{"id":570,"date":"2016-11-30T20:35:40","date_gmt":"2016-11-30T20:35:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=570"},"modified":"2019-05-30T16:30:06","modified_gmt":"2019-05-30T16:30:06","slug":"units-of-length","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/units-of-length\/","title":{"raw":"Units of Length","rendered":"Units of Length"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>LEARNING outcomes<\/h3>\r\n<div>\r\n<ul>\r\n \t<li>Define units of length and convert from one to another.<\/li>\r\n \t<li>Perform arithmetic calculations on units of length.<\/li>\r\n \t<li>Solve application problems involving units of length.<\/li>\r\n \t<li>Define units of weight and convert from one to another.<\/li>\r\n \t<li>Perform arithmetic calculations on units of weight.<\/li>\r\n \t<li>Solve application problems involving units of weight.<\/li>\r\n \t<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume.<\/li>\r\n \t<li>Define the metric prefixes and use them to perform basic conversions among metric units.<\/li>\r\n \t<li>Solve application problems involving metric units of length, mass, and volume.<\/li>\r\n \t<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\r\n \t<li>Convert from one temperature scale to the other, using conversion formulas.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280.jpg\"><img class=\"aligncenter wp-image-942\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280-1024x1024.jpg\" alt=\"coiled measuring tape spiraling against a red background\" width=\"600\" height=\"600\" \/><\/a>\r\n\r\nSuppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>$1.88 for 2 feet<\/i> of tubing and <i>$5.49 for 3 yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? You need to know about two <b>units of measurement<\/b>, yards and feet, in order to determine the answer.\r\n\r\n<b>Length<\/b> is the distance from one end of an object to the other end, or from one object to another. For example, the length of a letter-sized piece of paper is 11 inches. The system for measuring length in the United States is based on the four customary units of length: <b>inch<\/b>, <b>foot<\/b>, <b>yard<\/b>, and <b>mile<\/b>. Below are examples to show measurement in each of these units.\r\n<table border=\"1\" width=\"613\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Unit<\/b><\/td>\r\n<td><b>Description<\/b><\/td>\r\n<td><b>Image<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Inch\/Inches<\/td>\r\n<td>Some people donate their hair to be made into wigs for cancer patients who have lost hair as a result of treatment. One company requires hair donations to be at least 8 inches long.<\/td>\r\n<td><img id=\"Picture 1\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200906\/image049.jpg\" alt=\"A hand holding long cut-off hair\" width=\"64\" height=\"132\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Frame size of a bike: the distance from the center of the crank to the top of the seat tube. Frame size is usually measured in inches. This frame is 16 inches.<\/td>\r\n<td><img id=\"Picture 2\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200907\/image050.jpg\" alt=\"A black bicycle labeled with frame size and standover height\" width=\"264\" height=\"157\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Foot\/Feet<\/td>\r\n<td>Rugs are typically sold in standard lengths. One typical size is a rug that is 8 feet wide and 11 feet long. This is often described as an 8 by 11 rug.<\/td>\r\n<td><img id=\"Picture 3\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200909\/image051.jpg\" alt=\"A red and gold rug\" width=\"116\" height=\"174\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yard\/Yards<\/td>\r\n<td>Soccer fields vary some in their size. An official field can be any length between 100 and 130 yards.<\/td>\r\n<td><img id=\"Picture 4\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200910\/image052.gif\" alt=\"A cartoon depiction of a soccer field.\" width=\"255\" height=\"153\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mile\/Miles<\/td>\r\n<td>A marathon is 26.2 miles long. One marathon route is shown in the map to the right.<\/td>\r\n<td><img id=\"Picture 5\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200911\/image053.jpg\" alt=\"A marathon route.\" width=\"192\" height=\"323\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou can use any of these four U.S. customary measurement units to describe the length of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the length of a rug in feet rather than miles, and to describe a marathon in miles rather than inches.\r\n\r\nYou may need to convert between units of measurement. For example, you might want to express your height using feet and inches (5 feet 4 inches) or using only inches (64 inches). You need to know the unit equivalents in order to make these conversions between units.\r\n\r\nThe table below shows equivalents and conversion factors for the four customary units of measurement of length.