{"id":110,"date":"2023-06-05T15:29:51","date_gmt":"2023-06-05T15:29:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/the-metric-system\/"},"modified":"2023-07-23T16:52:05","modified_gmt":"2023-07-23T16:52:05","slug":"the-metric-system","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/the-metric-system\/","title":{"raw":"Metric System Basics","rendered":"Metric System Basics"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Define the metric prefixes<\/li>\r\n \t<li>Convert between Metric units of length, volume, and mass<\/li>\r\n \t<li>Solve application problems using metric units<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n\r\nThe mathematical skills in this section include the same unit ratio conversions that you performed in the previous sections together with multiplying and dividing by powers of 10.\r\n\r\nWhen multiplying a number by 10, we simply include an extra zero at the end. When multiplying by 100, we include two extra zeros. When multiplying by 1000, we include three extra zeros, and so on.\r\n\r\nEx. [latex]1\\cdot10=10 \\text{ , }23\\cdot10=230 \\text{ , }47\\cdot100=4700 \\text{ , etc.}[\/latex]\r\n\r\nWhen dividing a number by 10, we locate the existing decimal point and move it one place to the left. When dividing by 100, we move the decimal point two places to the left. When dividing by 1000, we move the decimal point three places to the left, and so on.\r\n\r\nEx. [latex] \\dfrac{10}{10}=1 \\text{ , } \\dfrac{234}{10}=23.4\\text{ , }\\dfrac{234}{100}=2.34\\text{ , etc.}[\/latex]\r\n\r\n<\/div>\r\n<h2>What Is Metric?<\/h2>\r\nThe metric system uses units such as <b>meter<\/b>, <b>liter<\/b>, and <b>gram<\/b> to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.\r\n\r\nIn addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the word <em>meter<\/em> is part of all of these units.\r\n\r\nThe metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a bit later. For now, notice how this idea of <em>getting bigger or smaller by 10<\/em>\u00a0is very different than the relationship between units in the U.S. customary system, where 3 feet equals 1 yard, and 16 ounces equals 1 pound.\r\n<h2>Length, Mass, and Volume<\/h2>\r\nThe table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.\r\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Length<\/b><\/td>\r\n<td><b>Mass<\/b><\/td>\r\n<td><b>Volume<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"3\"><i>basic units<\/i><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>meter<\/td>\r\n<td>gram<\/td>\r\n<td>liter<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"3\"><i>other units you may see<\/i><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilometer<\/td>\r\n<td>kilogram<\/td>\r\n<td>dekaliter<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>centimeter<\/td>\r\n<td>centigram<\/td>\r\n<td>centiliter<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>millimeter<\/td>\r\n<td>milligram<\/td>\r\n<td>milliliter<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn the metric system, the basic unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.\r\n\r\nThe basic metric unit of mass is the gram. A regular-sized paperclip has a mass of about 1 gram.\r\n\r\nAmong scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. You may notice that the word <em>mass<\/em>\u00a0is used here instead of <em>weight<\/em>. In the sciences and technical fields, a distinction is made between weight and mass. Weight is a measure of the pull of gravity on an object. For this reason, an object's weight would be different if it was weighed on Earth or on the moon because of the difference in the gravitational forces. However, the object's mass would remain the same in both places because mass measures the amount of substance in an object. As long as you are planning on only measuring objects on Earth, you can use mass\/weight fairly interchangeably, but it is worth noting that there is a difference!\r\n\r\nFinally, the basic metric unit of volume is the liter. A liter is slightly larger than a quart.\r\n<table border=\"1\" width=\"602\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201020\/image106.jpg\" width=\"162\" height=\"109\" \/><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201021\/image107.jpg\" width=\"148\" height=\"104\" \/><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201022\/image108.jpg\" width=\"94\" height=\"117\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The handle of a shovel is about 1 meter.<\/td>\r\n<td>A paperclip weighs about 1 gram.<\/td>\r\n<td>A medium-sized container of milk is about 1 liter.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIt helps to have a mental image of how large or small some units are between the customary and metric systems. The table below shows the relationship between some common units in both systems.\r\n<table border=\"1\" width=\"507\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><b>Common Measurements in Customary and Metric Systems<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>Length<\/i><\/td>\r\n<td>1 centimeter is a little less than half an inch.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>1.6 kilometers is about 1 mile.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>1 meter is about 3 inches longer than 1 yard.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>Mass<\/i><\/td>\r\n<td>1 kilogram is a little more than 2 pounds.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>\u00a0<\/i><\/td>\r\n<td>28 grams is about the same as 1 ounce.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>Volume<\/i><\/td>\r\n<td>1 liter is a little more than 1 quart.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>\u00a0<\/i><\/td>\r\n<td>4 liters is a little more than 1 gallon.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Prefixes in the Metric System<\/h2>\r\nThe metric system is a base 10 system. This means that each successive unit is 10 times larger than the previous one.\r\n\r\nThe names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the <b>prefix<\/b>. To tell whether the unit is measuring length, mass, or volume, you look at the base.\r\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"7\"><b>Prefixes in the Metric System<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><i>kilo-<\/i><\/td>\r\n<td><i>hecto-<\/i><\/td>\r\n<td><i>deka-<\/i><\/td>\r\n<td>meter\r\n\r\ngram\r\n\r\nliter<\/td>\r\n<td><i>deci-<\/i><\/td>\r\n<td><i>centi-<\/i><\/td>\r\n<td><i>milli-<\/i><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1,000 times <b>larger<\/b> than base unit<\/td>\r\n<td>100 times <b>larger<\/b> than base unit<\/td>\r\n<td>10 times <b>larger<\/b> than base unit<\/td>\r\n<td>base units<\/td>\r\n<td>10 times <b>smaller<\/b> than base unit<\/td>\r\n<td>100 times <b>smaller<\/b> than base unit<\/td>\r\n<td>1,000 times <b>smaller<\/b> than base unit<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nUsing this table as a reference, you can see the following:\r\n<ul>\r\n \t<li>A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).