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# Conversions of Length, Mass, Capacity in Metric Units

## Determine equivalent units of metric measurement for length, mass and capacity.

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Conversions of Length, Mass, Capacity in Metric Units

Caleb is playing a math game on the computer. He has to compare metric units by filling in the blank with the correct sign. His choices are greater than (>), less than (<), or equal to (=). This is the problem Caleb is working on.

5.5 g  4,500 mg\begin{align*}5.5 \ g \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ 4,500 \ mg\end{align*}

What should Caleb choose?

In this concept, you will learn to convert metric units of length, mass, or capacity.

### Converting Length and Mass in Metric Units

This concept combines a couple of different skills. Here you will combine converting metric units of length, mass, and capacity and multiplying decimals using powers of ten.

Converting metric units using powers of ten involves moving the decimal point.

Use this chart as a guide.

 Metri Unit kilo- hecto- deka- (base unit) meter/gram/liter deci- centi- milli- Symbol k h da m/g/L d c m Number 1,000 100 10 1 0.1 0.01 0.001

Here is a conversion problem.

\begin{align*}150 \ cm = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ mm\end{align*}

When you convert a larger unit to a smaller unit, multiply the number by a power of ten. 1 centimeter is equal to 10 millimeter. You multiply by a power of ten once or \begin{align*}10^1\end{align*}. Therefore, multiply 150 cm by 10.

\begin{align*}150 \ cm × 10 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ mm\end{align*}

Move the decimal point one place to the right when multiplying by 10. The decimal point in a whole number is after the number. Add a zero placeholder to 150.

\begin{align*}150 \ cm = 1,500 \ mm\end{align*}

Let’s look at this one involving capacity.

\begin{align*}1,250 \ mL = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\end{align*}

When you convert a smaller unit to a larger unit, divide the number by a power of ten. 1,000 milliliters is equal to 1 liter. You divide by a power of ten 3 times or \begin{align*}10^3\end{align*}. Divide 1250 milliliters by 1,000.

\begin{align*}1,250 \ mL \div 1,000 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\end{align*}

Move the decimal point three places to the left when dividing by 1,000.

\begin{align*}1,250 \ milliliters = 1.25 \ Liters\end{align*}

You can convert any unit of measure as long as you know the conversion equivalents and remember how to use powers of ten to move the decimal point to the left or to the right.

### Examples

#### Example 1

Earlier, you were given a problem about Caleb’s math problem.

Caleb has to compare \begin{align*}5.5 \ g \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ 4,500 \ mg\end{align*} complete the math problem.

First, convert 5.5 g to mg. You are converting a larger unit to a smaller unit so you will multiply.

\begin{align*}5.5 \ g = \underline{\;\;\;\;\;\;\;\;\;\;\;\;}\ mg\end{align*}

Then, multiply 5.5 by a power of \begin{align*}10^3\end{align*} or 1,000. Move the decimal point three places to the right.

\begin{align*}\begin{array}{rcl} 5.5 \ g \times 1,000 & = & \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;} \ mg\\ 5.5 \ g & = & 5,500 \ mg \end{array}\end{align*}

Next, substitute 5,500 mg for 5.5 g in the original problem and compare.

\begin{align*}5,500 \ mg \ \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ 4,500 \ mg\end{align*}

\begin{align*}5,500 \ mg > 4,500 \ mg\end{align*}

Caleb should answer that 5.5 g is greater than (>) 4,500 mg.

#### Example 2

Convert the units of measurement.

\begin{align*}12,350 \ mL = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\end{align*}

First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide. You know that a milliliter is one-thousandth of a liter.

Then, divide 12,350 by a power of \begin{align*}10^3\end{align*} or 1,000. Move the decimal point three places to the left.

\begin{align*}\begin{array}{rcl} 12,350 \ mL \div 1,000 & = & \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\\ 12,350 \ mL & = & 12.35 \ L \end{array}\end{align*}

12,350 milliliters is equal to 12.35 liters.

#### Example 3

Convert the units of measurement.

\begin{align*}1,340 \ mL = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\end{align*}

First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide.

Then, divide 1,340 mL by a power of \begin{align*}10^3\end{align*} or 1,000. Move the decimal point three places to the left.

\begin{align*}\begin{array}{rcl} 1,340 \ mL ÷ 1,000 & = & \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ L\\ 1,340 \ mL & = & 1.34 \ L \end{array}\end{align*}

1,340 milliliters is equal to 1.34 liters.

#### Example 4

Convert the units of measurement.

\begin{align*}66 \ g = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ mg\end{align*}

First, identify the unit conversion. You are converting a larger unit to a smaller unit so you will multiply.

Then, multiply 66 g by a power of \begin{align*}10^3\end{align*} or 1,000. Move the decimal point three places to the right.

\begin{align*}\begin{array}{rcl} 66\ g \times 1,000 & = & \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ mg\\ 66 \ mg & = & 0.066 \ mg \end{array}\end{align*}

66 grams is equal to 0.066 milligrams.

#### Example 5

Convert the units of measurement.

\begin{align*}1,123 \ m = \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ km\end{align*}

First, identify the unit conversion. You are converting a smaller unit to a larger unit so you will divide.

Then, divide 1,123 m by a power of \begin{align*}10^3\end{align*} or 1,000. Move the decimal point three places to the left.

\begin{align*}\begin{array}{rcl} 1,123 \ m \div 1,000 & = & \underline{\;\;\;\;\;\;\;\;\;\;\;\;} \ km\\ 1,123 \ m & = & 1.123 \ km \end{array}\end{align*}

1,123 meters is equal to 1.123 kilometers.

### Review

Convert the units of 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. 18. 7.5 L = ______ mL
19. 19. 0.5 L = ______ mL

To see the Review answers, open this PDF file and look for section 4.20.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

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”.