{"id":11031,"date":"2017-06-06T17:06:58","date_gmt":"2017-06-06T17:06:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=11031"},"modified":"2019-05-24T17:06:29","modified_gmt":"2019-05-24T17:06:29","slug":"making-unit-conversions-in-the-metric-system-of-measurement","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/making-unit-conversions-in-the-metric-system-of-measurement\/","title":{"raw":"Making Unit Conversions in the Metric System of Measurement","rendered":"Making Unit Conversions in the Metric System of Measurement"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert between Metric units of length, volume, and mass<\/li>\r\n \t<li>Use mixed units of measurement in the metric system<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3 data-type=\"title\">Make Unit Conversions in the Metric System<\/h3>\r\nIn the metric system, units are related by powers of [latex]10[\/latex]. The root words of their names reflect this relation. For example, the basic unit for measuring length is a meter. One kilometer is [latex]1000[\/latex] meters; the prefix <em data-effect=\"italics\">kilo-<\/em> means thousand. One centimeter is [latex]\\Large\\frac{1}{100}[\/latex] of a meter, because the prefix <em data-effect=\"italics\">centi-<\/em> means one one-hundredth (just like one cent is [latex]\\Large\\frac{1}{100}[\/latex] of one dollar).\r\n\r\nThe equivalencies of measurements in the metric system are shown in the reference table below. The common abbreviations for each measurement are given in parentheses.\r\n<table id=\"fs-id1448508\" summary=\"The table is labeled in the first row as \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"3\" data-align=\"center\">Metric Measurements<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\">Length<\/th>\r\n<th data-align=\"left\">Mass<\/th>\r\n<th data-align=\"left\">Volume\/Capacity<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]1[\/latex] kilometer (km) = [latex]1000[\/latex] m\r\n\r\n[latex]1[\/latex] hectometer (hm) = [latex]100[\/latex] m\r\n\r\n[latex]1[\/latex] dekameter (dam) = [latex]10[\/latex] m\r\n\r\n[latex]1[\/latex] meter (m) = [latex]1[\/latex] m\r\n\r\n[latex]1[\/latex] decimeter (dm) = [latex]0.1[\/latex] m\r\n\r\n[latex]1[\/latex] centimeter (cm) = [latex]0.01[\/latex] m\r\n\r\n[latex]1[\/latex] millimeter (mm) = [latex]0.001[\/latex] m<\/td>\r\n<td data-align=\"left\">[latex]1[\/latex] kilogram (kg) = [latex]1000[\/latex] g\r\n\r\n[latex]1[\/latex] hectogram (hg) = [latex]100[\/latex] g\r\n\r\n[latex]1[\/latex] dekagram (dag) = [latex]10[\/latex] g\r\n\r\n[latex]1[\/latex] gram (g) = [latex]1[\/latex] g\r\n\r\n[latex]1[\/latex] decigram (dg) = [latex]0.1[\/latex] g\r\n\r\n[latex]1[\/latex] centigram (cg) = [latex]0.01[\/latex] g\r\n\r\n[latex]1[\/latex] milligram (mg) = [latex]0.001[\/latex] g<\/td>\r\n<td data-align=\"left\">[latex]1[\/latex] kiloliter (kL) = [latex]1000[\/latex] L\r\n\r\n[latex]1[\/latex] hectoliter (hL) = [latex]100[\/latex] L\r\n\r\n[latex]1[\/latex] dekaliter (daL) = [latex]10[\/latex] L\r\n\r\n[latex]1[\/latex] liter (L) = [latex]1[\/latex] L\r\n\r\n[latex]1[\/latex] deciliter (dL) = [latex]0.1[\/latex] L\r\n\r\n[latex]1[\/latex] centiliter (cL) = [latex]0.01[\/latex] L\r\n\r\n[latex]1[\/latex] milliliter (mL) = [latex]0.001[\/latex] L<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]1[\/latex] meter = [latex]100[\/latex] centimeters\r\n\r\n[latex]1[\/latex] meter = [latex]1000[\/latex] millimeters<\/td>\r\n<td data-align=\"left\">[latex]1[\/latex] gram = [latex]100[\/latex] centigrams\r\n\r\n[latex]1[\/latex] gram = [latex]1000[\/latex] milligrams<\/td>\r\n<td data-align=\"left\">[latex]1[\/latex] liter = [latex]100[\/latex] centiliters\r\n\r\n[latex]1[\/latex] liter = [latex]1000[\/latex] milliliters<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTo make conversions in the metric system, we will use the same technique we did in the U.S. system. Using the identity property of multiplication, we will multiply by a conversion factor of one to get to the correct units.\r\n\r\nHave you ever run a [latex]\\text{5 k}[\/latex] or [latex]\\text{10 k}[\/latex] race? The lengths of those races are measured in kilometers. The metric system is commonly used in the United States when talking about the length of a race.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nNick ran a [latex]\\text{10-kilometer}[\/latex] race. How many meters did he run?