Length Learning Objective(s) · Define units of length and convert from one to another. · Perform arithmetic calculations on units of length. · Solve application problems involving units of length. Introduction Measurement is a number that describes the size or amount of something. You can measure many things like length, area, capacity, weight, temperature and time. In the United States, two main systems of measurement are used: the metric system and the U.S. customary measurement system. This topic addresses the measurement of length using the U.S. customary measurement system. Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: $1.88 for 2 feet of tubing and $5.49 for 3 yards 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 units of measurement, yards and feet, in order to determine the answer. Units of Length Length 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: inch, foot, yard, and mile. Below are examples to show measurement in each of these units.
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. 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. The table below shows equivalents and conversion factors for the four customary units of measurement of length.
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. Converting Between Units of Length You can use the conversion factors to convert a measurement, such as feet, to another type of measurement, such as inches. 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 If a length is measured in feet, and you’d
like to convert the length to yards, you can think, “I am converting from a shorter unit to a longer one, so the length in yards will be less than the length in feet.” You could use the conversion factor If a distance is measured in miles, and you want to know how many feet it is, you can think, “I 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.” You could use the conversion factor You can use the [factor label method] 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
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. In the problem above, you cancelled feet and foot leaving you with inches, which is what you were trying to find. What if you had used the wrong conversion factor? You could not cancel the feet because the unit is not the same in both 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. Here is another example of a length conversion using the factor label method.
Note that if the units do not cancel to give you the answer you are trying to find, you may not have used the correct conversion factor. How many feet are in A) 10,560 feet B) 30 feet C) 2,112 feet D) 13,200 feet Applying Unit Conversions 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. 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.
The next example uses the factor label method to solve a problem that requires converting from miles to feet.
Now let’s revisit the question from earlier.
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. A fence company is measuring a rectangular area in order to install a fence around its perimeter. If the length of the rectangular area is 130 yards and the width is 75 feet, what is the total length of the distance to be fenced? A) 410 yards B) 930 feet C) 710 feet D) 465 feet Summary 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. 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. What things are 6ft tall?That can be hard to visualize, so here are objects that are six feet long to help you while you're out and about.. The average height of a refrigerator. ... . The length of a twin or full-size mattress. ... . A Christmas tree. ... . Half of a Beetle Volkswagen. ... . Six bowling pins stacked on top of each other.. What is the symbol for FT and inches?For feet, a single apostrophe is used ('). For inches, a double apostrophe is used (”). Here's an example. 5′ 6″.
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