\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><b>Conversion Factors <\/b>\r\n\r\n<b>(longer to shorter units of measurement)<\/b><\/td>\r\n<td><b>Conversion Factors<\/b>\r\n\r\n<b>(shorter to longer units of measurement)<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 foot = 12 inches<\/td>\r\n<td>[latex] \\displaystyle \\frac{12\\ \\text{inches}}{1\\ \\text{foot}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\text{ foot}}{12\\text{ inches}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 yard = 3 feet<\/td>\r\n<td>[latex] \\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 mile = 5,280 feet<\/td>\r\n<td>[latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{\\text{1 mile}}{\\text{5,280 feet}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNote that each of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all since it is the same as multiplying by 1; it just changes the units that you are using to measure.\r\n<h2>Convert Between Different Units of Length<\/h2>\r\nYou can use the conversion factors to convert a measurement, such as feet, to another type of measurement, such as inches.\r\n\r\nNote that there are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor [latex] \\displaystyle \\frac{\\text{12 inches}}{\\text{1 foot}}[\/latex].\r\n\r\nIf a length is measured in feet, and you\u0092d like to convert the length to yards, you can think, \u0093I am converting from a shorter unit to a longer one, so the length in yards will be less than the length in feet.\u0094 You could use the conversion factor [latex] \\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex].\r\n\r\nIf a distance is measured in miles, and you want to know how many feet it is, you can think, \u0093I am converting from a longer unit of measurement to a shorter one, so the number of feet would be greater than the number of miles.\u0094 You could use the conversion factor [latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].\r\n\r\nYou can use the <b>factor<\/b> <b>label<\/b> <b>method<\/b> (also known as <b>dimensional analysis<\/b>) to convert a length from one unit of measure to another using the conversion factors. In the factor label method, you multiply by unit fractions to convert a measurement from one unit to another. Study the example below to see how the factor label method can be used to convert [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet into an equivalent number of inches.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many inches are in [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet?\r\n[reveal-answer q=\"284681\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"284681\"]\r\n\r\nBegin by reasoning about your answer. Since a foot is longer than an inch, this means the answer would be greater than [latex] \\displaystyle 3\\frac{1}{2}[\/latex].\r\n\r\nFind the conversion factor that compares inches and feet, with \u0093inches\u0094 in the numerator, and multiply.\r\n<p style=\"text-align: center;\">[latex]3\\frac{1}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\r\nRewrite the mixed number as an improper fraction before multiplying.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\r\nYou can cancel similar units when they appear in the numerator <i>and<\/i> the denominator. So here, cancel the similar units \u0093feet\u0094 and \u0093foot.\u0094 This eliminates this unit from the problem.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\r\nRewrite as multiplication of numerators and denominators.\r\n<p style=\"text-align: center;\">[latex]\\frac{7\\cdot12\\text{ inches}}{2}=\\frac{84\\text{ inches}}{2}=42\\text{ inches}[\/latex]<\/p>\r\nThere are 42 inches in [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that by using the factor label method you can cancel the units out of the problem, just as if they were numbers. You can only cancel if the unit being cancelled is in both the numerator and denominator of the fractions you are multiplying.\r\n\r\nIn the problem above, you cancelled <i>feet<\/i> and <i>foot<\/i> leaving you with <i>inches<\/i>, which is what you were trying to find.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\r\nWhat if you had used the wrong conversion factor?\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{1\\text{foor}}{12\\text{ inches}}=\\text{? inches}[\/latex]?<\/p>\r\nYou could not cancel the feet because the unit is not the same in <i>both <\/i>the numerator and the denominator. So if you complete the computation, you would still have both feet and inches in the answer and no conversion would take place.\r\n\r\nHere is another example of a length conversion using the factor label method.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many yards is 7 feet?\r\n[reveal-answer q=\"571283\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"571283\"]\r\n\r\nStart by reasoning about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. So your answer will be less than 7.\r\n\r\nFind the conversion factor that compares feet and yards, with yards in the numerator.\r\n<p style=\"text-align: center;\">[latex]7\\text{ feet}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\r\nCancel the similar units \u0093feet\u0094 and \u0093feet\u0094 leaving only yards.\r\n<p style=\"text-align: center;\">[latex]7\\cancel{\\text{ feet}}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=\\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]7\\cdot\\frac{1\\text{ yard}}{3}=\\text{? yards}[\/latex]<\/p>\r\n7 feet equals [latex] \\displaystyle 2\\frac{1}{3}[\/latex] yards.