# 4.23: Conversions of Length, Mass, Capacity in Metric Units

**At Grade**Created by: CK-12

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**Practice**Conversions of Length, Mass, Capacity in Metric Units

Have you ever tried to figure out something on the computer? Sometimes you will enter an incorrect answer, but because computers don't talk, you don't know why your answer is wrong. This is exactly what happened to Caleb. Take a look.

Before leaving the science museum, Caleb found a really cool computer game all about metrics. Caleb had been practicing his metric conversions while playing at the Metric Playground, but now it was time for him to apply what he had learned. The object of the game is to move the mountain climber up the mountain by solving problems involving metric lengths, weights and liquids. Each time a correct answer is given, the mountain climber moves up the mountain. You keep playing until the climber reaches the top. At the beginning of the game, Caleb sees this problem on the computer screen. It is a problem that requires Caleb to use greater than or less than symbols to compare values.

**5.5 grams _____ 4500 mg**

Caleb is unsure of the correct answer. He decides to skip this problem by pushing the NEXT button on the computer. Here is Caleb’s second problem.

**6.7 Liters × 10 = _____**

Caleb thought that the answer was 6700 so he entered that answer into the computer. TRY AGAIN popped up on his screen. Finally Caleb decided to try one more problem.

**1550 kg is one hundred times lighter than _____ kilograms**

Caleb is stuck again. **You can help Caleb. In this Concept you will learn all about comparing metric units of length, mass and capacity. You will also learn to convert units using powers of ten.**

### Guidance

This Concept combines a couple of different skills that we have already learned. We have learned all about metrics and about how to convert metric units of length, mass and capacity. We have also learned how to multiply decimals using powers of ten such as 10, 100, 1000.

**How can we put these two skills together?**

We can put them together by converting metric units using powers of ten. This will require us to move the decimal point as we did in earlier Concepts.

Convert 150 cm into mm by multiplying by a power of ten.

We know that there are 10 mm in 1 cm. When we go from a larger unit to a smaller unit we multiply. Therefore, we are going to multiply 150 cm by 10.

150 cm

**We know that when we multiply by 10 we move the decimal point one place to the right. The decimal point in a whole number is after the number. So we need to add a zero placeholder to 150.**

150 cm = 1500 mm

We can do this when we convert from a smaller unit to a larger unit too. Let’s look at this one involving capacity.

1250 milliliters = _____ L

We know that there are 1000 milliliters in one liter. We need to divide 1250 milliliters by 1000. To do this, we will move the decimal point three places to the left. The decimal point is after the number in a whole number.

1250 milliliters = 1.25 Liters

**We can complete this with any unit of measure as long as we know the conversion equivalents and remember how to use powers of ten to move the decimal point to the left or to the right.**

Here are some equivalence charts that you will need.

Here are a few conversions for you to try on your own.

#### Example A

**1340 ml = _____ Liters**

**Solution: 1.34 Liters**

#### Example B

**66 grams = _____ mg**

**Solution: .066**

#### Example C

**1123 m = _____ km**

**Solution: 1.123 km**

Now back to the original problem. We are going to help Caleb answer all three questions. Let’s start with the first one.

**5.5 grams _____ 4500 mg**

**There are 1000 mg in 1 gram. Therefore, if we change the 4500 milligrams to grams by moving the decimal point three places to the left, we end up with 4.5 grams. 5.5 is greater than 4.5.**

**5.5 grams > 4500 mg**

**The second problem requires multiplying by powers of ten.**

**6.7 liters × 10 = _____**

**To multiply by a power of ten we move the decimal point to the right. Here we are multiplying by 10, so we move the decimal point one place to the right.**

**6.7 liters × 10 = 67 liters**

**Our final problem involves division by powers of ten.**

**1550 kg is one hundred times lighter than _____ kilograms**

**We want to make 1550 kg 100 times lighter. To do this, we divide by 100. To divide by 100, a power of 10, we move the decimal point two places to the left.**

**15.5 kg is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Metric System
- a system of measurement

- Length
- the measurement of a object or distance from one end to the other

- Millimeter
- the smallest common metric unit of measuring length, found on a ruler

- Centimeter
- a small unit of measuring length, found on a ruler

- Meter
- approximately 3 feet, measured using a meter stick

- Kilometer
- a measurement used to measure longer distances, the largest common metric unit of measuring length

- Mass
- the weight of an object

- Capacity
- the amount of liquid an object or item can hold

### Guided Practice

Here is one for you to try on your own.

12,350 mL = _____ L

**Answer**

To figure this out, we can use the chart on equivalent metric units of capacity.

Next we divide by 1000.

**Our answer is 12.35 Liters.**

### Video Review

Here are videos for review.

James Sousa Metric Unit Conversion

### Practice

Directions: Convert each measurement using powers of ten.

1. 5.6 km = ______ m

2. 890 m = ______ km

3. 9230 m = ______ km

4. 40 cm = ______ mm

5. 5000 mm = ______ cm

6. 500 cm = ______ m

7. 7.9 m = ______ cm

8. 99 m = ______ cm

9. 460 cm = ______ m

10. 34 cm = ______ m

11. 4.3 km = ______ m

12. 760 m = ______ km

13. 4300 m = ______ km

14. 5000 g = ______ kg

15. 560 mL = ______ L

16. 6210 mL = ______ L

17. 8900 mL = ______ L

18. 7.5 L = ______ mL

19. .5 L = ______ mL

Capacity

The volume of liquid an object or item can hold. Customary units of capacity include fluid ounces, cups, pints, quarts and gallons.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.Mass

Mass is a measurement of the amount of matter in an object.Measurement

A measurement is the weight, height, length or size of something.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.Proportion

A proportion is an equation that shows two equivalent ratios.Ratio

A ratio is a comparison of two quantities that can be written in fraction form, with a colon or with the word “to”.### Image Attributions

## Description

## Learning Objectives

Here you'll learn to convert metric units of length, mass or capacity.