\r\n\r\n(credit: William Warby, Flickr)\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222500\/CNX_BMath_Figure_07_05_010.png\" alt=\"A photograph of 8 male runners in a track race.\" data-media-type=\"image\/png\" \/>\r\n\r\nSolution\r\nWe will convert kilometers to meters using the Identity Property of Multiplication and the equivalencies in the reference table from earlier.\r\n<table id=\"eip-id1168468595505\" class=\"unnumbered unstyled\" summary=\"Write the expression 10 kilometers times 1. Write 1 as a fraction relating kilometers and meters. The fraction will be 1000 meters over 1 kilometer. The expression becomes 10 kilometers times 1000 meters over 1 kilometer. Cancel the common units of kilometers. Multiply to get 10 times 1000 meters all over 1. Perform the multiplication to get 10,000 meters over 1 which simplifies to 10,000 meters.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]10[\/latex] kilometers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\r\n<td>[latex]10 \\color{red}{km}\\cdot 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]1[\/latex] as a fraction relating kilometers and meters.<\/td>\r\n<td>[latex]10 \\color{red}{km}\\cdot\\Large\\frac{1000 m}{1\\color{red}{km}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{10\\color{red}{km}\\cdot 1000 m}{1\\color{red}{km}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]10,000[\/latex] m<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Nick ran [latex]10,000[\/latex] meters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\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&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEleanor\u2019s newborn baby weighed [latex]3200[\/latex] grams. How many kilograms did the baby weigh?\r\n[reveal-answer q=\"690003\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"690003\"]\r\n\r\nSolution\r\nWe will convert grams to kilograms.\r\n<table id=\"eip-id1168468398524\" class=\"unnumbered unstyled\" summary=\"Write the expression 3200 grams times 1. Write 1 as a fraction relating kilograms and grams. The fraction will be 1 kilogram over 1000 grams. The expression becomes 3200 grams times 1 kilogram over 1000 grams. Cancel the common units of grams. Multiply to get 3200 times 1 kilograms all over 1000. Perform the multiplication to get 3200 kilograms over 1000 which simplifies to 3.2 kilograms.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3200 \\color{red}{grams}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\r\n<td>[latex]3200 \\color{red}{g}\\cdot 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]1[\/latex] as a fraction relating kilograms and grams.<\/td>\r\n<td>[latex]3200 \\color{red}{g}\\cdot\\Large\\frac{1 kg}{1000 \\color{red}{g}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]3200 \\color{red}{g}\\cdot\\Large\\frac{1 kg}{1000 \\color{red}{g}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{3200 kilograms}{1000}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td data-align=\"center\">[latex]3.2[\/latex] kilograms<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">The baby weighed [latex]3.2[\/latex] kilograms.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146844[\/ohm_question]\r\n\r\n[ohm_question]146845[\/ohm_question]\r\n\r\n<\/div>\r\nSince the metric system is based on multiples of ten, conversions involve multiplying by multiples of ten. In Decimal Operations, we learned how to simplify these calculations by just moving the decimal.\r\n\r\nTo multiply by [latex]10,100,\\text{or}1000[\/latex], we move the decimal to the right [latex]1,2,\\text{or}3[\/latex] places, respectively. To multiply by [latex]0.1,0.01,\\text{or}0.001[\/latex] we move the decimal to the left [latex]1,2,\\text{or}3[\/latex] places respectively.\r\n\r\nWe can apply this pattern when we make measurement conversions in the metric system.\r\n\r\nIn the previous example, we changed [latex]3200[\/latex] grams to kilograms by multiplying by [latex]\\Large\\frac{1}{1000}\\normalsize\\left(\\text{or}0.001\\right)[\/latex]. This is the same as moving the decimal [latex]3[\/latex] places to the left.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222509\/CNX_BMath_Figure_07_05_015_img.png\" alt=\"Multiplying 3200 by 1 over 1000 gives 3.2. Notice that the answer, 3.2, is similar to the original value, 3200, just with the decimal moved three places to the left.