\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<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=117507&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=986&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom10\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=992&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=993&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<h2>Apply Unit Conversions With Length<\/h2>\r\nThere are times when you will need to perform computations on measurements that are given in different units. For example, consider the tubing problem given earlier. You must decide which of the two options is a better price, and you have to compare prices given in different unit measurements.\r\n\r\nIn order to compare, you need to convert the measurements into one single, common unit of measurement. To be sure you have made the computation accurately, think about whether the unit you are converting to is smaller or larger than the number you have. Its relative size will tell you whether the number you are trying to find is greater or lesser than the given number.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAn interior decorator needs border trim for a home she is wallpapering. She needs 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room. How many yards of border trim does she need?\r\n\r\n[reveal-answer q=\"483916\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"483916\"]\r\n\r\nYou need to find the total length of border trim that is needed for all three rooms in the house. Since the measurements for each room are given in feet, you can add the numbers.\r\n<p style=\"text-align: center;\">[latex]15\\text{ feet}+30\\text{ feet}+26\\text{ feet}=71\\text{ feet}[\/latex]<\/p>\r\nHow many yards is 71 feet?\r\n\r\nReason about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. Expect your answer to be less than 71. Use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\frac{71\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{71\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}={23}\\frac{2}{3}\\text{ yards}[\/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\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126605&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\nThe next example uses the factor label method to solve a problem that requires converting from miles to feet.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTwo runners were comparing how much they had trained earlier that day. Jo said, \u0093According to my pedometer, I ran 8.3 miles.\u0094 Alex said, \u0093That\u0092s a little more than what I ran. I ran 8.1 miles.\u0094 How many more feet did Jo run than Alex?\r\n[reveal-answer q=\"508168\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"508168\"]\r\n\r\nYou need to find the difference between the distance Jo ran and the distance Alex ran. Since both distances are given in the same unit, you can subtract and keep the unit the same.\r\n<p style=\"text-align: center;\">[latex]8.3\\text{ miles}-8.1\\text{ miles}=0.2\\text{ mile}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]0.2\\text{ mile}=\\frac{2}{10}\\text{ mile}[\/latex]<\/p>\r\nSince the problem asks for the difference in <i>feet<\/i>, you must convert from miles to feet. How many feet is 0.2 mile? Reason about the size of your answer. Since a mile is longer than a foot, the distance when expressed as feet will be a number greater than 0.2.\r\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\text{ mile}=[\/latex] ___ feet<\/p>\r\nUse the conversion factor [latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\frac{2\\text{mile}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex] = ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2\\cancel{\\text{mile}}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\cancel{\\text{ mile}}}[\/latex] = ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\cdot\\frac{5,280\\text{ feet}}{1}[\/latex] = ___ feet<\/p>\r\nMultiply. Divide.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{2\\bullet \\text{5,280 feet}}{10\\bullet 1}[\/latex]= ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{10,560\\text{ feet}}{10}[\/latex]= ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{\\text{10,560 feet}}{\\text{10}}[\/latex]= 1,056 feet<\/p>\r\nJo ran 1,056 feet further than Alex.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next example we show how to compare the price of two different kinds of tubing for a project you are making. One\u00a0type of tubing is given in cost per yards, and the other is given in cost per feet. It is easier to make a comparison when the units are the same, so we convert one price into the same units as the other. For problems like this, it doesn't matter which cost you convert, either one will work.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYou are walking through a hardware store and notice two sales on tubing.\r\n\r\n3 yards of Tubing A costs $5.49.\r\n\r\nTubing B sells for $1.88 for 2 feet.\r\n\r\nEither tubing is acceptable for your project. Which tubing is less expensive?\r\n[reveal-answer q=\"468145\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"468145\"]\r\nFind the unit price for each tubing. This will make it easier to compare.