The easiest way to convert from one unit of measurement to another is to use conversion factors. A conversion factor is a ratio of equivalent measurements that is used to convert a quantity expressed in one unit to another unit. Suppose you want to convert the height of Mount Everest, 8848 meters, into kilometers. Based on the prefix kilo-, you know that 1 kilometer is 1000 meters. This ratio gives you two possible conversion factors.

$\genfrac{}{}{0.1ex}{}{1 km}{1000 m}\genfrac{}{}{0.1ex}{}{1000 m}{1 km}$

Figure 17 Nutrition labels often have some measurements listed in grams and milligrams.

Calculating How many grams are in 160 milligrams?

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Since you are converting from meters to kilometers, the number should get smaller. Multiplying by the conversion factor on the left yields a smaller number.

$8848 \cancel{m}\times \genfrac{}{}{0.1ex}{}{1km}{1000\cancel{m}}=8.848km$

Notice that the meter units cancel, leaving you with kilometers (the larger unit).

To convert 8.848 kilometers back into meters, multiply by the conversion factor on the right. Since you are converting from kilometers to meters, the number should get larger.

$8.848 k\cancel{m}\times \genfrac{}{}{0.1ex}{}{1000m}{1 k\cancel{m}}=8848m$

In this case, the kilometer units cancel, leaving you with meters.

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