# Metric Conversions

The Metric System is based on the number 10. All metric conversions involve multiplying or dividing by a power of 10.

Let's start with the base units.

In the metric system, you measure weight in grams, liquid volume in liters, and length or distance in meters. If you want smaller or bigger units, you add a prefix to these base units (e.g., a small unit of measurement is a centimeter and a large unit of weight is a kilogram) and either divide or multiply by a power of 10. The prefixes are the same, no matter what the base unit. So, if you know how to find a kilogram, you also know how to find a kilometer or a kiloliter!

What are the prefixes and what do they mean?

Prefixes: | kilo | hecto | deca |
gram liter meter | deci | centi | milli |

Equal to how many base units: | 1,000 | 100 | 10 | 1 | $\dfrac{1}{10}$ | $\dfrac{1}{100}$ | $\dfrac{1}{1,000}$ |

So, why is it so easy to do conversion in the metric system?

Think of each column (prefix) as a level. The distance between each levels is 10. Each time you move to the right, you are multiplying by 10. Each time you move to the left you are dividing by 10.

Multiplying by ten is the same as moving the decimal point to the right. Dividing by 10 is the same as moving the decimal point to the left.

So, if you are converting in a way that moves to the left, you move the decimal to the left the same number of levels you move to the left. If you convert to the right, move the decimal the same number of decimal places as you move levels to the right.

*Example: *

*How many millimeters are there in 6 meters?*

- Start at meter.
- Millimeter is to the right of meter in the chart.
- Count how many columns you have to move: 1 to deci, 2 to centi, 3 to milli.
- Start with 6 meters.
- Move the decimal point 3 places to the right: $6.\curvearrowright \curvearrowright \curvearrowright = 6000.$
- There are 6,000 millimeters in 6 meters.

Many people like to sketch out the 7 units above when they have to convert a lot of metric units. You can also print out and use the reference card below, which gives you the units, in order, so that you can figure out how many places to move the decimal in order to convert.

#### Practice Problems:

## Metric Conversion

Find the following conversions:

- 5 m =
**___**cm - 5 m =
**___**mm - 5 m =
**___**km - 12,000 mg =
**___**g - 12,000 mg =
**___**cg - 12,000 mg =
**___**kg - 500 kl =
**___**l - 500 kl =
**___**cl - 500 kl =
**___**ml - 500 kl =
**___**dkl - 7,300 mm =
**___**cm - 7,300 mm =
**___**m - 7,300 mm =
**___**dm - 7,300 mm =
**___**km

#### Answer Key:

- 5 m =