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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

### Themetric systemof 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.

Now that you have reviewed these units of measurement, we can look at converting among the different units of measurement. Just like we used proportions when we converted among customary units of measurement, we can use proportions and ratios here too.

How do we use proportions to convert among metric units of measure?

First, set up the proportion in the same way you used to find actual measurements from scale drawings. Use the conversion factor as the first ratio, and the known and unknown units in the second ratio.

How many centimeters are in 5 meters?

First, set up a proportion.

The conversion factor is the number of centimeters in 1 meter. We can look at the chart above and see that there are 100 centimeters in 1 meters. That is our first ratio: \begin{align*}\frac{100 \ centimeters}{1 \ meter}\end{align*}.

Now write the second ratio.

The known unit is 5 meters. The unknown unit is \begin{align*}x\end{align*} centimeters. Make sure that the second ratio follows the form of the first ratio: centimeters over meters.

\begin{align*}\frac{100 \ centimeters}{1 \ meters} = \frac{x \ centimeters}{5 \ meters}\end{align*}

Now cross-multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}(1)x &= 100(5)\\ x &= 500\end{align*}

There are 500 centimeters in 5 meters.

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 \ liters\end{align*}.

Next, set up a proportion.

The conversion factor is the number of milliliters in a liter.

\begin{align*}\frac{1000 \ milliliters}{1 \ liter}\end{align*}

Now write the second ratio, making sure it follows the form of the first ratio.

\begin{align*}\frac{1000 \ milliliters}{1 \ liter} = \frac{x \ milliliters}{6 \ liters}\end{align*}

Cross-multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}(1)x &= 1000(6)\\ x &= 6000\end{align*}

He will need 6000 milliliters of water.

Convert each measurement.

4500 ml = ____ Liters

5.5 grams = ____milligrams

40 mm = ____centimeters

### Vocabulary

Metric System
a system of measurement commonly used outside of the United States. It contains units such as meters, milliliters and grams.

### Guided Practice

Kyle is going to be traveling with his family over the winter holidays. He wants to figure out how many kilometers it is from his home in Cincinatti to his grandparents home in Chicago. Which unit of measurement should Kyle use?

First, let’s think about the correct unit of measurement for Kyle to use.

If Kyle is measuring a far distance, he needs a measure of length. We know that the metric units for measuring length are millimeters, centimeters, meters and kilometers. Kyle is measuring the distance between two cities. It makes the most sense for him to use the largest unit for measuring length, and that is kilometers.

Kyle would use kilometers to measure the distance.

### Practice

Directions: Solve each problem.

1. 3 km = _____ m
2. 2000 m = _____ km
3. 5.5 km = _____ m
4. 2500 m = _____ km
5. 12000 m = _____ km
6. 500 cm = _____ m
7. 6000 cm = _____ m
8. 4 m = _____ cm
9. 11 m = _____ cm
10. 50 mm = _____ cm
11. 3 cm = _____ mm
12. 15 cm = _____ mm
13. 2000 g = _____ kg
14. 35000 g = _____ kg
15. 7 kg = _____ g

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