Juliana wants to build a doghouse. She has a few long pieces of wood. Her instructions say that she needs to cut one of the boards in to a piece that is 200 centimeters long, but she only has a meter stick. She wants to figure out if she can measure the entire length using only the meter stick. How can she compare the 200 cm to the meter stick?

In this concept, you will learn how to compare measurements that have different units.

### Comparing Measurements of Different Units

The word **equivalent** means equal.

Here is a measurement chart of equivalent measurements.

\begin{align*}1 \ cm & = 10 \ mm\\ 1 \ m & = 100 \ cm\\ 1 \ m & = 1000\ mm\\ 1 \ km & = 1000\ m\end{align*}

Let’s say that you wanted to compare two different units to figure out which is greater and which is less. You can use the chart to help you.

5 cm ______ 70 mm

The first thing that you need to do is convert the measurements so that the unit of measurement is the same.

You need to have either all mm or all cm. It doesn’t matter which one you choose, as long as it is the same unit. Let’s use cm.

\begin{align*}70 \ mm &= \underline{\;\;\;\;\;\;\;\;\;\;} \ cm\\ 70 \div 10 &= 7\end{align*}

70 mm = 7 cm.

Let’s rewrite the problem.

5 cm ______ 7 cm

Use greater than >, less than < or equal to = to compare the measurements.

5 cm < 7 cm

The answer is 5 cm < 70 mm.

Let's try an example.

7000 m ______ 8 km

Here you have two different units of measurement. You have meters and kilometers.

First, convert both to the same unit. Let’s convert to meters this time.

8 km \begin{align*}=\end{align*} 8 \begin{align*}\times\end{align*} 1000 \begin{align*}=\end{align*} 8000 m

Then, compare.

7000 m < 8000 m

The answer is 7000 m is less than 8 km.

### Examples

#### Example 1

Earlier, you were given a problem about Juliana's doghouse.

She needs to measure 200 cm, and she only has a meter stick. How does 200 cm compare to 1 m?

200 cm _____ 1 meter

First, decide which unit of measurement you would like to use.

m

Next, convert cm to m.

200 cm \begin{align*}\div \end{align*} 100 = 2 m

Then, compare the two measurements.

2 m > 1 m

The answer is that 2 m is greater than 1 m. Juliana can measure 200 cm with the meter stick, but she would need to use the meter stick twice.

#### Example 2

Convert and compare the pair of measurements.

12 m ______ 1000 mm

First, decide which unit of measurement you would like to use.

mm

Next, convert the m to mm.

12 m \begin{align*}\times \end{align*} 1000 = 12,000mm

Then, compare the measurements.

12,000 mm > 1000 mm

The answer is 12 m is greater than 1000 mm.

#### Example 3

Convert and compare the pair of measurements.

7 m ______ 7000 mm

First, decide which unit of measurement you would like to use.

mm

Next, convert the m to mm.

7 m \begin{align*}\times \end{align*} 1000 = 7000mm

Then, compare the two measurements.

7000 m = 7000 m

The answer is that 7m is equal to 7000 mm.

#### Example 4

Convert and compare the pair of measurements.

3 km ______ 3300 m

First, decide which unit of measurement you would like to use.

m

Next, convert the km to m.

3 km \begin{align*}\times \end{align*} 1000 = 3000 m

Then, compare the two measurements.

3000 m < 3300 m

The answer is that 3 km is less than 3300 m.

#### Example 5

Convert and compare the pair of measurements.

1000 mm ______ 20 cm

First, decide which unit of measurement you would like to use.

cm

Next, convert mm to cm

1000 mm \begin{align*}\div \end{align*} 10 = 100 cm

Then, compare the two measurements.

100 cm > 20 cm

The answer is 1000 mm is greater than 20 cm.

### Review

Compare metric lengths using <, >, or =

- 6 cm ______ 60 mm
- 8 cm ______ 90 mm
- 10 mm ______ 4 cm
- 40 mm ______ 6 cm
- 5 km ______ 4000 m
- 7 km ______ 7500 m
- 11 m ______ 1200 cm
- 9 km ______ 9000 m
- 100 mm ______ 750 cm
- 18 km ______ 1500 m
- 1000 m ______ 19 km
- 10 m ______ 100 cm
- .25 m _______ 1 km
- 6 km ______ 6000 m
- 7 km ______ 8000 m

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.9.