![]() In our 10-kilometer race example, we would simply multiply 10 (our initial measurement in kilometers) by 10 5 (or 100,000 - the number of centimeters in a kilometer).The units in the denominator will cancel with the units of your initial measurement, leaving your answer in terms of your desired units. In simple conversions like we're dealing with here, just label the units of your initial measurement as you normally would, then label your conversion factor with the fraction (desired units)/(units of your initial measurement). You'll also be asked to show how you converted your initial unit label to its final form. Sometimes, especially in schoolwork, it's not enough to simply give the correct number. ![]() Remember that this number should be a power of ten given by the number of spaces under the arrow you drew in the steps above. Converting from a large unit to a smaller unit means you should multiply your original measurement by the amount that its units differ from the desired final units. Thus, you know that there are 100,000 centimeters in 1 kilometer.įor "large to small" conversions, multiply by the appropriate power of ten. In other words, centimeters are 100,000 times (or 10 5, etc.) times smaller than kilometers. This means that kilometers and centimeters differ by a conversion factor of five powers of ten, also written as ten to the fifth power, 10 5, or 10 × 10 × 10 × 10 × 10 = 100,000.
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