<\/li>\r\n \t<li>A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).<\/li>\r\n \t<li>A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).<\/li>\r\n<\/ul>\r\nHere is a similar table that just shows the metric units of measurement for mass, along with their size relative to 1 gram (the base unit). The common abbreviations for these metric units have been included as well.\r\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"7\"><b>Measuring Mass in the Metric System<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kilogram(kg)<\/td>\r\n<td>hectogram(hg)<\/td>\r\n<td>dekagram(dag)<\/td>\r\n<td>gram(g)<\/td>\r\n<td>decigram(dg)<\/td>\r\n<td>centigram(cg)<\/td>\r\n<td>milligram(mg)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1,000 grams<\/td>\r\n<td>100 grams<\/td>\r\n<td>10 grams<\/td>\r\n<td>gram<\/td>\r\n<td>0.1 gram<\/td>\r\n<td>0.01 gram<\/td>\r\n<td>0.001 gram<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the prefixes remain constant through the metric system, you could create similar charts for length and volume. The prefixes have the same meanings whether they are attached to the units of length (meter), mass (gram), or volume (liter).\r\n<div class=\"textbox shaded\">\r\n\r\nYou may find one of the sayings below helpful to remember the order of the metric prefixes.\r\n<table style=\"border-collapse: collapse; width: 50.0038%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 3.55399%; text-align: center;\"><strong>Kilo (k)<\/strong><\/td>\r\n<td style=\"width: 2.96695%; text-align: center;\"><strong>Hecto (h)<\/strong><\/td>\r\n<td style=\"width: 1.99924%; text-align: center;\"><strong>Deka (da)<\/strong><\/td>\r\n<td style=\"width: 5.33537%; text-align: center;\"><strong>Ones\/Units\/Base (m\/L\/g)<\/strong><\/td>\r\n<td style=\"width: 3.21977%; text-align: center;\"><strong>Deci (d)<\/strong><\/td>\r\n<td style=\"width: 1.47493%; text-align: center;\"><strong>Centi (c)<\/strong><\/td>\r\n<td style=\"width: 1.47493%; text-align: center;\"><strong>Milli (m)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 3.55399%;\">Kids<\/td>\r\n<td style=\"width: 2.96695%;\">Have<\/td>\r\n<td style=\"width: 1.99924%;\">Dropped<\/td>\r\n<td style=\"width: 5.33537%;\">Over<\/td>\r\n<td style=\"width: 3.21977%;\">Dead<\/td>\r\n<td style=\"width: 1.47493%;\">Converting<\/td>\r\n<td style=\"width: 1.47493%;\">Metrics<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 3.55399%;\">Kim<\/td>\r\n<td style=\"width: 2.96695%;\">Has<\/td>\r\n<td style=\"width: 1.99924%;\">Dirty<\/td>\r\n<td style=\"width: 5.33537%;\">Underwear<\/td>\r\n<td style=\"width: 3.21977%;\">Don't<\/td>\r\n<td style=\"width: 1.47493%;\">Check<\/td>\r\n<td style=\"width: 1.47493%;\">Mine<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 3.55399%;\">King<\/td>\r\n<td style=\"width: 2.96695%;\">Henry<\/td>\r\n<td style=\"width: 1.99924%;\">Died<\/td>\r\n<td style=\"width: 5.33537%;\">By<\/td>\r\n<td style=\"width: 3.21977%;\">Drinking<\/td>\r\n<td style=\"width: 1.47493%;\">Chocolate<\/td>\r\n<td style=\"width: 1.47493%;\">Milk<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nWhich of the following sets of three units are all metric measurements of <strong>length<\/strong>?\r\n\r\nA) inch, foot, yard\r\n\r\nB) kilometer, centimeter, millimeter\r\n\r\nC) kilogram, gram, centigram\r\n\r\nD) kilometer, foot, decimeter\r\n\r\n[reveal-answer q=\"728320\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"728320\"]\r\n\r\nB) kilometer, centimeter, millimeter\r\n\r\nAll of these measurements are from the metric system. You can tell they are measurements of length because they all contain the word <em>meter<\/em>.\r\n\r\n[\/hidden-answer]\r\n\r\n[ohm_question]126793-126794-126795[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Converting Units Up and Down the Metric Scale<\/h2>\r\nConverting between metric units of measure requires knowledge of the metric prefixes and an understanding of the decimal system.\r\n\r\nFor instance, you can figure out how many centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, so you expect that one dekagram will equal many centigrams.\r\n\r\nIn the table, each unit is 10 times larger than the one to its immediate right. This means that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many milligrams are in one decigram?\r\n\r\n[reveal-answer q=\"363102\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"363102\"]\r\n\r\nIdentify locations of milligrams and decigrams.\r\n<table style=\"height: 22px;\">\r\n<tbody>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 76.6563px;\">kg<\/td>\r\n<td style=\"height: 11px; width: 80.6563px;\">hg<\/td>\r\n<td style=\"height: 11px; width: 101.656px;\">dag<\/td>\r\n<td style=\"height: 11px; width: 54.6563px;\">g<\/td>\r\n<td style=\"height: 11px; width: 80.6563px;\">dg<\/td>\r\n<td style=\"height: 11px; width: 77.6563px;\">cg<\/td>\r\n<td style=\"height: 11px; width: 94.6563px;\">mg<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 76.6563px;\">^<\/td>\r\n<td style=\"height: 11px; width: 80.6563px;\">^<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDecigrams (dg) are larger than milligrams (mg), so you expect there to be many mg in one dg.\r\n\r\nDg is 10 times larger than a cg, and a cg is 10 times larger than a mg.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\times10[\/latex]<\/td>\r\n<td>[latex]\\times10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>kg<\/td>\r\n<td>hg<\/td>\r\n<td>dag<\/td>\r\n<td>g<\/td>\r\n<td>dg<\/td>\r\n<td>cg<\/td>\r\n<td>mg<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\downarrow[\/latex]<\/td>\r\n<td>[latex]\\uparrow[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">[latex]\\rightarrow[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince you are going from a larger unit to a smaller unit, multiply.\r\n\r\n<i>Multiply: 1 \u00b7 10 \u00b7 10, to find the number of milligrams in one decigram.\u00a0<\/i>\r\n<p style=\"text-align: center;\">[latex]1\\text{ dg}\\cdot10\\cdot10=100\\text{ mg}[\/latex]<\/p>\r\nThere are 100 milligrams (mg) in 1 decigram (dg).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nConvert 3,085 milligrams to grams.\r\n\r\n[reveal-answer q=\"353889\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"353889\"]\r\n\r\nOne gram is 1,000 times larger than a milligram, so you can move the decimal point in 3,085 three places to the left.\r\n\r\n[\/hidden-answer]\r\n\r\n[ohm_question]1000-1001-1005[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert 1 centimeter to kilometers.\r\n\r\n[reveal-answer q=\"4330\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"4330\"]\r\n\r\nIdentify locations of kilometers and centimeters.