# 4.6.5: Multiple Metric Conversions

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## Equivalent Metric Units of Length

Corey measures the distance between two trees in his backyard. He finds that the measurement is 8 meters, but he wants to express the measurement in centimeters. How many centimeters are in 8 meters?

In this concept, you will learn how to convert with metric units of measurements.

### Converting Using Whole Number Values

Length measures how long something is from one end to the other end.

Here are the common metric units of length from smallest to largest.

millimeter is the smallest unit. Millimeters are most useful when measuring really tiny things. You can find millimeters on some rulers.

centimeter is the next smallest unit. Centimeters can also be found on a ruler.

meter is a little more than 3 feet.

kilometer is used to measure longer distances.

Here is a chart to help with the conversions.

1 km=1000 m

1 m=100 cm

1 cm=10 mm

Now that you know the conversions, you can change one unit to another unit.

5 km = ____ m

You can convert larger units to smaller units by multiplying. There are 1000 meters in one kilometer.

5 km=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ m

5×1000=5000 m

Here's an example of converting smaller units to larger units.

600 cm = ______ m

You can convert smaller units to larger units by dividing. There are 100 cm in one meter.

600 ÷ 100 = 6

### Examples

Example 4.6.5.1

Earlier, you were given a problem about Corey's measurement of his tree.

His measurement is 8 meters, but he wants to convert it to centimeters. How many centimeters are equal to 8 meters?

8 m = _____ cm

Solution

First, determine if the conversion is from smaller units to larger units or larger units to smaller units.

Larger to smaller

Next, perform the appropriate operation.

8 × 100

Then, write the value.

800

The answer is 800 cm. The distance between the two trees is 800 cm.

Example 4.6.5.2

Find the equivalent metric measurement.

6 m = ______ mm

Solution

First, determine if the conversion is from smaller units to larger units or larger units to smaller units.

Larger to smaller

Next, perform the appropriate operation.

6 × 1000

Then, write the value.

6000

Example 4.6.5.3

Find the equivalent metric measurement.

2000 mm = ______ cm

Solution

First, determine if the conversion is from smaller units to larger units or larger units to smaller units.

Smaller to larger

Next, perform the appropriate operation.

2000 ÷ 10

Then, write the value.

200

Example 4.6.5.4

Find the equivalent metric measurement.

3 km = _____ m

Solution

First, determine if the conversion is from smaller units to larger units or larger units to smaller units.

Larger to smaller

Next, perform the appropriate operation.

3 × 1000

Then, write the value.

3000

Example 4.6.5.5

Find the equivalent metric measurement.

4000 cm = ______ m

Solution

First, determine if the conversion is from smaller units to larger units or larger units to smaller units.

Smaller to larger

Next, perform the appropriate operation.

4000 ÷ 100

Then, write the value.

40

### Review

Complete the following metric equivalents.

1. 6 km = ______ m
2. 5 m = ______ cm
3. 100 cm = ______ m
4. 400 cm = ______ m
5. 9 km = ______ m
6. 2000 m = ______ km
7. 20 mm = ______ cm
8. 8 cm = ______ mm
9. 900 cm = ______ m
10. 12 m = ______ cm
11. 10 cm = ______ mm
12. 100 cm = _____ mm
13. 6700 m = ______ km
14. 8200 m = ______ km
15. 12,500 m = ______ km

To see the Review answers, open this PDF file and look for section 3.5.

### Vocabulary

Term Definition
Centimeter A centimeter is a very small unit of metric measure. A centimeter is one hundredth of one meter.
Kilometer A kilometer is a common metric unit of length that is equal to 1,000 meters.
Length Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.
Meter A meter is a common metric unit of length that is slightly larger than a yard.
Metric System The metric system is a system of measurement commonly used outside of the United States. It contains units such as meters, liters, and grams, all in multiples of ten.
Millimeter A millimeter is the smallest common metric unit of length.