Converting Units Up and Down the Metric Scale
Converting between metric units of measure requires knowledge of the metric prefixes and an understanding of the decimal system.
The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is [latex]10[/latex] times larger than a hundredth; a hundredth is [latex]10[/latex] times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.
The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert [latex]1[/latex] centimeter to kilometers.
Factor Label Method
There is yet another method that you can use to convert metric measurements: the factor label method. You used this method when you were converting measurement units within the U.S. customary system.
The factor label method works the same in the metric system; it relies on the use of unit fractions and the canceling of intermediate units. The table below shows some of the unit equivalents and unit fractions for length in the metric system. (You should notice that all of the unit fractions contain a factor of [latex]10[/latex]. Remember that the metric system is based on the notion that each unit is [latex]10[/latex] times larger than the one that came before it.)
Also, notice that two new prefixes have been added here: [latex]M[/latex] for mega- (which is very big) and [latex]\mu[/latex] for micro- (which is very small). The symbol [latex]\mu[/latex] is a greek lower-case letter pronounced mew.
| Unit Equivalents | Conversion Factors | |
| [latex]1[/latex] meter = [latex]1,000,000[/latex] micrometers | [latex]\displaystyle \frac{1\ m}{1,000,000\ \mu m}[/latex] | [latex]\displaystyle \frac{1,000,000\ \mu m}{1\ m}[/latex] |
| [latex]1[/latex] meter = [latex]1,000[/latex] millimeters | [latex]\displaystyle \frac{1\ m}{1,000\ mm}[/latex] | [latex]\displaystyle \frac{1,000\ mm}{1\ m}[/latex] |
| [latex]1[/latex] meter = [latex]100[/latex] centimeters | [latex]\displaystyle \frac{1\ m}{100\ cm}[/latex] | [latex]\displaystyle \frac{100\ cm}{1\ m}[/latex] |
| [latex]1[/latex] meter = [latex]10[/latex] decimeters | [latex]\displaystyle \frac{1\ m}{10\ dm}[/latex] | [latex]\displaystyle \frac{10\ dm}{1\ m}[/latex] |
| [latex]1[/latex] dekameter = [latex]10[/latex] meters | [latex]\displaystyle \frac{1\ dam}{10\ m}[/latex] | [latex]\displaystyle \frac{10\ m}{1\ dam}[/latex] |
| [latex]1[/latex] hectometer = [latex]100[/latex] meters | [latex]\displaystyle \frac{1\ hm}{100\ m}[/latex] | [latex]\displaystyle \frac{100\ m}{1\ hm}[/latex] |
| [latex]1[/latex] kilometer = [latex]1,000[/latex] meters | [latex]\displaystyle \frac{1\ km}{1,000\ m}[/latex] | [latex]\displaystyle \frac{1,000\ m}{1\ km}[/latex] |
| [latex]1[/latex] megameter = [latex]1,000,000[/latex] meters | [latex]\displaystyle \frac{1\ Mm}{1,000,000\ m}[/latex] | [latex]\displaystyle \frac{1,000,000\ m}{1\ Mm}[/latex] |
Understanding Context and Performing Conversions
Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves. Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data.
The first step in solving any real-world problem is to understand its context. This will help you figure out what kinds of solutions are reasonable (and the problem itself may give you clues about what types of conversions are necessary). Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. But it may be easier because of the relation of the units to the powers of [latex]10[/latex]. We still must make sure to add or subtract like units.