Often, measurements must be converted from one unit to another. We can do this by using unit fractions or by moving the decimal point. Let’s use unit fractions fi rst. 2 Use Unit Fractions to Convert Between Units Since we know the relationships between the units of measurement in the metric system, we can write them as unit fractions to convert from one unit to another. We will use the unit fractions just as we did in Section 7.1. Use unit fractions to change to the indicated unit. a) 83 km to m b) 162 mm to m c) 1.5 m to cm Solution a) Step 1: Identify the units given and the units we want to get. Write down the relationship between those units. We are given km and want to convert to m. The relationship is 1 km 1000 m Step 2: Multiply the given measurement by the unit fraction relating the unit given and the unit we want to get so that the given unit will divide out and leave us with the unit we want. 83 km 1000 m 1 km 83 km 1 1000 m 1 km Divide out the unit of kilometers. 83,000 m 1 Multiply. 83,000 m Simplify. So, 83 km 83,000 m. b) We are given 162 mm and want to convert to m. The relationship is 1000 mm 1 m Multiply the given measurement by the unit fraction so that millimeters divide out and meters remain. 162 mm 1 m 1000 mm 162 mm 1 1 m 1000 mm Divide out the unit of millimeters. 162 m 1000 Multiply. 0.162 m Simplify. Therefore, 162 mm 0.162 m. Notice that when we multiplied by the unit fraction, we did not divide out common factors of 162 and 1000. This is because we want to express the answer as a decimal. EXAMPLE 3 Does this seem similar to Objective 3 of Section 7.1? www.mhhe.com/messersmith SECTION 7.2 The Metric System: Length 449
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