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>km<\/td>\r\n<td>hm<\/td>\r\n<td>dam<\/td>\r\n<td>m<\/td>\r\n<td>dm<\/td>\r\n<td>cm<\/td>\r\n<td>mm<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>^<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>^<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nKilometers (km) are larger than centimeters (cm), so you expect there to be less than one km in a cm.\r\n\r\nCm is 10 times smaller than a dm; a dm is 10 times smaller than a m, etc.\r\n\r\nSince you are going from a smaller unit to a larger unit, divide.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\div10[\/latex]<\/td>\r\n<td>[latex]\\div10[\/latex]<\/td>\r\n<td>[latex]\\div10[\/latex]<\/td>\r\n<td>[latex]\\div10[\/latex]<\/td>\r\n<td>[latex]\\div10[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>km<\/td>\r\n<td>hm<\/td>\r\n<td>dam<\/td>\r\n<td>m<\/td>\r\n<td>dm<\/td>\r\n<td>cm<\/td>\r\n<td>mm<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>^<\/td>\r\n<td>[latex]\\leftarrow[\/latex]<\/td>\r\n<td>[latex]\\leftarrow[\/latex]<\/td>\r\n<td>[latex]\\leftarrow[\/latex]<\/td>\r\n<td>[latex]\\leftarrow[\/latex]<\/td>\r\n<td>^<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDivide: [latex]1\\div10\\div10\\div10\\div10\\div10[\/latex], to find the number of kilometers in one centimeter.<em>\u00a0<\/em>\r\n<p style=\"text-align: center;\">[latex]1\\text{ cm}\\div10\\div10\\div10\\div10\\div10=0.00001\\text{ km}[\/latex]<\/p>\r\n1 centimeter (cm) = 0.00001 kilometers (km).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]998[\/ohm_question]\r\n\r\n<\/div>\r\nOnce you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.\r\n\r\nHere is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:\r\n<p style=\"text-align: center;\">[latex] \\displaystyle kg\\quad hg\\quad dag\\quad g\\quad d\\underbrace{g\\quad c}_{1}\\underbrace{g\\quad m}_{2}g[\/latex]<\/p>\r\nThis question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: [latex] \\displaystyle 1\\ dg=1\\underbrace{0}_{1}\\underbrace{0}_{2}.\\ mg[\/latex].\r\n\r\nThe same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle k\\underbrace{m\\quad h}_{5}\\underbrace{m\\quad d}_{4}\\underbrace{am\\quad }_{3}\\underbrace{m\\quad d}_{2}\\underbrace{m\\quad c}_{1}m\\quad mm[\/latex]<\/p>\r\nNote that instead of moving to the right, you are now moving to the left \u0097so the decimal point must do the same:\r\n<p style=\"text-align: center;\">[latex] \\displaystyle 1\\ cm=0.\\underbrace{0}_{5}\\underbrace{0}_{4}\\underbrace{0}_{3}\\underbrace{0}_{2}\\underbrace{1}_{1}\\ km[\/latex].<\/p>\r\n\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nHow many milliliters are in 1 liter?\r\n\r\n[reveal-answer q=\"95548\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"95548\"]\r\n\r\nThere are 10 milliliters in a centiliter, 10 centiliters in a deciliter, and 10 deciliters in a liter. Multiply: [latex]10\\cdot10\\cdot10[\/latex], to find the number of milliliters in a liter, 1,000.\r\n\r\n[\/hidden-answer]\r\n\r\n[ohm_question]999[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Dimensional Analysis<\/h2>\r\nThere is yet another method that you can use to convert metric measurements:\u00a0<b>dimensional analysis<\/b>. You used this method when you were converting measurement units within the U.S. customary system.\r\n\r\nDimensional analysis works the same in the metric system; it relies on the use of unit fractions and the cancelling of intermediate units. The table below shows some of the <b>unit equivalents<\/b> and <b>unit fractions<\/b> for length in the metric system. (You should notice that all of the unit fractions contain a factor of 10. Remember that the metric system is based on the notion that each unit is 10 times larger than the one that came before it.)\r\n\r\nAlso, notice that two new prefixes have been added here: [latex]M[\/latex] for mega- (which is very big) and [latex]\\mu[\/latex] for micro- (which is very small). The symbol [latex]\\mu[\/latex] is a greek lower-case letter pronounced\u00a0<em>mew<\/em>.\r\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Unit Equivalents<\/b><\/td>\r\n<td colspan=\"2\"><b>Conversion Factors<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 meter = 1,000,000 micrometers<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ m}{1,000,000\\ \\mu m}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1,000,000\\ \\mu m}{1\\ m}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 meter = 1,000 millimeters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ m}{1,000\\ mm}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1,000\\ mm}{1\\ m}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 meter = 100 centimeters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ m}{100\\ cm}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{100\\ cm}{1\\ m}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 meter = 10 decimeters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ m}{10\\ dm}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{10\\ dm}{1\\ m}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 dekameter = 10 meters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ dam}{10\\ m}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{10\\ m}{1\\ dam}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 hectometer = 100 meters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ hm}{100\\ m}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{100\\ m}{1\\ hm}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 kilometer = 1,000 meters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ km}{1,000\\ m}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1,000\\ m}{1\\ km}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 megameter = 1,000,000 meters<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\ Mm}{1,000,000\\ m}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1,000,000\\ m}{1\\ Mm}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen applying dimensional analysis in the metric system, be sure to check that you are not skipping over any intermediate units of measurement!\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert 7,225 centimeters to meters.\r\n\r\n[reveal-answer q=\"461145\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"461145\"]\r\n\r\nMeters is larger than centimeters, so you expect your answer to be less than 7,225.\r\n<p style=\"text-align: center;\">[latex]7,225\\text{ cm}=\\text{___ m}[\/latex]<\/p>\r\nUsing the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to m.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{7,225\\ cm}{1}\\cdot \\frac{1\\ m}{100\\ cm}=\\_\\_\\_ m[\/latex]<\/p>\r\nCancel similar units, multiply, and simplify.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{7,225\\ \\cancel{cm}}{1}\\cdot \\frac{1\\text{ m}}{100\\ \\cancel{\\text{cm}}}=\\_\\_\\_m[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{7,225}{1}\\cdot \\frac{1\\text{ m}}{100}=\\frac{7,225}{100}\\text{m}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{7,225\\text{ m}}{100}=72.25\\text{ m}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]7,225\\text{ centimeters}=72.25\\text{ meters}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nConvert 32.5 kilometers to meters.