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Factor Label Method of Unit Conversion Example 1 Given: 5.82 x 107 g = ? kg There are four steps in converting one unit to another. 1. The relationship between one unit and another is called an equivalent. Determine the equivalent between the desired and unwanted unit. If there is not a direct equivalent known then relate both units to be converted to a common unit. Write an equivalent for each pair of units if there is more than one conversion to be made. 1000 g = 1 kg equivalent 2. A conversion factor is a ratio of one side of the equivalent to the other. There are always two conversion factors per equivalent. Write conversion factors based on the equivalent. Take the left side the equivalent and divide by the right side. Take the right side of the equivalent and divide by the left. Repeat this step for each equivalent. 1000 g 1 kg 1 kg 1000g Conversion factors 3. Pick the conversion factor that will cancel the unwanted unit and leave the wanted unit. The unit of g will cancel because it is in the numerator and denominator and leave kg as a unit. Repeat until all unwanted units cancel. 1 kg 1000g 4. Carry out mathematical operations to compute the final answer. 1 kg 1 kg 5.82 x 107 g 5.82 x 104 kg 5.82 x 107 x 1000 1000 g Example 2 2.78 x 108 km = ______ Gm 1. Equivalents 1 Gm = 109 m 1 km = 1000 m 2. Conversion factors 1 km 1000 m 1 Gm 109 m 1000 m 1 km 109 m 1 Gm 3. Pick conversion factors that cancel unwanted units and leaves desired units. 1000 m 1 km 1 Gm 109 m 4. 1 Gm 1000 m 1 Gm 8 2.78 x 108 km 2.78 x 102 Gm 9 2.78 x 10 x 1000 x 9 10 1 km 10 m Example 3 25 km m ? hr s 1. Equivalents 1 km = 1000 m 1 hr = 3600 s 2. Conversion factors 1 km 1000 m 1000 m 1 km 1 hr 3600 s 3600 s 1 hr 3. Pick the conversion factors that cancels unwanted unit. 1000 m 1 km 1 hr 3600 s 4. 25 km 1000 m 1 hr 1 m 6.9 25 x 1000 m x hr 1 km 3600s 3600 s s