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# 4.14: Convert Metric Units of Measurement

Difficulty Level: At Grade Created by: CK-12
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Practice Conversions of Length, Mass, Capacity in Metric Units

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Josh and his sister Karen were working on homework when the topic of Everest and the metric system came up.

“What about meters?” Karen asked. “How many meters high is Mount Everest?”

“Why are you always thinking of things that cause me more work?” Josh asked, but then he smiled at Karen. “It’s alright. I was thinking of that today anyway.”

“How can we figure it out?” Karen asked.

“Well first, we need to know how many feet are in 1 meter. I already looked that up online, and I found out that there are 3.28 feet in 1 meter. Now I know that the height of Mount Everest is 29,035 feet high, so we can work from there,” Josh explained.

“Yeah, but how?”

“Well, we can use proportions.”

Let’s stop right there. Do you know how to use a proportion to figure out this metric conversion? Well, pay attention to this Concept and if you aren’t sure how to do it now, you will know by the end of it.

### Guidance

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.

Write these units of measurement down in your notebooks.

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: 100 centimeters1 meter\begin{align*}\frac{100 \ centimeters}{1 \ meter}\end{align*}.

Now write the second ratio.

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

100 centimeters1 meters=x centimeters5 meters\begin{align*}\frac{100 \ centimeters}{1 \ meters} = \frac{x \ centimeters}{5 \ meters}\end{align*}

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

(1)xx=100(5)=500\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 2×3=6 liters\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.

1000 milliliters1 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.

1000 milliliters1 liter=x milliliters6 liters\begin{align*}\frac{1000 \ milliliters}{1 \ liter} = \frac{x \ milliliters}{6 \ liters}\end{align*}

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

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

He will need 6000 milliliters of water.

Convert each measurement.

#### Example A

4500 ml = ____ Liters

Solution: 4.5 liters

#### Example B

5.5 grams = ____milligrams

Solution: 5500 mg

#### Example C

40 mm = ____centimeters

Solution: 4 cm

Now let's go back to the dilemma from the beginning of the Concept.

First, let’s write a proportion. Josh told us that there are 3.28 feet in 1 meter. That is our first ratio in the proportion.

3.281\begin{align*}\frac{3.28}{1}\end{align*}

Next, we write the second ratio. That compares the unknown number of meters, our variable with the current height of Everest in feet.

29,035x\begin{align*}\frac{29,035}{x}\end{align*}

Our proportion is:

3.281=29035x\begin{align*}\frac{3.28}{1}= \frac{29035}{x}\end{align*}

Next, we cross multiply and solve.

The answer is that Mount Everest is about 8852 meters high. We did need to round the answer, so that is why we used the word “about” in our answer.

### 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

Here is one for you to try on your own.

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?

Solution

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

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

Color Highlighted Text Notes

### Vocabulary Language: English

TermDefinition
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”.

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