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.

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.

Unit	Description	Image
Inch/Inches	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.
	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.
Foot/Feet	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.
Yard/Yards	Soccer fields vary some in their size. An official field can be any length between 100 and 130 yards.
Mile/Miles	A marathon is 26.2 miles long. One marathon route is shown in the map to the right.

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.

Convert Between Different 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 [latex]\displaystyle \frac{\text{12 inches}}{\text{1 foot}}[/latex].

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 [latex]\displaystyle \frac{\text{1 yard}}{\text{3 feet}}[/latex].

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 [latex]\displaystyle \frac{5,280\text{ feet}}{1\text{ mile}}[/latex].

You can use dimensional analysis (also known as factor label method) to convert a length from one unit of measure to another using the conversion factors. In dimensional analysis, 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.

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.

[latex]\frac{7}{2}\cancel{\text{feet}}\cdot\frac{12\text{ inches}}{\cancel{1\text{foot}}}=\text{? inches}[/latex]

What if you had used the wrong conversion factor?

[latex]\frac{7}{2}\text{feet}\cdot\frac{1\text{foor}}{12\text{ inches}}=\text{? inches}[/latex]?

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 dimensional analysis.

Apply Unit Conversions With Length

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 dimensional analysis to solve a problem that requires converting from miles to feet.

In the next example we show how to compare the price of two different kinds of tubing for a project you are making. One type 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.

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.

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 dimensional analysis 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.