\r\n<h4>Tubing A<\/h4>\r\nFind the cost per yard of Tubing A by dividing the cost of 3 yards of the tubing by 3.\r\n<p style=\"text-align: center;\">3 yards = $5.49<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{5.49\\div3}{3\\text{ yards}\\div3}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\r\nTubing B is sold by the foot. Find the cost per foot by dividing $1.88 by 2 feet.\r\n<h4>Tubing B<\/h4>\r\n<p style=\"text-align: center;\">2 feet = $1.88<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1.88\\div2}{2\\text{ feet}\\div2}=\\frac{\\$0.94}{1\\text{ foot}}[\/latex]<\/p>\r\nTo compare the prices, you need to have the same unit of measure.\r\n\r\nUse the conversion factor [latex] \\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex], cancel and multiply.\r\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\text{ foot}}\\cdot\\frac{3\\text{ feet}}{1\\text{ yard}}=\\frac{\\$\\text{____}}{\\text{____ yard}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\cancel{\\text{ foot}}}\\cdot\\frac{3\\cancel{\\text{ feet}}}{1\\text{ yard}}=\\frac{\\$2.82}{1\\text{ yard}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\$2.82\\text{ per yard}[\/latex]<\/p>\r\nCompare prices for 1 yard of each tubing.\r\n\r\nTubing A: $1.83 per yard\r\n\r\nTubing B: $2.82 per yard\r\n\r\nTubing A is less expensive than Tubing B.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the problem above, you could also have found the price per foot for each kind of tubing and compared the unit prices of each per foot.\r\n\r\nYou need to convert from one unit of measure to another if you are solving problems that include measurements involving more than one type of measurement. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and\/or the factor label method shown in this topic.The four basic units of measurement that are used in the U.S. customary measurement system are: inch, foot, yard, and mile. Typically, people use yards, miles, and sometimes feet to describe long distances. Measurement in inches is common for shorter objects or lengths.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>LEARNING outcomes<\/h3>\n<div>\n<ul>\n<li>Define units of length and convert from one to another.<\/li>\n<li>Perform arithmetic calculations on units of length.<\/li>\n<li>Solve application problems involving units of length.<\/li>\n<li>Define units of weight and convert from one to another.<\/li>\n<li>Perform arithmetic calculations on units of weight.<\/li>\n<li>Solve application problems involving units of weight.<\/li>\n<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume.<\/li>\n<li>Define the metric prefixes and use them to perform basic conversions among metric units.<\/li>\n<li>Solve application problems involving metric units of length, mass, and volume.<\/li>\n<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\n<li>Convert from one temperature scale to the other, using conversion formulas.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-942\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280-1024x1024.jpg\" alt=\"coiled measuring tape spiraling against a red background\" width=\"600\" height=\"600\" \/><\/a><\/p>\n<p>Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>$1.88 for 2 feet<\/i> of tubing and <i>$5.49 for 3 yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? You need to know about two <b>units of measurement<\/b>, yards and feet, in order to determine the answer.<\/p>\n<p><b>Length<\/b> is the distance from one end of an object to the other end, or from one object to another. For example, the length of a letter-sized piece of paper is 11 inches. The system for measuring length in the United States is based on the four customary units of length: <b>inch<\/b>, <b>foot<\/b>, <b>yard<\/b>, and <b>mile<\/b>. Below are examples to show measurement in each of these units.<\/p>\n<table cellpadding=\"0\" style=\"width: 613px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Unit<\/b><\/td>\n<td><b>Description<\/b><\/td>\n<td><b>Image<\/b><\/td>\n<\/tr>\n<tr>\n<td>Inch\/Inches<\/td>\n<td>Some people donate their hair to be made into wigs for cancer patients who have lost hair as a result of treatment. One company requires hair donations to be at least 8 inches long.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 1\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200906\/image049.jpg\" alt=\"A hand holding long cut-off hair\" width=\"64\" height=\"132\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Frame size of a bike: the distance from the center of the crank to the top of the seat tube. Frame size is usually measured in inches. This frame is 16 inches.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 2\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200907\/image050.jpg\" alt=\"A black bicycle labeled with frame size and standover height\" width=\"264\" height=\"157\" \/><\/td>\n<\/tr>\n<tr>\n<td>Foot\/Feet<\/td>\n<td>Rugs are typically sold in standard lengths. One typical size is a rug that is 8 feet wide and 11 feet long. This is often described as an 8 by 11 rug.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 3\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200909\/image051.jpg\" alt=\"A red and gold rug\" width=\"116\" height=\"174\" \/><\/td>\n<\/tr>\n<tr>\n<td>Yard\/Yards<\/td>\n<td>Soccer fields vary some in their size. An official field can be any length between 100 and 130 yards.