\r\n\r\n[reveal-answer q=\"574914\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"574914\"]\r\n\r\n32,500 meters\r\n\r\n[latex] \\displaystyle \\frac{32.5\\text{ km}}{1}\\cdot \\frac{1,000\\text{ m}}{1\\text{ km}}=\\frac{32,500\\text{ m}}{1}[\/latex].\r\n\r\nThe km units cancel, leaving the answer in m.\r\n\r\n[\/hidden-answer]\r\n\r\n[ohm_question]18877[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIf you have a prescription for 5,000 mg of medicine, and upon getting it filled, the dosage reads 5g of medicine, did the pharmacist make a mistake?\r\n\r\n[reveal-answer q=\"600572\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"600572\"]\r\n\r\nConvert mg to g.\r\n<p style=\"text-align: center;\">[latex]5,000\\text{ mg}=\\text{___ g}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{5,000\\text{ mg}}{1}\\cdot \\frac{1\\text{ g}}{1,000\\text{ mg}}=\\text{ g}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{5,000\\cancel{\\text{mg}}}{1}\\cdot \\frac{1\\text{ g}}{1,000\\ \\cancel{\\text{mg}}}=\\text{ g}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{5,000\\cdot 1\\text{ g}}{1\\cdot 1,000}=\\frac{5,000\\text{ g}}{1,000}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{5,000\\text{ g}}{1,000}=5\\text{ g}[\/latex]<\/p>\r\n[latex]5\\text{ g}=5,000\\text{ mg}[\/latex], so the pharmacist did not make a mistake.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146841[\/ohm_question]\r\n\r\n[ohm_question]146842[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Understanding Context and Performing Conversions<\/h2>\r\nLearning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.\r\n<div class=\"textbox\"><strong>TIP:<\/strong> To solve these problems effectively, you need to understand the context of a problem, perform conversions, and then check the reasonableness of your answer. Do all three of these steps and you will succeed in whatever measurement system you find yourself using.<\/div>\r\nThe first step in solving any real-world problem is to understand its context. This will help you figure out what kinds of solutions are reasonable (and the problem itself may give you clues about what types of conversions are necessary). Here is an example.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nMarcus bought at 2 meter board, and cut off a piece 1 meter and 35 cm long. How much board is left?\r\n\r\n[reveal-answer q=\"701860\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"701860\"]\r\n\r\nTo answer this question, we will need to subtract.\r\n\r\nFirst convert all measurements to one unit. Here we will convert to centimeters.\r\n\r\n[latex]2\\text{ meters}-1\\text{ meter and }35\\text{ cm}[\/latex]\r\n\r\nUse the factor label method and unit fractions to convert from meters to centimeters.\r\n\r\n[latex] \\displaystyle \\frac{2\\text{ m}}{1}\\cdot \\frac{100\\text{ cm}}{1\\text{ m}}=\\text{ cm}[\/latex]\r\n\r\nCancel, multiply, and solve.\r\n\r\nConvert the 1 meter to centimeters, and combine with the additional 35 centimeters.\r\n\r\nSubtract the cut length from the original board length.\r\n\r\n[latex] \\displaystyle \\frac{2\\ \\cancel{\\text{m}}}{1}\\cdot \\frac{100\\text{ cm}}{1\\ \\cancel{\\text{ m}}}=\\text{ cm}[\/latex]\r\n\r\n[latex] \\displaystyle \\frac{200\\text{ cm}}{1}=200\\text{ cm}[\/latex]\r\n\r\n[latex]1\\text{ meter}+35\\text{ cm}[\/latex]\r\n\r\n[latex]100\\text{ cm}+35\\text{ cm}[\/latex]\r\n\r\n[latex]135\\text{ cm}[\/latex]\r\n\r\n[latex]200\\text{ cm}-135\\text{ cm}[\/latex]\r\n\r\n[latex]65\\text{ cm}[\/latex]\r\n\r\nThere is 65 cm of board left.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThis problem asked for the difference between two quantities. The easiest way to find this is to convert one quantity so that both quantities are measured in the same unit, and then subtract one from the other.\r\n\r\nAn example with a different context, but still requiring conversions, is shown below.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA faucet drips 10 ml every minute. How much water will be wasted in a week?\r\n\r\n[reveal-answer q=\"642392\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"642392\"]\r\n\r\nStart by calculating how much water will be used in a week using the factor label method to convert the time units.\r\n\r\n[latex] \\displaystyle \\frac{10\\ ml}{1\\text{ minute}}\\cdot \\frac{60\\text{ minute}}{1\\text{ hour}}\\cdot \\frac{24\\text{ hours}}{1\\text{ day}}\\cdot \\frac{7\\text{ days}}{1\\text{ week}}[\/latex]\r\n\r\nCancel, multiply and solve.\r\n\r\n[latex] \\displaystyle \\frac{10\\ ml}{1\\text{ }\\cancel{\\text{minute}}}\\cdot \\frac{60\\text{ }\\cancel{\\text{minute}}}{1\\text{ }\\cancel{\\text{hour}}}\\cdot \\frac{24\\text{ }\\cancel{\\text{hours}}}{1\\text{ }\\cancel{\\text{day}}}\\cdot \\frac{7\\text{ }\\cancel{\\text{days}}}{1\\text{ week}}[\/latex]\r\n\r\n[latex] \\displaystyle \\frac{10\\centerdot 60\\centerdot 24\\centerdot 7\\ ml}{1\\centerdot 1\\centerdot 1\\centerdot 1\\text{ week}}[\/latex]\r\n\r\nTo give a more useable answer, convert this into liters.\r\n\r\n[latex] \\displaystyle \\frac{100800\\ ml}{1\\text{ week}}[\/latex]\r\n\r\nCancel, multiply and solve.\r\n\r\n[latex] \\displaystyle \\frac{100800\\text{ ml}}{1\\text{ week}}\\centerdot \\frac{1\\text{ L}}{1000\\text{ ml}}[\/latex]\r\n\r\n[latex] \\displaystyle \\frac{100800\\text{ }\\cancel{\\text{ml}}}{1\\text{ week}}\\centerdot \\frac{1\\text{ L}}{1000\\text{ }\\cancel{\\text{ml}}}[\/latex]\r\n\r\n[latex] \\displaystyle \\frac{100800\\text{ L}}{1000\\text{ week}}[\/latex]=[latex] \\displaystyle 100.8\\frac{\\text{L}}{\\text{week}}[\/latex]\r\n\r\nThe faucet wastes about 100.8 liters each week.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nA bread recipe calls for 600 g of flour. How many kilograms of flour would you need to make 5 loaves?\r\n\r\n[reveal-answer q=\"838013\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"838013\"]\r\n\r\nMultiplying 600 g per loaf by the 5 loaves,\r\n\r\n[latex]600\\text{g}\\cdot5=3000\\text{g}[\/latex]\r\n\r\nUsing factor labels or the <em>move the decimal<\/em>\u00a0method, convert this to 3 kilograms.\r\n\r\nYou will need 3 kg of flour to make 5 loaves.\r\n\r\n[\/hidden-answer]\r\n\r\n[ohm_question]1002-117516[\/ohm_question]\r\n\r\n<\/div>\r\n<h2><\/h2>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Define the metric prefixes<\/li>\n<li>Convert between Metric units of length, volume, and mass<\/li>\n<li>Solve application problems using metric units<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<p>The mathematical skills in this section include the same unit ratio conversions that you performed in the previous sections together with multiplying and dividing by powers of 10.<\/p>\n<p>When multiplying a number by 10, we simply include an extra zero at the end. When multiplying by 100, we include two extra zeros. When multiplying by 1000, we include three extra zeros, and so on.