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# Applications of Metric Unit Conversions

## Convert between measures in word problems

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Practice Applications of Metric Unit Conversions

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Convert Metric Units of Measurement in Real-World Situations

Jessica works in a science lab. She needs to convert the liquid measure that she is working with from liters to milliliters. She has been given 3.5 liters to convert. If each container that Jessica has holds 100 milliliters, how many containers will she need?

In this concept, you will learn to convert metric units of measurement in real-world situations.

### Converting Metric Units of Measurements

The metric system of measurement is the primary measurement system in many countries; it contains units such as meters, kilometers and liters. Let’s review the metric units of measurement.

#### Metric Units of Measurement

Now, let’s look at a real-world problem involving converting metric units.

A scale model of a building has a height of 1.5 meters. The scale of the model is \begin{align*}1 \ cm = 0.5 \ m\end{align*}. What is the actual height of the building?

First, set up a proportion to change 1.5 m to cm.

\begin{align*}\frac{100 \ cm}{1 \ m}=\frac{x \ cm}{1.5 \ m}\end{align*}

Next, cross multiply to solve for the number of centimeters for the height of the scale model.

\begin{align*}\begin{array}{rcl} \frac{100}{1} &=& \frac{x}{1.5} \\ 1x &=& 100 \times 1.5 \\ x &=& 150 \end{array}\end{align*}

Next, set up a proportion to find the height of the actual model.

\begin{align*}\frac{1 \ cm}{0.5 \ m}=\frac{150 \ cm}{x \ m}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{0.5} &=& \frac{150}{x} \\ 1x &=& 0.5 \times 150 \\ x &=& 75 \end{array}\end{align*}

The actual height of the building is 75 meters.

### Examples

#### Example 1

Earlier, you were given a problem about Jessica’s scientific measurements.

Jessica is given 3.5 L of liquid and needs to fill containers with 100 mL each. Jessica needs to know how many containers she will need.

First, set up a proportion to change 3.5 L to mL.

\begin{align*}\frac{1000 \ mL}{1 \ L}=\frac{x \ mL}{3.5 \ L}\end{align*}

Next, cross multiply to solve for the number of milliliters Jessica has.

\begin{align*}\begin{array}{rcl} \frac{1000}{1} &=& \frac{x}{3.5} \\ 1x &=& 1000 \times 3.5 \\ x &=& 3500 \end{array}\end{align*}

Next, divide by 100 to find the number of containers.

\begin{align*}\frac{3500 \ mL}{100 \ mL}=35\end{align*}

Jessica will need 35 containers.

#### Example 2

Marcy is making beef stew. Her recipe calls for 900 grams of beef. She looks in the refrigerator and sees that she has 1.5 kilograms of beef wrapped in a package. Marcy isn’t sure how much of the beef she should use. Does Marcy have enough beef for her recipe?

First, set up a proportion to change 1.5 kg to g.

\begin{align*}\frac{1000 \ g}{1 \ kg}=\frac{x \ g}{1.5 \ kg}\end{align*}

Next, cross multiply to solve for the number of grams of beef Marcy has in her refrigerator.

\begin{align*}\begin{array}{rcl} \frac{1000}{1} &=& \frac{x}{1.5} \\ 1x &=& 1000 \times 1.5 \\ x &=& 1500 \end{array}\end{align*}

Marcy has 1500 grams of meat, but only needs 900 grams for her recipe. She will have 600 grams of meat left over.

#### Example 3

If the scale used for a model is \begin{align*}1 \ cm=0.5 \ m\end{align*} and the scale measurement is 3.2 meters, what is the actual measurement?

First, set up a proportion to change 3.2 m to cm.

\begin{align*}\frac{100 \ cm}{1 \ m}=\frac{x \ cm}{3.2 \ m}\end{align*}

Next, cross multiply to solve for the number of centimeters for the height of the scale model.

\begin{align*}\begin{array}{rcl} \frac{100}{1} &=& \frac{x}{3.2} \\ 1x &=& 100 \times 3.2 \\ x &=& 320 \end{array}\end{align*}

Next, set up a proportion to find the height of the actual model.

\begin{align*}\frac{1 \ cm}{0.5 \ m}=\frac{320 \ cm}{x \ m}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{0.5} &=& \frac{320}{x} \\ 1x &=& 0.5 \times 320 \\ x &=& 160 \end{array}\end{align*}

The actual height of the building is 160 meters.

#### Example 4

If the scale used for a model is \begin{align*}1 \ cm = 0.5 \ m\end{align*} and the scale measurement is 0.75 meters, what is the actual measurement?

First, set up a proportion to change 0.75 m to cm.

\begin{align*}\frac{100 \ cm}{1 \ m}=\frac{x \ cm}{0.75 \ m}\end{align*}

Next, cross multiply to solve for the number of centimeters for the height of the scale model.

\begin{align*}\begin{array}{rcl} \frac{100}{1} &=& \frac{x}{0.75} \\ 1x &=& 100 \times 0.75 \\ x &=& 75 \end{array}\end{align*}

Next, set up a proportion to find the height of the actual model.

\begin{align*}\frac{1 \ cm}{0.5 \ m}=\frac{75 \ cm}{x \ m}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{0.5} &=& \frac{75}{x} \\ 1x &=& 0.5 \times 75 \\ x &=& 37.5 \end{array}\end{align*}

The actual height of the building is 37.5 meters.

#### Example 5

If the scale used for a model is \begin{align*}1 \ cm = 0.5 \ m\end{align*} and the scale measurement is 0.25 m, what is the actual measurement?

First, set up a proportion to change 0.25 m to cm.

\begin{align*}\frac{100 \ cm}{1 \ m}=\frac{x \ cm}{0.25 \ m}\end{align*}

Next, cross multiply to solve for the number of centimeters for the height of the scale model.

\begin{align*}\begin{array}{rcl} \frac{100}{1} &=& \frac{x}{0.25} \\ 1x &=& 100 \times 0.25 \\ x &=& 25 \end{array}\end{align*}

Next, set up a proportion to find the height of the actual model.

\begin{align*}\frac{1 \ cm}{0.5 \ m}=\frac{25 \ cm}{x \ m}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{0.5} &=& \frac{25}{x} \\ 1x &=& 0.5 \times 25 \\ x &=& 12.5 \end{array}\end{align*}

The actual height of the building is 12.5 meters.

### Review

Figure out the measurements if the scale is \begin{align*}1 \ cm = 0.5 \ m\end{align*}.

1. 3.5 m

2. 10 m

3. 6.5 m

4. 0.5 m

5. 2.5 m

6. 2.2 m

7. 4.5 m

8. 4 m

9. 3 m

10. 11 m

Solve each problem.

11. A recipe calls for 400 grams of flour. If Leena makes one quarter of the recipe, how many kilograms of flour will she need?

12. Two buildings are 9 centimeters apart on a map. The scale of the map is \begin{align*}0.5 \text{ centimeter} = 2 \text{ kilometers}\end{align*}.. What is the actual distance between the two buildings in meters?

13. A scale model of a tower is 1.25 meters tall. The scale of the model is \begin{align*}0.5 \ cm = 5 \ meters\end{align*}. What is the actual height of the tower in meters?

14. A scale drawing of a conference center includes a meeting room that measures 1.5 centimeters by 2.5 centimeters. If the scale of the drawing is \begin{align*}1 \text{ centimeter} = 2 \text{ meters}\end{align*}, what is the area of the meeting room in square centimeters?

15. Samir ran a race that was 10 kilometers long. About how many meters did Samir run?

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### Vocabulary Language: English

TermDefinition
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.