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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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Practice Conversions of Length, Mass, Capacity in Metric Units
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Convert Metric Units of Measurement

Veera drives big rigs all over the country. She knows that the semitrailer she’s driving is 3.5 m high. The bridge she’s about to go over is 352.5 cm high. Will Veera’s truck fit under the bridge?

In this concept, you will learn to convert metric units of measurement.

### Metric System

The metric system of measurement is the primary measurement system in many countries; it contains units such as meters, kilometers and liters. You can remember the conversions by learning the prefixes: milli-means thousandth, centi-means hundredth, and kilo-means thousand. So a millimeter is one-thousandth of a meter, and a kilometer is one thousand meters.

Metric Units of Measurement

Now that you have reviewed these units of measurement, you can look at converting among the different units of measurement.

Let’s look at an example.

How many centimeters are in 5 meters?

First, set up a proportion.

\begin{align*}\frac{1\ m}{100\ cm}= \frac{5\ m}{x\ cm} \end{align*}

Next, cross multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} \frac{1}{100} &=& \frac{5}{x} \\ 1x &=& 5 \times 100 \\ x &=& 500 \end{array}\end{align*}The answer is 500.

Therefore 5 meters is equal to 500 centimeters.

Let’s look at another example.

Henry is making a recipe for lemonade that uses 2 liters of water. If he makes 3 batches of the recipe, how many milliliters of water will he need?

First find the total number of liters he needs.

If there are 2 liters in one batch, and he is making 3 batches, then he will need \begin{align*} 2 \times 3 = 6\end{align*} liters.

Next, set up a proportion.

\begin{align*}\frac{1\ L}{1000\ mL} = \frac{6\ L}{x\ mL} \end{align*}

Then, cross multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} \frac{1}{1000} &=& \frac{6}{x} \\ 1x &=& 6 \times 1000 \\ x &=& 6000 \end{array}\end{align*}

Therefore 6 liters is equal to 6000 milliliters.

### Examples

#### Example 1

Earlier, you were given a problem about Veera and her tall bridge.

Veera needs to determine the height of the 352.2 cm bridge in meters in order to compare it to the truck. If the bridge height is greater than 3.5 m, the truck will fit under the bridge.

First, set up a proportion.

\begin{align*}\frac{1\ m}{100\ cm} = \frac{x\ m}{352.5\ cm} \end{align*}

Next, cross multiply.

\begin{align*}\begin{array}{rcl} \frac{1}{100} &=& \frac{x}{352.5} \\ 100x &=& 1 \times 352.5 \\ 100x &=& 352.5 \end{array}\end{align*}

Then, divide both sides by 100 to solve for \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 100x &=& 352.5\\ \frac{100x}{100} &=& \frac{352.5}{100} \\ x &=& 3.525 \end{array}\end{align*}

The bridge clearance is 3.525 m. This means the truck has 0.025 m or 2.5 cm clearance.

#### Example 2

Convert 4500 ml into liters.

First, set up a proportion.

\begin{align*}\frac{1\ L}{1000\ mL} = \frac{x\ L}{4500\ mL} \end{align*}

Next, cross multiply.

\begin{align*} \begin{array}{rcl} \frac{1}{1000} &=& \frac{x}{4500} \\ 1000x &=& 1 \times 4500 \\ 1000x &=& 4500 \end{array}\end{align*}

Then divide both sides by 1000 to solve for \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 1000x &=& 4500 \\ \frac{1000x}{1000} &=& \frac{4500}{1000} \\ x &=& 4.5 \end{array}\end{align*}The answer is 4.5.

Therefore 4.5 liters is equal to 4500 milliliters.

#### Example 3

Convert 5.5 grams into milligrams.

First, set up a proportion.

\begin{align*}\frac{1\ g}{1000\ mg} = \frac{5.5\ g}{x\ mg} \end{align*}

Next, cross multiply to solve for \begin{align*}x\end{align*} .

\begin{align*}\begin{array}{rcl} \frac{1}{1000} &=& \frac{5.5}{x} \\ 1x &=& 5.5 \times 1000 \\ x &=& 5500 \end{array}\end{align*}The answer is 5500.

Therefore 5.5 grams is equal to 5500 milligrams.

#### Example 4

Convert 40 mm into centimeters.

First, set up a proportion.

\begin{align*}\frac{1\ cm}{10\ mm}= \frac{x\ cm}{40\ mm} \end{align*}

Next, cross multiply.

\begin{align*} \begin{array}{rcl} \frac{1}{10} &=& \frac{x}{40} \\ 10x &=& 1 \times 40 \\ 10x &=& 40 \end{array}\end{align*} Then, divide both sides by 10 to solve for \begin{align*}x\end{align*}.

\begin{align*} \begin{array}{rcl} 10x &=& 40 \\ \frac{10x}{10} &=& \frac{40}{10} \\ x &=& 4 \end{array}\end{align*}The answer is 4.

Therefore 4 cm is equal to 40 mm.

### Review

Solve each problem.

1. \begin{align*}3 \ km = \underline{\;\;\;\;\;\;\;\;\;} \ m\end{align*}

2. \begin{align*}2000 \ m =\underline{\;\;\;\;\;\;\;\;\;} \ km\end{align*}

3. \begin{align*}5.5 \ km = \underline{\;\;\;\;\;\;\;\;\;} \ m\end{align*}

4. \begin{align*}2500 \ m = \underline{\;\;\;\;\;\;\;\;\;} \ km\end{align*}

5. \begin{align*}12000 \ m = \underline{\;\;\;\;\;\;\;\;\;} \ km\end{align*}

6. \begin{align*}500 \ cm = \underline{\;\;\;\;\;\;\;\;\;} \ m\end{align*}

7. \begin{align*}6000 \ cm = \underline{\;\;\;\;\;\;\;\;\;} \ m\end{align*}

8. \begin{align*}4 \ m = \underline{\;\;\;\;\;\;\;\;\;} \ cm\end{align*}

9. \begin{align*}11 \ m = \underline{\;\;\;\;\;\;\;\;\;} \ cm\end{align*}

10. \begin{align*}50 \ mm = \underline{\;\;\;\;\;\;\;\;\;} \ cm\end{align*}

11. \begin{align*}3 \ cm = \underline{\;\;\;\;\;\;\;\;\;} \ mm\end{align*}

12. \begin{align*}15 \ cm = \underline{\;\;\;\;\;\;\;\;\;} \ mm\end{align*}

13. \begin{align*}2000 \ g = \underline{\;\;\;\;\;\;\;\;\;} \ kg\end{align*}

14. \begin{align*}35000 \ g = \underline{\;\;\;\;\;\;\;\;\;} \ kg\end{align*}

15. \begin{align*}7 \ kg = \underline{\;\;\;\;\;\;\;\;\;} \ g\end{align*}

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### Vocabulary Language: English

Measurement

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

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”.