<\/p>\n<p>Ex. [latex]1\\cdot10=10 \\text{ , }23\\cdot10=230 \\text{ , }47\\cdot100=4700 \\text{ , etc.}[\/latex]<\/p>\n<p>When dividing a number by 10, we locate the existing decimal point and move it one place to the left. When dividing by 100, we move the decimal point two places to the left. When dividing by 1000, we move the decimal point three places to the left, and so on.<\/p>\n<p>Ex. [latex]\\dfrac{10}{10}=1 \\text{ , } \\dfrac{234}{10}=23.4\\text{ , }\\dfrac{234}{100}=2.34\\text{ , etc.}[\/latex]<\/p>\n<\/div>\n<h2>What Is Metric?<\/h2>\n<p>The metric system uses units such as <b>meter<\/b>, <b>liter<\/b>, and <b>gram<\/b> to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.<\/p>\n<p>In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the word <em>meter<\/em> is part of all of these units.<\/p>\n<p>The metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a bit later. For now, notice how this idea of <em>getting bigger or smaller by 10<\/em>\u00a0is very different than the relationship between units in the U.S. customary system, where 3 feet equals 1 yard, and 16 ounces equals 1 pound.<\/p>\n<h2>Length, Mass, and Volume<\/h2>\n<p>The table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Length<\/b><\/td>\n<td><b>Mass<\/b><\/td>\n<td><b>Volume<\/b><\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\"><i>basic units<\/i><\/td>\n<\/tr>\n<tr>\n<td>meter<\/td>\n<td>gram<\/td>\n<td>liter<\/td>\n<\/tr>\n<tr>\n<td colspan=\"3\"><i>other units you may see<\/i><\/td>\n<\/tr>\n<tr>\n<td>kilometer<\/td>\n<td>kilogram<\/td>\n<td>dekaliter<\/td>\n<\/tr>\n<tr>\n<td>centimeter<\/td>\n<td>centigram<\/td>\n<td>centiliter<\/td>\n<\/tr>\n<tr>\n<td>millimeter<\/td>\n<td>milligram<\/td>\n<td>milliliter<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In the metric system, the basic unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.<\/p>\n<p>The basic metric unit of mass is the gram. A regular-sized paperclip has a mass of about 1 gram.<\/p>\n<p>Among scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. You may notice that the word <em>mass<\/em>\u00a0is used here instead of <em>weight<\/em>. In the sciences and technical fields, a distinction is made between weight and mass. Weight is a measure of the pull of gravity on an object. For this reason, an object&#8217;s weight would be different if it was weighed on Earth or on the moon because of the difference in the gravitational forces. However, the object&#8217;s mass would remain the same in both places because mass measures the amount of substance in an object. As long as you are planning on only measuring objects on Earth, you can use mass\/weight fairly interchangeably, but it is worth noting that there is a difference!<\/p>\n<p>Finally, the basic metric unit of volume is the liter. A liter is slightly larger than a quart.<\/p>\n<table cellpadding=\"0\" style=\"width: 602px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201020\/image106.jpg\" width=\"162\" height=\"109\" alt=\"image\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201021\/image107.jpg\" width=\"148\" height=\"104\" alt=\"image\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201022\/image108.jpg\" width=\"94\" height=\"117\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td>The handle of a shovel is about 1 meter.<\/td>\n<td>A paperclip weighs about 1 gram.<\/td>\n<td>A medium-sized container of milk is about 1 liter.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>It helps to have a mental image of how large or small some units are between the customary and metric systems. The table below shows the relationship between some common units in both systems.<\/p>\n<table cellpadding=\"0\" style=\"width: 507px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><\/td>\n<td><b>Common Measurements in Customary and Metric Systems<\/b><\/td>\n<\/tr>\n<tr>\n<td><i>Length<\/i><\/td>\n<td>1 centimeter is a little less than half an inch.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>1.6 kilometers is about 1 mile.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>1 meter is about 3 inches longer than 1 yard.<\/td>\n<\/tr>\n<tr>\n<td><i>Mass<\/i><\/td>\n<td>1 kilogram is a little more than 2 pounds.<\/td>\n<\/tr>\n<tr>\n<td><i>\u00a0<\/i><\/td>\n<td>28 grams is about the same as 1 ounce.<\/td>\n<\/tr>\n<tr>\n<td><i>Volume<\/i><\/td>\n<td>1 liter is a little more than 1 quart.<\/td>\n<\/tr>\n<tr>\n<td><i>\u00a0<\/i><\/td>\n<td>4 liters is a little more than 1 gallon.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Prefixes in the Metric System<\/h2>\n<p>The metric system is a base 10 system. This means that each successive unit is 10 times larger than the previous one.<\/p>\n<p>The names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the <b>prefix<\/b>. To tell whether the unit is measuring length, mass, or volume, you look at the base.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td colspan=\"7\"><b>Prefixes in the Metric System<\/b><\/td>\n<\/tr>\n<tr>\n<td><i>kilo-<\/i><\/td>\n<td><i>hecto-<\/i><\/td>\n<td><i>deka-<\/i><\/td>\n<td>meter<\/p>\n<p>gram<\/p>\n<p>liter<\/td>\n<td><i>deci-<\/i><\/td>\n<td><i>centi-<\/i><\/td>\n<td><i>milli-<\/i><\/td>\n<\/tr>\n<tr>\n<td>1,000 times <b>larger<\/b> than base unit<\/td>\n<td>100 times <b>larger<\/b> than base unit<\/td>\n<td>10 times <b>larger<\/b> than base unit<\/td>\n<td>base units<\/td>\n<td>10 times <b>smaller<\/b> than base unit<\/td>\n<td>100 times <b>smaller<\/b> than base unit<\/td>\n<td>1,000 times <b>smaller<\/b> than base unit<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Using this table as a reference, you can see the following:<\/p>\n<ul>\n<li>A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).<\/li>\n<li>A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).<\/li>\n<li>A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).<\/li>\n<\/ul>\n<p>Here is a similar table that just shows the metric units of measurement for mass, along with their size relative to 1 gram (the base unit). The common abbreviations for these metric units have been included as well.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td colspan=\"7\"><b>Measuring Mass in the Metric System<\/b><\/td>\n<\/tr>\n<tr>\n<td>kilogram(kg)<\/td>\n<td>hectogram(hg)<\/td>\n<td>dekagram(dag)<\/td>\n<td>gram(g)<\/td>\n<td>decigram(dg)<\/td>\n<td>centigram(cg)<\/td>\n<td>milligram(mg)<\/td>\n<\/tr>\n<tr>\n<td>1,000 grams<\/td>\n<td>100 grams<\/td>\n<td>10 grams<\/td>\n<td>gram<\/td>\n<td>0.1 gram<\/td>\n<td>0.01 gram<\/td>\n<td>0.001 gram<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the prefixes remain constant through the metric system, you could create similar charts for length and volume. The prefixes have the same meanings whether they are attached to the units of length (meter), mass (gram), or volume (liter).