6<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Metric Steps Conversion<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1314\/2015\/12\/03204520\/Screen-Shot-2015-12-11-at-3.16.35-PM.png\" alt=\"Metric steps showing the units like steps up stairs. It begins with micro, then takes three steps up to milli, then centi, deci, the base units (m, L, g), then deka, hecto, kilo, three steps and then Mega.\" width=\"629\" height=\"260\" \/><\/h2>\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-103\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>College Chemistry 1. <strong>Authored by<\/strong>: Jessica Garber-Morales  . <strong>Provided by<\/strong>: Tidewater Community College  . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.tcc.edu\/%20%20\">http:\/\/www.tcc.edu\/%20%20<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/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><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-103-1\">Selection modified from: Boundless Scientific Notation 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/scientific-notation-187-3705\/  <a href=\"#return-footnote-103-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-103-2\">Selection modified from: Boundless Significant Figures 2014 CC-BY-SA 3.0 https:\/\/www.boundless.com\/chemistry\/textbooks\/boundless-chemistry-textbook\/introduction-to-chemistry- 1\/measurement-uncertainty-30\/significant-figures-188-7529\/  <a href=\"#return-footnote-103-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-103-3\">Selection modified from: Mrs. Patton 2014 CC-BY-SA Dimensional Analysis with Samples http:\/\/math- mrspatton.wikispaces.com\/file\/links\/Dimensional+Analysis+with+Samples.doc  <a href=\"#return-footnote-103-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":74,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"College Chemistry 1\",\"author\":\"Jessica Garber-Morales  \",\"organization\":\"Tidewater Community College  \",\"url\":\"http:\/\/www.tcc.edu\/  \",\"project\":\"\",\"license\":\"cc-by\",\"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-103","chapter","type-chapter","status-publish","hentry"],"part":40,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapters\/103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/wp\/v2\/users\/74"}],"version-history":[{"count":21,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapters\/103\/revisions"}],"predecessor-version":[{"id":731,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapters\/103\/revisions\/731"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/parts\/40"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapters\/103\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/wp\/v2\/media?parent=103"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/pressbooks\/v2\/chapter-type?post=103"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/wp\/v2\/contributor?post=103"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chemistry1labs\/wp-json\/wp\/v2\/license?post=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}