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 4\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200910\/image052.gif\" alt=\"A cartoon depiction of a soccer field.\" width=\"255\" height=\"153\" \/><\/td>\n<\/tr>\n<tr>\n<td>Mile\/Miles<\/td>\n<td>A marathon is 26.2 miles long. One marathon route is shown in the map to the right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 5\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200911\/image053.jpg\" alt=\"A marathon route.\" width=\"192\" height=\"323\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You can use any of these four U.S. customary measurement units to describe the length of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the length of a rug in feet rather than miles, and to describe a marathon in miles rather than inches.<\/p>\n<p>You may need to convert between units of measurement. For example, you might want to express your height using feet and inches (5 feet 4 inches) or using only inches (64 inches). You need to know the unit equivalents in order to make these conversions between units.<\/p>\n<p>The table below shows equivalents and conversion factors for the four customary units of measurement of length.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Unit Equivalents<\/b><\/td>\n<td><b>Conversion Factors <\/b><\/p>\n<p><b>(longer to shorter units of measurement)<\/b><\/td>\n<td><b>Conversion Factors<\/b><\/p>\n<p><b>(shorter to longer units of measurement)<\/b><\/td>\n<\/tr>\n<tr>\n<td>1 foot = 12 inches<\/td>\n<td>[latex]\\displaystyle \\frac{12\\ \\text{inches}}{1\\ \\text{foot}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1\\text{ foot}}{12\\text{ inches}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 yard = 3 feet<\/td>\n<td>[latex]\\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 mile = 5,280 feet<\/td>\n<td>[latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{\\text{1 mile}}{\\text{5,280 feet}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that each of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all since it is the same as multiplying by 1; it just changes the units that you are using to measure.<\/p>\n<h2>Convert Between Different Units of Length<\/h2>\n<p>You can use the conversion factors to convert a measurement, such as feet, to another type of measurement, such as inches.<\/p>\n<p>Note that there are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor [latex]\\displaystyle \\frac{\\text{12 inches}}{\\text{1 foot}}[\/latex].<\/p>\n<p>If a length is measured in feet, and you\u0092d like to convert the length to yards, you can think, \u0093I am converting from a shorter unit to a longer one, so the length in yards will be less than the length in feet.\u0094 You could use the conversion factor [latex]\\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex].<\/p>\n<p>If a distance is measured in miles, and you want to know how many feet it is, you can think, \u0093I am converting from a longer unit of measurement to a shorter one, so the number of feet would be greater than the number of miles.\u0094 You could use the conversion factor [latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].<\/p>\n<p>You can use the <b>factor<\/b> <b>label<\/b> <b>method<\/b> (also known as <b>dimensional analysis<\/b>) to convert a length from one unit of measure to another using the conversion factors. In the factor label method, you multiply by unit fractions to convert a measurement from one unit to another. Study the example below to see how the factor label method can be used to convert [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet into an equivalent number of inches.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many inches are in [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q284681\">Show Solution<\/span><\/p>\n<div id=\"q284681\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by reasoning about your answer. Since a foot is longer than an inch, this means the answer would be greater than [latex]\\displaystyle 3\\frac{1}{2}[\/latex].<\/p>\n<p>Find the conversion factor that compares inches and feet, with \u0093inches\u0094 in the numerator, and multiply.<\/p>\n<p style=\"text-align: center;\">[latex]3\\frac{1}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\n<p>Rewrite the mixed number as an improper fraction before multiplying.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\n<p>You can cancel similar units when they appear in the numerator <i>and<\/i> the denominator. So here, cancel the similar units \u0093feet\u0094 and \u0093foot.\u0094 This eliminates this unit from the problem.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\n<p>Rewrite as multiplication of numerators and denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7\\cdot12\\text{ inches}}{2}=\\frac{84\\text{ inches}}{2}=42\\text{ inches}[\/latex]<\/p>\n<p>There are 42 inches in [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that by using the factor label method you can cancel the units out of the problem, just as if they were numbers. You can only cancel if the unit being cancelled is in both the numerator and denominator of the fractions you are multiplying.