<\/p>\n<div class=\"textbox shaded\">\n<p>You may find one of the sayings below helpful to remember the order of the metric prefixes.<\/p>\n<table style=\"border-collapse: collapse; width: 50.0038%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.55399%; text-align: center;\"><strong>Kilo (k)<\/strong><\/td>\n<td style=\"width: 2.96695%; text-align: center;\"><strong>Hecto (h)<\/strong><\/td>\n<td style=\"width: 1.99924%; text-align: center;\"><strong>Deka (da)<\/strong><\/td>\n<td style=\"width: 5.33537%; text-align: center;\"><strong>Ones\/Units\/Base (m\/L\/g)<\/strong><\/td>\n<td style=\"width: 3.21977%; text-align: center;\"><strong>Deci (d)<\/strong><\/td>\n<td style=\"width: 1.47493%; text-align: center;\"><strong>Centi (c)<\/strong><\/td>\n<td style=\"width: 1.47493%; text-align: center;\"><strong>Milli (m)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.55399%;\">Kids<\/td>\n<td style=\"width: 2.96695%;\">Have<\/td>\n<td style=\"width: 1.99924%;\">Dropped<\/td>\n<td style=\"width: 5.33537%;\">Over<\/td>\n<td style=\"width: 3.21977%;\">Dead<\/td>\n<td style=\"width: 1.47493%;\">Converting<\/td>\n<td style=\"width: 1.47493%;\">Metrics<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.55399%;\">Kim<\/td>\n<td style=\"width: 2.96695%;\">Has<\/td>\n<td style=\"width: 1.99924%;\">Dirty<\/td>\n<td style=\"width: 5.33537%;\">Underwear<\/td>\n<td style=\"width: 3.21977%;\">Don&#8217;t<\/td>\n<td style=\"width: 1.47493%;\">Check<\/td>\n<td style=\"width: 1.47493%;\">Mine<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.55399%;\">King<\/td>\n<td style=\"width: 2.96695%;\">Henry<\/td>\n<td style=\"width: 1.99924%;\">Died<\/td>\n<td style=\"width: 5.33537%;\">By<\/td>\n<td style=\"width: 3.21977%;\">Drinking<\/td>\n<td style=\"width: 1.47493%;\">Chocolate<\/td>\n<td style=\"width: 1.47493%;\">Milk<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Which of the following sets of three units are all metric measurements of <strong>length<\/strong>?<\/p>\n<p>A) inch, foot, yard<\/p>\n<p>B) kilometer, centimeter, millimeter<\/p>\n<p>C) kilogram, gram, centigram<\/p>\n<p>D) kilometer, foot, decimeter<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q728320\">Show Solution<\/span><\/p>\n<div id=\"q728320\" class=\"hidden-answer\" style=\"display: none\">\n<p>B) kilometer, centimeter, millimeter<\/p>\n<p>All of these measurements are from the metric system. You can tell they are measurements of length because they all contain the word <em>meter<\/em>.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm126793\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=126793-126794-126795&theme=oea&iframe_resize_id=ohm126793&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Converting Units Up and Down the Metric Scale<\/h2>\n<p>Converting between metric units of measure requires knowledge of the metric prefixes and an understanding of the decimal system.<\/p>\n<p>For instance, you can figure out how many centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, so you expect that one dekagram will equal many centigrams.<\/p>\n<p>In the table, each unit is 10 times larger than the one to its immediate right. This means that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many milligrams are in one decigram?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q363102\">Show Solution<\/span><\/p>\n<div id=\"q363102\" class=\"hidden-answer\" style=\"display: none\">\n<p>Identify locations of milligrams and decigrams.<\/p>\n<table style=\"height: 22px;\">\n<tbody>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 76.6563px;\">kg<\/td>\n<td style=\"height: 11px; width: 80.6563px;\">hg<\/td>\n<td style=\"height: 11px; width: 101.656px;\">dag<\/td>\n<td style=\"height: 11px; width: 54.6563px;\">g<\/td>\n<td style=\"height: 11px; width: 80.6563px;\">dg<\/td>\n<td style=\"height: 11px; width: 77.6563px;\">cg<\/td>\n<td style=\"height: 11px; width: 94.6563px;\">mg<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 76.6563px;\">^<\/td>\n<td style=\"height: 11px; width: 80.6563px;\">^<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Decigrams (dg) are larger than milligrams (mg), so you expect there to be many mg in one dg.<\/p>\n<p>Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]\\times10[\/latex]<\/td>\n<td>[latex]\\times10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>kg<\/td>\n<td>hg<\/td>\n<td>dag<\/td>\n<td>g<\/td>\n<td>dg<\/td>\n<td>cg<\/td>\n<td>mg<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\downarrow[\/latex]<\/td>\n<td>[latex]\\uparrow[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">[latex]\\rightarrow[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since you are going from a larger unit to a smaller unit, multiply.<\/p>\n<p><i>Multiply: 1 \u00b7 10 \u00b7 10, to find the number of milligrams in one decigram.\u00a0<\/i><\/p>\n<p style=\"text-align: center;\">[latex]1\\text{ dg}\\cdot10\\cdot10=100\\text{ mg}[\/latex]<\/p>\n<p>There are 100 milligrams (mg) in 1 decigram (dg).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Convert 3,085 milligrams to grams.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q353889\">Show Solution<\/span><\/p>\n<div id=\"q353889\" class=\"hidden-answer\" style=\"display: none\">\n<p>One gram is 1,000 times larger than a milligram, so you can move the decimal point in 3,085 three places to the left.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm1000\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=1000-1001-1005&theme=oea&iframe_resize_id=ohm1000&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert 1 centimeter to kilometers.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q4330\">Show Solution<\/span><\/p>\n<div id=\"q4330\" class=\"hidden-answer\" style=\"display: none\">\n<p>Identify locations of kilometers and centimeters.<\/p>\n<table>\n<tbody>\n<tr>\n<td>km<\/td>\n<td>hm<\/td>\n<td>dam<\/td>\n<td>m<\/td>\n<td>dm<\/td>\n<td>cm<\/td>\n<td>mm<\/td>\n<\/tr>\n<tr>\n<td>^<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>^<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Kilometers (km) are larger than centimeters (cm), so you expect there to be less than one km in a cm.<\/p>\n<p>Cm is 10 times smaller than a dm; a dm is 10 times smaller than a m, etc.<\/p>\n<p>Since you are going from a smaller unit to a larger unit, divide.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]\\div10[\/latex]<\/td>\n<td>[latex]\\div10[\/latex]<\/td>\n<td>[latex]\\div10[\/latex]<\/td>\n<td>[latex]\\div10[\/latex]<\/td>\n<td>[latex]\\div10[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>km<\/td>\n<td>hm<\/td>\n<td>dam<\/td>\n<td>m<\/td>\n<td>dm<\/td>\n<td>cm<\/td>\n<td>mm<\/td>\n<\/tr>\n<tr>\n<td>^<\/td>\n<td>[latex]\\leftarrow[\/latex]<\/td>\n<td>[latex]\\leftarrow[\/latex]<\/td>\n<td>[latex]\\leftarrow[\/latex]<\/td>\n<td>[latex]\\leftarrow[\/latex]<\/td>\n<td>^<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Divide: [latex]1\\div10\\div10\\div10\\div10\\div10[\/latex], to find the number of kilometers in one centimeter.