\" data-media-type=\"image\/png\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nConvert: 1. [latex]350[\/latex] liters to kiloliters 2. [latex]4.1[\/latex] liters to milliliters.\r\n[reveal-answer q=\"633374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"633374\"]\r\n\r\nSolution\r\n1. We will convert liters to kiloliters. In the reference table, we see that [latex]\\text{1 kiloliter}=\\text{1000 liters}[\/latex].\r\n<table id=\"eip-id1168466338427\" class=\"unnumbered unstyled\" summary=\"Beginning with 350 liters, multiply by 1 writing 1 as a fraction that relates liters to kiloliters. The fraction will be 1 kiloliter over 1000 liters. The expression becomes 350 liters times 1 kiloliter over 1000 liters. Cancel the common units of liters. Multiplying by 1 over 1000 is the same as just moving the decimal 3 units to the left. Taking 350 and moving the decimal 3 places to the left gives 0.35. The answer is 0.35 kiloliters.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]350[\/latex] L<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply by [latex]1[\/latex], writing [latex]1[\/latex] as a fraction relating liters to kiloliters.<\/td>\r\n<td>[latex]350 L \\cdot\\Large\\frac{1 kl}{1000 L}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]350 \\color{blue}{L} \\cdot\\Large\\frac{1 kl}{1000 \\color{blue}{L}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Move the decimal [latex]3[\/latex] units to the left.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222512\/CNX_BMath_Figure_07_05_026_img-03.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0.35[\/latex] kL<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. We will convert liters to milliliters. In the reference table, we see that [latex]\\text{1 liter}=1000\\text{milliliters.}[\/latex]\r\n<table id=\"eip-id1168467184678\" class=\"unnumbered unstyled\" summary=\"Beginning with 4.1 liters, multiply by 1 writing 1 as a fraction that relates liters to milliliters. The fraction will be 1000 milliliters over 1 liter. The expression becomes 4.1 liters times 1000 milliliter over 1 liter. Cancel the common units of liters. Multiplying by 1000 is the same as just moving the decimal 3 units to the right. Taking 4.1 and moving the decimal 3 places to the right gives 4100. The answer is 4100 milliliters.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4.1[\/latex] L<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply by [latex]1[\/latex], writing [latex]1[\/latex] as a fraction relating milliliters to liters.<\/td>\r\n<td>[latex]4.1 L \\cdot\\Large\\frac{1000 ml}{1 L}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]4.1 L \\color{blue}{L} \\cdot\\Large\\frac{1000 ml}{1 \\color{blue}{L}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Move the decimal [latex]3[\/latex] units to the right.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222515\/CNX_BMath_Figure_07_05_027_img-03.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4100[\/latex] mL<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146868[\/ohm_question]\r\n\r\n[ohm_question]146869[\/ohm_question]\r\n\r\n[ohm_question]146870[\/ohm_question]\r\n\r\n[ohm_question]146871[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Use Mixed Units of Measurement in the Metric System<\/h3>\r\nPerforming arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. But it may be easier because of the relation of the units to the powers of [latex]10[\/latex]. We still must make sure to add or subtract like units.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRyland is [latex]1.6[\/latex] meters tall. His younger brother is [latex]85[\/latex] centimeters tall. How much taller is Ryland than his younger brother?\r\n[reveal-answer q=\"935546\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"935546\"]\r\n\r\nSolution\r\nWe will subtract the lengths in meters. Convert [latex]85[\/latex] centimeters to meters by moving the decimal [latex]2[\/latex] places to the left; [latex]85[\/latex] cm is the same as [latex]0.85[\/latex] m.\r\nNow that both measurements are in meters, subtract to find out how much taller Ryland is than his brother.\r\n\r\n[latex]\\begin{array}{}\\\\ \\\\ \\hfill \\text{1.60 m}\\\\ \\hfill \\underset{\\text{_______}}{\\text{-0.85 m}}\\\\ \\hfill \\text{0.75 m}\\end{array}[\/latex]\r\nRyland is [latex]0.75[\/latex] meters taller than his brother.