Note All of the relationships are approximations except for the relationship between inches and centimeters. Since 1 inch exactly equals 2.54 centimeters, we can use the equal sign: . For all other conversions, we use the symbol for is approximately equal to: . We will use unit fractions to convert between the two measurement systems. This method is one that is used often in nursing and science courses as well. EXAMPLE 1 As of January 2011, Michael Johnson of the United States was the world record holder in the 400 - m race. Convert 400 m to yards. Round the answer to the nearest tenth. Solution First, identify the units we are given and the units we want to get. Since we are given meters and we want to convert to yards, write down the relationship between meters and yards: 1 yd 0.91 m. Next, multiply the measurement we are given, 400 m, by the unit fraction relating yards and meters so that the meters divide out and we will be left with yards. 400 m 1 yd 0.91 m 400 m 1 1 yd 0.91 m Divide out the unit of meters. 400 yd 0.91 Multiply. 439.6 yd Simplify. 400 m 439.6 yd. Therefore, a 400-meter race is approximately 439.6 yd. YOU TRY 1 A marathon is, offi cially, 42.195 km. Convert this number to miles. Round the answer to the nearest tenth. Look at Example 1. If we had tried to multiply 400 m by the unit fraction 400 m relating meters and yards as 1 0.91 m 1 yd , the units of meters would not divide out. That’s how we know this is the wrong way to do this problem! If this happens the first time you try to convert between units, don’t panic. Write the unit fraction the other way to see whether the correct units will divide out. Let’s convert between other units. www.mhhe.com/messersmith SECTION 7.5 Metric–U.S. Customary Conversions and Temperature 473
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