<em>\u00a0<\/em><\/p>\n<p style=\"text-align: center;\">[latex]1\\text{ cm}\\div10\\div10\\div10\\div10\\div10=0.00001\\text{ km}[\/latex]<\/p>\n<p>1 centimeter (cm) = 0.00001 kilometers (km).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm998\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=998&theme=oea&iframe_resize_id=ohm998&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Once you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.<\/p>\n<p>Here is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle kg\\quad hg\\quad dag\\quad g\\quad d\\underbrace{g\\quad c}_{1}\\underbrace{g\\quad m}_{2}g[\/latex]<\/p>\n<p>This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: [latex]\\displaystyle 1\\ dg=1\\underbrace{0}_{1}\\underbrace{0}_{2}.\\ mg[\/latex].<\/p>\n<p>The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle k\\underbrace{m\\quad h}_{5}\\underbrace{m\\quad d}_{4}\\underbrace{am\\quad }_{3}\\underbrace{m\\quad d}_{2}\\underbrace{m\\quad c}_{1}m\\quad mm[\/latex]<\/p>\n<p>Note that instead of moving to the right, you are now moving to the left \u0097so the decimal point must do the same:<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle 1\\ cm=0.\\underbrace{0}_{5}\\underbrace{0}_{4}\\underbrace{0}_{3}\\underbrace{0}_{2}\\underbrace{1}_{1}\\ km[\/latex].<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>How many milliliters are in 1 liter?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q95548\">Show Solution<\/span><\/p>\n<div id=\"q95548\" class=\"hidden-answer\" style=\"display: none\">\n<p>There are 10 milliliters in a centiliter, 10 centiliters in a deciliter, and 10 deciliters in a liter. Multiply: [latex]10\\cdot10\\cdot10[\/latex], to find the number of milliliters in a liter, 1,000.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm999\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=999&theme=oea&iframe_resize_id=ohm999&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Dimensional Analysis<\/h2>\n<p>There is yet another method that you can use to convert metric measurements:\u00a0<b>dimensional analysis<\/b>. You used this method when you were converting measurement units within the U.S. customary system.<\/p>\n<p>Dimensional analysis works the same in the metric system; it relies on the use of unit fractions and the cancelling of intermediate units. The table below shows some of the <b>unit equivalents<\/b> and <b>unit fractions<\/b> for length in the metric system. (You should notice that all of the unit fractions contain a factor of 10. Remember that the metric system is based on the notion that each unit is 10 times larger than the one that came before it.)<\/p>\n<p>Also, notice that two new prefixes have been added here: [latex]M[\/latex] for mega- (which is very big) and [latex]\\mu[\/latex] for micro- (which is very small). The symbol [latex]\\mu[\/latex] is a greek lower-case letter pronounced\u00a0<em>mew<\/em>.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Unit Equivalents<\/b><\/td>\n<td colspan=\"2\"><b>Conversion Factors<\/b><\/td>\n<\/tr>\n<tr>\n<td>1 meter = 1,000,000 micrometers<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ m}{1,000,000\\ \\mu m}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1,000,000\\ \\mu m}{1\\ m}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 meter = 1,000 millimeters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ m}{1,000\\ mm}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1,000\\ mm}{1\\ m}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 meter = 100 centimeters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ m}{100\\ cm}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{100\\ cm}{1\\ m}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 meter = 10 decimeters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ m}{10\\ dm}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{10\\ dm}{1\\ m}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 dekameter = 10 meters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ dam}{10\\ m}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{10\\ m}{1\\ dam}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 hectometer = 100 meters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ hm}{100\\ m}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{100\\ m}{1\\ hm}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 kilometer = 1,000 meters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ km}{1,000\\ m}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1,000\\ m}{1\\ km}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 megameter = 1,000,000 meters<\/td>\n<td>[latex]\\displaystyle \\frac{1\\ Mm}{1,000,000\\ m}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1,000,000\\ m}{1\\ Mm}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When applying dimensional analysis in the metric system, be sure to check that you are not skipping over any intermediate units of measurement!<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert 7,225 centimeters to meters.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q461145\">Show Solution<\/span><\/p>\n<div id=\"q461145\" class=\"hidden-answer\" style=\"display: none\">\n<p>Meters is larger than centimeters, so you expect your answer to be less than 7,225.<\/p>\n<p style=\"text-align: center;\">[latex]7,225\\text{ cm}=\\text{___ m}[\/latex]<\/p>\n<p>Using the factor label method, write 7,225 cm as a fraction and use unit fractions to convert it to m.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{7,225\\ cm}{1}\\cdot \\frac{1\\ m}{100\\ cm}=\\_\\_\\_ m[\/latex]<\/p>\n<p>Cancel similar units, multiply, and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{7,225\\ \\cancel{cm}}{1}\\cdot \\frac{1\\text{ m}}{100\\ \\cancel{\\text{cm}}}=\\_\\_\\_m[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{7,225}{1}\\cdot \\frac{1\\text{ m}}{100}=\\frac{7,225}{100}\\text{m}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{7,225\\text{ m}}{100}=72.25\\text{ m}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]7,225\\text{ centimeters}=72.25\\text{ meters}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Convert 32.5 kilometers to meters.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q574914\">Show Solution<\/span><\/p>\n<div id=\"q574914\" class=\"hidden-answer\" style=\"display: none\">\n<p>32,500 meters<\/p>\n<p>[latex]\\displaystyle \\frac{32.5\\text{ km}}{1}\\cdot \\frac{1,000\\text{ m}}{1\\text{ km}}=\\frac{32,500\\text{ m}}{1}[\/latex].<\/p>\n<p>The km units cancel, leaving the answer in m.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm18877\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=18877&theme=oea&iframe_resize_id=ohm18877&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>If you have a prescription for 5,000 mg of medicine, and upon getting it filled, the dosage reads 5g of medicine, did the pharmacist make a mistake?