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146872[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDena\u2019s recipe for lentil soup calls for [latex]150[\/latex] milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?\r\n[reveal-answer q=\"972412\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"972412\"]\r\n\r\nSolution\r\nWe will find the amount of olive oil in milliliters then convert to liters.\r\n<table id=\"eip-id1168463790852\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Triple [latex]150[\/latex] mL<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to algebra.<\/td>\r\n<td>[latex]3\\cdot 150\\text{mL}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]450\\text{mL}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to liters.<\/td>\r\n<td>[latex]450\\text{mL}\\cdot\\Large\\frac{0.001\\text{L}}{1\\text{mL}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]0.45\\text{L}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Dena needs [latex]0.45[\/latex] liter of olive oil.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146873[\/ohm_question]\r\n\r\n[ohm_question]146874[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert between Metric units of length, volume, and mass<\/li>\n<li>Use mixed units of measurement in the metric system<\/li>\n<\/ul>\n<\/div>\n<h3 data-type=\"title\">Make Unit Conversions in the Metric System<\/h3>\n<p>In the metric system, units are related by powers of [latex]10[\/latex]. The root words of their names reflect this relation. For example, the basic unit for measuring length is a meter. One kilometer is [latex]1000[\/latex] meters; the prefix <em data-effect=\"italics\">kilo-<\/em> means thousand. One centimeter is [latex]\\Large\\frac{1}{100}[\/latex] of a meter, because the prefix <em data-effect=\"italics\">centi-<\/em> means one one-hundredth (just like one cent is [latex]\\Large\\frac{1}{100}[\/latex] of one dollar).<\/p>\n<p>The equivalencies of measurements in the metric system are shown in the reference table below. The common abbreviations for each measurement are given in parentheses.<\/p>\n<table id=\"fs-id1448508\" summary=\"The table is labeled in the first row as\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"3\" data-align=\"center\">Metric Measurements<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th data-align=\"left\">Length<\/th>\n<th data-align=\"left\">Mass<\/th>\n<th data-align=\"left\">Volume\/Capacity<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]1[\/latex] kilometer (km) = [latex]1000[\/latex] m<\/p>\n<p>[latex]1[\/latex] hectometer (hm) = [latex]100[\/latex] m<\/p>\n<p>[latex]1[\/latex] dekameter (dam) = [latex]10[\/latex] m<\/p>\n<p>[latex]1[\/latex] meter (m) = [latex]1[\/latex] m<\/p>\n<p>[latex]1[\/latex] decimeter (dm) = [latex]0.1[\/latex] m<\/p>\n<p>[latex]1[\/latex] centimeter (cm) = [latex]0.01[\/latex] m<\/p>\n<p>[latex]1[\/latex] millimeter (mm) = [latex]0.001[\/latex] m<\/td>\n<td data-align=\"left\">[latex]1[\/latex] kilogram (kg) = [latex]1000[\/latex] g<\/p>\n<p>[latex]1[\/latex] hectogram (hg) = [latex]100[\/latex] g<\/p>\n<p>[latex]1[\/latex] dekagram (dag) = [latex]10[\/latex] g<\/p>\n<p>[latex]1[\/latex] gram (g) = [latex]1[\/latex] g<\/p>\n<p>[latex]1[\/latex] decigram (dg) = [latex]0.1[\/latex] g<\/p>\n<p>[latex]1[\/latex] centigram (cg) = [latex]0.01[\/latex] g<\/p>\n<p>[latex]1[\/latex] milligram (mg) = [latex]0.001[\/latex] g<\/td>\n<td data-align=\"left\">[latex]1[\/latex] kiloliter (kL) = [latex]1000[\/latex] L<\/p>\n<p>[latex]1[\/latex] hectoliter (hL) = [latex]100[\/latex] L<\/p>\n<p>[latex]1[\/latex] dekaliter (daL) = [latex]10[\/latex] L<\/p>\n<p>[latex]1[\/latex] liter (L) = [latex]1[\/latex] L<\/p>\n<p>[latex]1[\/latex] deciliter (dL) = [latex]0.1[\/latex] L<\/p>\n<p>[latex]1[\/latex] centiliter (cL) = [latex]0.01[\/latex] L<\/p>\n<p>[latex]1[\/latex] milliliter (mL) = [latex]0.001[\/latex] L<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]1[\/latex] meter = [latex]100[\/latex] centimeters<\/p>\n<p>[latex]1[\/latex] meter = [latex]1000[\/latex] millimeters<\/td>\n<td data-align=\"left\">[latex]1[\/latex] gram = [latex]100[\/latex] centigrams<\/p>\n<p>[latex]1[\/latex] gram = [latex]1000[\/latex] milligrams<\/td>\n<td data-align=\"left\">[latex]1[\/latex] liter = [latex]100[\/latex] centiliters<\/p>\n<p>[latex]1[\/latex] liter = [latex]1000[\/latex] milliliters<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>To make conversions in the metric system, we will use the same technique we did in the U.S. system. Using the identity property of multiplication, we will multiply by a conversion factor of one to get to the correct units.