<\/p>\n<p>In the problem above, you cancelled <i>feet<\/i> and <i>foot<\/i> leaving you with <i>inches<\/i>, which is what you were trying to find.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\n<p>What if you had used the wrong conversion factor?<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{1\\text{foor}}{12\\text{ inches}}=\\text{? inches}[\/latex]?<\/p>\n<p>You could not cancel the feet because the unit is not the same in <i>both <\/i>the numerator and the denominator. So if you complete the computation, you would still have both feet and inches in the answer and no conversion would take place.<\/p>\n<p>Here is another example of a length conversion using the factor label method.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many yards is 7 feet?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q571283\">Show Solution<\/span><\/p>\n<div id=\"q571283\" class=\"hidden-answer\" style=\"display: none\">\n<p>Start by reasoning about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. So your answer will be less than 7.<\/p>\n<p>Find the conversion factor that compares feet and yards, with yards in the numerator.<\/p>\n<p style=\"text-align: center;\">[latex]7\\text{ feet}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\n<p>Cancel the similar units \u0093feet\u0094 and \u0093feet\u0094 leaving only yards.<\/p>\n<p style=\"text-align: center;\">[latex]7\\cancel{\\text{ feet}}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=\\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]7\\cdot\\frac{1\\text{ yard}}{3}=\\text{? yards}[\/latex]<\/p>\n<p>7 feet equals [latex]\\displaystyle 2\\frac{1}{3}[\/latex] yards.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=117507&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=986&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom10\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=992&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=993&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<h2>Apply Unit Conversions With Length<\/h2>\n<p>There are times when you will need to perform computations on measurements that are given in different units. For example, consider the tubing problem given earlier. You must decide which of the two options is a better price, and you have to compare prices given in different unit measurements.<\/p>\n<p>In order to compare, you need to convert the measurements into one single, common unit of measurement. To be sure you have made the computation accurately, think about whether the unit you are converting to is smaller or larger than the number you have. Its relative size will tell you whether the number you are trying to find is greater or lesser than the given number.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>An interior decorator needs border trim for a home she is wallpapering. She needs 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room. How many yards of border trim does she need?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q483916\">Show Solution<\/span><\/p>\n<div id=\"q483916\" class=\"hidden-answer\" style=\"display: none\">\n<p>You need to find the total length of border trim that is needed for all three rooms in the house. Since the measurements for each room are given in feet, you can add the numbers.<\/p>\n<p style=\"text-align: center;\">[latex]15\\text{ feet}+30\\text{ feet}+26\\text{ feet}=71\\text{ feet}[\/latex]<\/p>\n<p>How many yards is 71 feet?<\/p>\n<p>Reason about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. Expect your answer to be less than 71. Use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{71\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{71\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}={23}\\frac{2}{3}\\text{ yards}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126605&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<p>The next example uses the factor label method to solve a problem that requires converting from miles to feet.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Two runners were comparing how much they had trained earlier that day. Jo said, \u0093According to my pedometer, I ran 8.3 miles.\u0094 Alex said, \u0093That\u0092s a little more than what I ran. I ran 8.1 miles.\u0094 How many more feet did Jo run than Alex?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q508168\">Show Solution<\/span><\/p>\n<div id=\"q508168\" class=\"hidden-answer\" style=\"display: none\">\n<p>You need to find the difference between the distance Jo ran and the distance Alex ran. Since both distances are given in the same unit, you can subtract and keep the unit the same.<\/p>\n<p style=\"text-align: center;\">[latex]8.3\\text{ miles}-8.1\\text{ miles}=0.2\\text{ mile}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]0.2\\text{ mile}=\\frac{2}{10}\\text{ mile}[\/latex]<\/p>\n<p>Since the problem asks for the difference in <i>feet<\/i>, you must convert from miles to feet. How many feet is 0.2 mile? Reason about the size of your answer. Since a mile is longer than a foot, the distance when expressed as feet will be a number greater than 0.2.