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# Conversion of Systems of Measure

## Convert between measures in word problems

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Practice Conversion of Systems of Measure
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Use Metric and Customary Units of Measurement in Problem Solving

Have you ever worked with customary and metric units of measurement together? This involves conversion. Take a look at this dilemma.

Omar has a dog that weighs 30 pounds. About how many kilograms does Omar’s dog weigh?

### Guidance

Did you know that you can convert between customary and metric units of measurement? These measurement conversions will be estimates, because you cannot make an exact measurement when converting between systems of measurement.

There are some common benchmarks you can use.

Length

An inch is about 2.5 centimeters.

A meter is slightly longer than a yard.

A kilometer is about 0.6 of a mile.

Capacity

A liter is about the same as a quart.

Mass

A kilogram is a little more than 2 pounds.

Write these benchmarks down in your notebook.

Now look at this situation.

Randy ran a 20 kilometer race. How many miles did Randy run?

To figure this out, we have to use a comparison between kilometers and miles. A kilometer is about .6 of a mile. That is our first ratio.

1 km.6 mile

Next, we have to look at how many kilometers, Randy actually ran. He ran 20 kilometers. We are looking for his miles. That forms our second ratio, and we can now write a proportion.

1 km.6 mile=20 kmx miles

Lastly, we cross multiply and solve for x\begin{align*}x\end{align*}.

20×.6=x miles\begin{align*}20 \times .6 = x \ miles\end{align*}

Randy ran 12 miles in his race.

Notice that we solved this problems by using ratios and proportions. As long as you keep in mind what you are comparing, you can solve any measurement conversion problem in this way!

Solve each by using benchmarks.

#### Example A

John ran 5 kilometers. How many miles did he run?

Solution: 3.1 miles

#### Example B

Kary measured out 12 inches on a ruler. About how many centimeters would that be?

Solution: 30 cm

#### Example C

Sandy ran 15 meters. About how many feet is that?

Solution: 45 feet

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

Use an estimated conversion factor to write a ratio. We will compare kilograms to pounds. One kilogram is about 2 pounds, or 1 kilogram2 pounds\begin{align*}\frac{1 \ kilogram}{2 \ pounds}\end{align*}.

Next, write a proportion and solve.

1 kilogram2 poundsx(2)2xx=x kilograms30 pounds=1(30)=30=15

Omar’s dog weighs about 15 kilograms.

### 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.

How many meters are in 67 feet?

Solution

20.421\begin{align*}20.421\end{align*}

### Practice

Directions: Answer each question by using benchmarks.

1. About how many centimeters is in one inch?
2. About how many centimeters is in three inches?
3. About how many inches is in 5 centimeters?
4. About how many centimeters is in 1 foot?
5. About how many centimeters is in 3 feet?
6. About how many centimeters is in 1 yard?
7. About how many meters are there in one yard?
8. About how many meters are there in three yards?
9. About how many yards are there in twenty -four meters?
10. About how many feet are there in eighteen meters?
11. About how many kilometers are there in 1.8 miles?
12. About how many miles are there in 10 kilometers?
13. About how many miles are there in 30 kilometers?
14. About how many miles are there in 15 kilometers?
15. About how many kilometers are there in 10 miles?

### Vocabulary Language: English

Customary System

Customary System

The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc.
Metric System

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.
Proportion

Proportion

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

Ratio

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