<\/p>\n<p>Have you ever run a [latex]\\text{5 k}[\/latex] or [latex]\\text{10 k}[\/latex] race? The lengths of those races are measured in kilometers. The metric system is commonly used in the United States when talking about the length of a race.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Nick ran a [latex]\\text{10-kilometer}[\/latex] race. How many meters did he run?<\/p>\n<p>(credit: William Warby, Flickr)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222500\/CNX_BMath_Figure_07_05_010.png\" alt=\"A photograph of 8 male runners in a track race.\" data-media-type=\"image\/png\" \/><\/p>\n<p>Solution<br \/>\nWe will convert kilometers to meters using the Identity Property of Multiplication and the equivalencies in the reference table from earlier.<\/p>\n<table id=\"eip-id1168468595505\" class=\"unnumbered unstyled\" summary=\"Write the expression 10 kilometers times 1. Write 1 as a fraction relating kilometers and meters. The fraction will be 1000 meters over 1 kilometer. The expression becomes 10 kilometers times 1000 meters over 1 kilometer. Cancel the common units of kilometers. Multiply to get 10 times 1000 meters all over 1. Perform the multiplication to get 10,000 meters over 1 which simplifies to 10,000 meters.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]10[\/latex] kilometers<\/td>\n<\/tr>\n<tr>\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\n<td>[latex]10 \\color{red}{km}\\cdot 1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write [latex]1[\/latex] as a fraction relating kilometers and meters.<\/td>\n<td>[latex]10 \\color{red}{km}\\cdot\\Large\\frac{1000 m}{1\\color{red}{km}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{10\\color{red}{km}\\cdot 1000 m}{1\\color{red}{km}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]10,000[\/latex] m<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Nick ran [latex]10,000[\/latex] meters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\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<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Eleanor\u2019s newborn baby weighed [latex]3200[\/latex] grams. How many kilograms did the baby weigh?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q690003\">Show Solution<\/span><\/p>\n<div id=\"q690003\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will convert grams to kilograms.<\/p>\n<table id=\"eip-id1168468398524\" class=\"unnumbered unstyled\" summary=\"Write the expression 3200 grams times 1. Write 1 as a fraction relating kilograms and grams. The fraction will be 1 kilogram over 1000 grams. The expression becomes 3200 grams times 1 kilogram over 1000 grams. Cancel the common units of grams. Multiply to get 3200 times 1 kilograms all over 1000. Perform the multiplication to get 3200 kilograms over 1000 which simplifies to 3.2 kilograms.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3200 \\color{red}{grams}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\n<td>[latex]3200 \\color{red}{g}\\cdot 1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write [latex]1[\/latex] as a fraction relating kilograms and grams.<\/td>\n<td>[latex]3200 \\color{red}{g}\\cdot\\Large\\frac{1 kg}{1000 \\color{red}{g}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]3200 \\color{red}{g}\\cdot\\Large\\frac{1 kg}{1000 \\color{red}{g}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{3200 kilograms}{1000}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td data-align=\"center\">[latex]3.2[\/latex] kilograms<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td data-align=\"center\">The baby weighed [latex]3.2[\/latex] kilograms.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146844\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146844&theme=oea&iframe_resize_id=ohm146844&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146845\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146845&theme=oea&iframe_resize_id=ohm146845&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Since the metric system is based on multiples of ten, conversions involve multiplying by multiples of ten. In Decimal Operations, we learned how to simplify these calculations by just moving the decimal.