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q600572\">Show Solution<\/span><\/p>\n<div id=\"q600572\" class=\"hidden-answer\" style=\"display: none\">\n<p>Convert mg to g.<\/p>\n<p style=\"text-align: center;\">[latex]5,000\\text{ mg}=\\text{___ g}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{5,000\\text{ mg}}{1}\\cdot \\frac{1\\text{ g}}{1,000\\text{ mg}}=\\text{ g}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{5,000\\cancel{\\text{mg}}}{1}\\cdot \\frac{1\\text{ g}}{1,000\\ \\cancel{\\text{mg}}}=\\text{ g}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{5,000\\cdot 1\\text{ g}}{1\\cdot 1,000}=\\frac{5,000\\text{ g}}{1,000}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{5,000\\text{ g}}{1,000}=5\\text{ g}[\/latex]<\/p>\n<p>[latex]5\\text{ g}=5,000\\text{ mg}[\/latex], so the pharmacist did not make a mistake.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146841\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146841&theme=oea&iframe_resize_id=ohm146841&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146842\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146842&theme=oea&iframe_resize_id=ohm146842&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Understanding Context and Performing Conversions<\/h2>\n<p>Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.<\/p>\n<div class=\"textbox\"><strong>TIP:<\/strong> To solve these problems effectively, you need to understand the context of a problem, perform conversions, and then check the reasonableness of your answer. Do all three of these steps and you will succeed in whatever measurement system you find yourself using.<\/div>\n<p>The first step in solving any real-world problem is to understand its context. This will help you figure out what kinds of solutions are reasonable (and the problem itself may give you clues about what types of conversions are necessary). Here is an example.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Marcus bought at 2 meter board, and cut off a piece 1 meter and 35 cm long. How much board is left?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q701860\">Show Solution<\/span><\/p>\n<div id=\"q701860\" class=\"hidden-answer\" style=\"display: none\">\n<p>To answer this question, we will need to subtract.<\/p>\n<p>First convert all measurements to one unit. Here we will convert to centimeters.<\/p>\n<p>[latex]2\\text{ meters}-1\\text{ meter and }35\\text{ cm}[\/latex]<\/p>\n<p>Use the factor label method and unit fractions to convert from meters to centimeters.<\/p>\n<p>[latex]\\displaystyle \\frac{2\\text{ m}}{1}\\cdot \\frac{100\\text{ cm}}{1\\text{ m}}=\\text{ cm}[\/latex]<\/p>\n<p>Cancel, multiply, and solve.<\/p>\n<p>Convert the 1 meter to centimeters, and combine with the additional 35 centimeters.<\/p>\n<p>Subtract the cut length from the original board length.<\/p>\n<p>[latex]\\displaystyle \\frac{2\\ \\cancel{\\text{m}}}{1}\\cdot \\frac{100\\text{ cm}}{1\\ \\cancel{\\text{ m}}}=\\text{ cm}[\/latex]<\/p>\n<p>[latex]\\displaystyle \\frac{200\\text{ cm}}{1}=200\\text{ cm}[\/latex]<\/p>\n<p>[latex]1\\text{ meter}+35\\text{ cm}[\/latex]<\/p>\n<p>[latex]100\\text{ cm}+35\\text{ cm}[\/latex]<\/p>\n<p>[latex]135\\text{ cm}[\/latex]<\/p>\n<p>[latex]200\\text{ cm}-135\\text{ cm}[\/latex]<\/p>\n<p>[latex]65\\text{ cm}[\/latex]<\/p>\n<p>There is 65 cm of board left.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>This problem asked for the difference between two quantities. The easiest way to find this is to convert one quantity so that both quantities are measured in the same unit, and then subtract one from the other.<\/p>\n<p>An example with a different context, but still requiring conversions, is shown below.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A faucet drips 10 ml every minute. How much water will be wasted in a week?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q642392\">Show Solution<\/span><\/p>\n<div id=\"q642392\" class=\"hidden-answer\" style=\"display: none\">\n<p>Start by calculating how much water will be used in a week using the factor label method to convert the time units.<\/p>\n<p>[latex]\\displaystyle \\frac{10\\ ml}{1\\text{ minute}}\\cdot \\frac{60\\text{ minute}}{1\\text{ hour}}\\cdot \\frac{24\\text{ hours}}{1\\text{ day}}\\cdot \\frac{7\\text{ days}}{1\\text{ week}}[\/latex]<\/p>\n<p>Cancel, multiply and solve.<\/p>\n<p>[latex]\\displaystyle \\frac{10\\ ml}{1\\text{ }\\cancel{\\text{minute}}}\\cdot \\frac{60\\text{ }\\cancel{\\text{minute}}}{1\\text{ }\\cancel{\\text{hour}}}\\cdot \\frac{24\\text{ }\\cancel{\\text{hours}}}{1\\text{ }\\cancel{\\text{day}}}\\cdot \\frac{7\\text{ }\\cancel{\\text{days}}}{1\\text{ week}}[\/latex]<\/p>\n<p>[latex]\\displaystyle \\frac{10\\centerdot 60\\centerdot 24\\centerdot 7\\ ml}{1\\centerdot 1\\centerdot 1\\centerdot 1\\text{ week}}[\/latex]<\/p>\n<p>To give a more useable answer, convert this into liters.<\/p>\n<p>[latex]\\displaystyle \\frac{100800\\ ml}{1\\text{ week}}[\/latex]<\/p>\n<p>Cancel, multiply and solve.<\/p>\n<p>[latex]\\displaystyle \\frac{100800\\text{ ml}}{1\\text{ week}}\\centerdot \\frac{1\\text{ L}}{1000\\text{ ml}}[\/latex]<\/p>\n<p>[latex]\\displaystyle \\frac{100800\\text{ }\\cancel{\\text{ml}}}{1\\text{ week}}\\centerdot \\frac{1\\text{ L}}{1000\\text{ }\\cancel{\\text{ml}}}[\/latex]<\/p>\n<p>[latex]\\displaystyle \\frac{100800\\text{ L}}{1000\\text{ week}}[\/latex]=[latex]\\displaystyle 100.8\\frac{\\text{L}}{\\text{week}}[\/latex]<\/p>\n<p>The faucet wastes about 100.8 liters each week.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>A bread recipe calls for 600 g of flour. How many kilograms of flour would you need to make 5 loaves?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q838013\">Show Solution<\/span><\/p>\n<div id=\"q838013\" class=\"hidden-answer\" style=\"display: none\">\n<p>Multiplying 600 g per loaf by the 5 loaves,<\/p>\n<p>[latex]600\\text{g}\\cdot5=3000\\text{g}[\/latex]<\/p>\n<p>Using factor labels or the <em>move the decimal<\/em>\u00a0method, convert this to 3 kilograms.<\/p>\n<p>You will need 3 kg of flour to make 5 loaves.<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"ohm1002\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=1002-117516&theme=oea&iframe_resize_id=ohm1002&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2><\/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-110\">\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>Question ID 126793, 126794. 126795. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Question ID 998, 999, 1000, 1001, 1005, 18877. <strong>Authored by<\/strong>: David Lippman. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/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":503070,"menu_order":18,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Question ID 126793, 126794. 126795\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID 998, 999, 1000, 1001, 1005, 18877\",\"author\":\"David 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