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\text{ mile}=[\/latex] ___ feet<\/p>\n<p>Use the conversion factor [latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\text{mile}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex] = ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\cancel{\\text{mile}}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\cancel{\\text{ mile}}}[\/latex] = ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\cdot\\frac{5,280\\text{ feet}}{1}[\/latex] = ___ feet<\/p>\n<p>Multiply. Divide.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{2\\bullet \\text{5,280 feet}}{10\\bullet 1}[\/latex]= ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{10,560\\text{ feet}}{10}[\/latex]= ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{10,560 feet}}{\\text{10}}[\/latex]= 1,056 feet<\/p>\n<p>Jo ran 1,056 feet further than Alex.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the next example we show how to compare the price of two different kinds of tubing for a project you are making. One\u00a0type of tubing is given in cost per yards, and the other is given in cost per feet. It is easier to make a comparison when the units are the same, so we convert one price into the same units as the other. For problems like this, it doesn&#8217;t matter which cost you convert, either one will work.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>You are walking through a hardware store and notice two sales on tubing.<\/p>\n<p>3 yards of Tubing A costs $5.49.<\/p>\n<p>Tubing B sells for $1.88 for 2 feet.<\/p>\n<p>Either tubing is acceptable for your project. Which tubing is less expensive?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q468145\">Show Solution<\/span><\/p>\n<div id=\"q468145\" class=\"hidden-answer\" style=\"display: none\">\nFind the unit price for each tubing. This will make it easier to compare.<\/p>\n<h4>Tubing A<\/h4>\n<p>Find the cost per yard of Tubing A by dividing the cost of 3 yards of the tubing by 3.<\/p>\n<p style=\"text-align: center;\">3 yards = $5.49<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{5.49\\div3}{3\\text{ yards}\\div3}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\n<p>Tubing B is sold by the foot. Find the cost per foot by dividing $1.88 by 2 feet.<\/p>\n<h4>Tubing B<\/h4>\n<p style=\"text-align: center;\">2 feet = $1.88<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1.88\\div2}{2\\text{ feet}\\div2}=\\frac{\\$0.94}{1\\text{ foot}}[\/latex]<\/p>\n<p>To compare the prices, you need to have the same unit of measure.<\/p>\n<p>Use the conversion factor [latex]\\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex], cancel and multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\text{ foot}}\\cdot\\frac{3\\text{ feet}}{1\\text{ yard}}=\\frac{\\$\\text{____}}{\\text{____ yard}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\cancel{\\text{ foot}}}\\cdot\\frac{3\\cancel{\\text{ feet}}}{1\\text{ yard}}=\\frac{\\$2.82}{1\\text{ yard}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\$2.82\\text{ per yard}[\/latex]<\/p>\n<p>Compare prices for 1 yard of each tubing.<\/p>\n<p>Tubing A: $1.83 per yard<\/p>\n<p>Tubing B: $2.82 per yard<\/p>\n<p>Tubing A is less expensive than Tubing B.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the problem above, you could also have found the price per foot for each kind of tubing and compared the unit prices of each per foot.<\/p>\n<p>You need to convert from one unit of measure to another if you are solving problems that include measurements involving more than one type of measurement. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and\/or the factor label method shown in this topic.The four basic units of measurement that are used in the U.S. customary measurement system are: inch, foot, yard, and mile. Typically, people use yards, miles, and sometimes feet to describe long distances. Measurement in inches is common for shorter objects or lengths.<\/p>\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-570\">\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>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>Units of Length. <strong>Authored by<\/strong>: Developmental Math 2014An Open Program. <strong>Provided by<\/strong>: Monterey Institute for Technology and Education (MITE). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/dl.dropboxusercontent.com\/u\/28928849\/MAT142\/MeasurementNROC.pdf\">https:\/\/dl.dropboxusercontent.com\/u\/28928849\/MAT142\/MeasurementNROC.pdf<\/a>. <strong>Project<\/strong>: Developmental Mathu2014An Open Program. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>meter-tape-measure-measure-gage. <strong>Authored by<\/strong>: EME. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/meter-tape-measure-measure-gage-512181\/\">https:\/\/pixabay.com\/en\/meter-tape-measure-measure-gage-512181\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>Question ID 117507. <strong>Authored by<\/strong>: Volpe, Amy. <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>Question ID 986. <strong>Authored by<\/strong>: Lippman, David. <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>Question ID 126605. <strong>Authored by<\/strong>: Day, Alyson. <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":21,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Units of 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