<\/p>\n<p>To multiply by [latex]10,100,\\text{or}1000[\/latex], we move the decimal to the right [latex]1,2,\\text{or}3[\/latex] places, respectively. To multiply by [latex]0.1,0.01,\\text{or}0.001[\/latex] we move the decimal to the left [latex]1,2,\\text{or}3[\/latex] places respectively.<\/p>\n<p>We can apply this pattern when we make measurement conversions in the metric system.<\/p>\n<p>In the previous example, we changed [latex]3200[\/latex] grams to kilograms by multiplying by [latex]\\Large\\frac{1}{1000}\\normalsize\\left(\\text{or}0.001\\right)[\/latex]. This is the same as moving the decimal [latex]3[\/latex] places to the left.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222509\/CNX_BMath_Figure_07_05_015_img.png\" alt=\"Multiplying 3200 by 1 over 1000 gives 3.2. Notice that the answer, 3.2, is similar to the original value, 3200, just with the decimal moved three places to the left.\" data-media-type=\"image\/png\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Convert: 1. [latex]350[\/latex] liters to kiloliters 2. [latex]4.1[\/latex] liters to milliliters.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q633374\">Show Solution<\/span><\/p>\n<div id=\"q633374\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n1. We will convert liters to kiloliters. In the reference table, we see that [latex]\\text{1 kiloliter}=\\text{1000 liters}[\/latex].<\/p>\n<table id=\"eip-id1168466338427\" class=\"unnumbered unstyled\" summary=\"Beginning with 350 liters, multiply by 1 writing 1 as a fraction that relates liters to kiloliters. The fraction will be 1 kiloliter over 1000 liters. The expression becomes 350 liters times 1 kiloliter over 1000 liters. Cancel the common units of liters. Multiplying by 1 over 1000 is the same as just moving the decimal 3 units to the left. Taking 350 and moving the decimal 3 places to the left gives 0.35. The answer is 0.35 kiloliters.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]350[\/latex] L<\/td>\n<\/tr>\n<tr>\n<td>Multiply by [latex]1[\/latex], writing [latex]1[\/latex] as a fraction relating liters to kiloliters.<\/td>\n<td>[latex]350 L \\cdot\\Large\\frac{1 kl}{1000 L}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]350 \\color{blue}{L} \\cdot\\Large\\frac{1 kl}{1000 \\color{blue}{L}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Move the decimal [latex]3[\/latex] units to the left.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222512\/CNX_BMath_Figure_07_05_026_img-03.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0.35[\/latex] kL<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. We will convert liters to milliliters. In the reference table, we see that [latex]\\text{1 liter}=1000\\text{milliliters.}[\/latex]<\/p>\n<table id=\"eip-id1168467184678\" class=\"unnumbered unstyled\" summary=\"Beginning with 4.1 liters, multiply by 1 writing 1 as a fraction that relates liters to milliliters. The fraction will be 1000 milliliters over 1 liter. The expression becomes 4.1 liters times 1000 milliliter over 1 liter. Cancel the common units of liters. Multiplying by 1000 is the same as just moving the decimal 3 units to the right. Taking 4.1 and moving the decimal 3 places to the right gives 4100. The answer is 4100 milliliters.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4.1[\/latex] L<\/td>\n<\/tr>\n<tr>\n<td>Multiply by [latex]1[\/latex], writing [latex]1[\/latex] as a fraction relating milliliters to liters.<\/td>\n<td>[latex]4.1 L \\cdot\\Large\\frac{1000 ml}{1 L}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]4.1 L \\color{blue}{L} \\cdot\\Large\\frac{1000 ml}{1 \\color{blue}{L}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Move the decimal [latex]3[\/latex] units to the right.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222515\/CNX_BMath_Figure_07_05_027_img-03.png\" alt=\".