Have you ever used metrics in a real-world problem? Take a look at this situation.

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?

Many situations require metric conversions. This Concept will show you how to do this in relation to real-world dilemmas.

### 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 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.

This is especially useful when converting metric units of measurement in real-world problems. Take a look at this dilemma.

**A scale model of a building has a height of 1.5 meters. The scale of the model is 1 cm = 0.5 m. What is the actual height of the building?**

**The scale is in centimeters, but the scale model height is given in meters. First convert the scale height to centimeters. Then find the height of the building.**

\begin{align*}\frac{1 \ meter}{100 \ centimeters} = \frac{1.5 \ meters}{x \ centimeters}\end{align*}

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

\begin{align*}(1)x &= 100(1.5)\\ x &= 150\end{align*}

**The height of the scale model is 150 centimeters. Now find the height of the actual building.**

\begin{align*}\frac{1 \ centimeter}{0.5 \ meter} = \frac{150 \ centimeters}{x \ meters}\end{align*}

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

\begin{align*}(1)x &= 150(0.5)\\ x &= 75\end{align*}

**The actual building is 75 meters tall.**

Figure out the actual measurements if the scale is \begin{align*}1 cm = .5 m\end{align*}.

#### Example A

If the scale measurement is 3.2 meters, what is the actual measurement?

**Solution: \begin{align*}160 m\end{align*}**

#### Example B

If the scale measurement is .75 meters, what is the actual measurement?

**Solution: \begin{align*}37.5 m\end{align*}**

#### Example C

If the scale measurement is .25 m, what is the actual measurement?

**Solution: \begin{align*}12.5 m\end{align*}**

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

**First, notice that there are two parts to this problem. First, let’s figure out how many milliliters are equal to 3.5 liters.**

There are 1000 milliliters in one liter.

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

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

\begin{align*}3500 \ mL = x\end{align*}

**Now we can work on figuring out the number of containers Jessica will need.** Each container holds 100 mL. We can divide 3500 mL by 100 mL.

\begin{align*}3500 \div 100 = 35 \ containers\end{align*}

**Jessica will need 35 containers to hold all of the liquid.**

### 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.

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. Figure out how much of the beef Marcy needs for her recipe.

**Solution**

**First, let’s think about the difference between grams and kilograms. We can call this scaling because we are comparing one measurement to another.**

There are 1000 grams in 1 kilogram. We can write that as our first ratio.

\begin{align*}\frac{1000 \ grams}{1 \ kilogram}\end{align*}

Now we know that Marcy has 1.5 kilograms of beef and she needs 900 grams. Next, we need to convert the kilograms that Marcy has to grams so we can figure out how much of the whole she will need.

**We write a proportion.**

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

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

\begin{align*}1500 \ g = x\end{align*}

**Now let’s think about Marcy.** She has 1500 grams of meat, but only needs 900 grams. **She will have 600 grams of meat left over.**

### Video Review

Converting Between Metric Units

### Practice

Directions: Figure out the actual measurements if the scale is \begin{align*}1 cm = .5 m\end{align*}.

- 3.5 m
- 10 m
- 6.5 m
- .5 m
- 2.5 m
- 2.2 m
- 4.5 m
- 4 m
- 3 m
- 11 m

Directions: Solve each problem.

- A recipe calls for 400 grams of flour. If Leena makes one quarter of the recipe, how many kilograms of flour will she need?
- Two buildings are 9 centimeters apart on a map. The scale of the map is 0.5 centimeter = 2 kilometers. What is the actual distance between the two buildings in meters?
- A scale model of a tower is 1.25 meters tall. The scale of the model is 0.5 cm = 5 meters. What is the actual height of the tower in meters?
- 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 1 centimeter = 2 meters, what is the area of the meeting room in square centimeters?
- Samir ran a race that was 10 kilometers long. About how many meters did Samir run?