\" data-media-type=\"image\/png\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]4100[\/latex] mL<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146868\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146868&theme=oea&iframe_resize_id=ohm146868&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146869\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146869&theme=oea&iframe_resize_id=ohm146869&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146870\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146870&theme=oea&iframe_resize_id=ohm146870&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146871\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146871&theme=oea&iframe_resize_id=ohm146871&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Use Mixed Units of Measurement in the Metric System<\/h3>\n<p>Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. But it may be easier because of the relation of the units to the powers of [latex]10[\/latex]. We still must make sure to add or subtract like units.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Ryland is [latex]1.6[\/latex] meters tall. His younger brother is [latex]85[\/latex] centimeters tall. How much taller is Ryland than his younger brother?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q935546\">Show Solution<\/span><\/p>\n<div id=\"q935546\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will subtract the lengths in meters. Convert [latex]85[\/latex] centimeters to meters by moving the decimal [latex]2[\/latex] places to the left; [latex]85[\/latex] cm is the same as [latex]0.85[\/latex] m.<br \/>\nNow that both measurements are in meters, subtract to find out how much taller Ryland is than his brother.<\/p>\n<p>[latex]\\begin{array}{}\\\\ \\\\ \\hfill \\text{1.60 m}\\\\ \\hfill \\underset{\\text{_______}}{\\text{-0.85 m}}\\\\ \\hfill \\text{0.75 m}\\end{array}[\/latex]<br \/>\nRyland is [latex]0.75[\/latex] meters taller than his brother.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146872\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146872&theme=oea&iframe_resize_id=ohm146872&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Dena\u2019s recipe for lentil soup calls for [latex]150[\/latex] milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q972412\">Show Solution<\/span><\/p>\n<div id=\"q972412\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will find the amount of olive oil in milliliters then convert to liters.<\/p>\n<table id=\"eip-id1168463790852\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td>Triple [latex]150[\/latex] mL<\/td>\n<\/tr>\n<tr>\n<td>Translate to algebra.<\/td>\n<td>[latex]3\\cdot 150\\text{mL}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]450\\text{mL}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to liters.<\/td>\n<td>[latex]450\\text{mL}\\cdot\\Large\\frac{0.001\\text{L}}{1\\text{mL}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.45\\text{L}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Dena needs [latex]0.45[\/latex] liter of olive oil.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146873\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146873&theme=oea&iframe_resize_id=ohm146873&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146874\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146874&theme=oea&iframe_resize_id=ohm146874&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-11031\">\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 146874, 146873, 146872, 146871, 146870, 146869, 146868. <strong>Authored 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, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":21229,"menu_order":25,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146874, 146873, 146872, 146871, 146870, 146869, 146868\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"a72faeb9-1646-4f92-b0d0-876f01dbe9aa","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-11031","chapter","type-chapter","status-publish","hentry"],"part":7831,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/11031","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/21229"}],"version-history":[{"count":18,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/11031\/revisions"}],"predecessor-version":[{"id":15798,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/11031\/revisions\/15798"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/7831"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/11031\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=11031"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=11031"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=11031"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=11031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}