# 3.9: Metric Length Comparison

**At Grade**Created by: CK-12

**Practice**Metric Length Comparison

Have you ever had to compare metric units of length? Have you ever been confused by metrics?

Julie is really enjoying working at the ice cream stand. She loves talking with the people and the ice cream snacks are definitely a benefit. However, she is very confused about the size of the ice cream cones. Mr. Harris, the stand owner, used to be a math teacher so he loves to have fun with the customers. Because of this, the stand serves cones in different measurement units. It is famous for its mathematical ice cream cones. This has been very frustrating for Julie. Yesterday, a customer wanted to know whether a Kiddie Cone 1 was smaller or larger than a Kiddie Cone 2. One is in centimeters and one is in millimeters.

Kiddie cone 1 = 80 mm

Kiddie cone 2 = 6 cm

Julie needs to understand these measurements so that she can compare them. Then she will be able to give an answer to the customer.

**Pay attention and you will be able to help Julie with this dilemma at the end of the Concept.**

### Guidance

In an earlier Concept, you learned how to convert metric lengths. You learned that there are 10 millimeters in one centimeter and that you can change millimeters to centimeters by dividing. You also learned that we can change centimeters to millimeters by multiplying.

We can call these measurements *equivalents.*

The word equivalent means equal. When we know which measurement is equal to another measurement, then we can tell what is equal to what.

Here is a measurement chart of equivalents.

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

Let’s say that we wanted to compare two different units to figure out which is greater and which is less. We could use the chart to help us.

5 cm ______ 70 mm

How can we successfully compare these two values?

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

Here we have cm and mm. We need to have either all mm or all cm. It doesn’t matter which one we 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*}

Our answer is 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

So 5 cm < 70 mm

*Take a minute to write down a few notes on these steps.*

Here is another one.

7000 m ______ 8 km

Here we have two different units of measurement. We have meters and kilometers. Our first step is to 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

Now we can compare.

7000 m < 8000 m

**Our answer is 7000 m < 8 km.**

Now let's practice. Convert and compare each pair of measurements.

#### Example A

**7 m ______ 7000 mm**

**Solution: =**

#### Example B

**3 km ______ 3300 m**

**Solution: <**

#### Example C

**1000 mm ______ 20 cm**

**Solution: >**

Do you know how to help Julie? Here is the original problem once again.

**Let’s look at the first customer’s question.**

**The first customer is comparing Kiddie Cone 1 with Kiddie Cone 2. Let’s look at the measurements for each of these cones.**

Kiddie Cone 1 = 80 mm

Kiddie Cone 2 = 6 cm

We need to convert the units both to millimeters or both to centimeters. Let’s use cm. We go from a smaller unit to a larger unit so we divide. There are 10 mm in 1 centimeters therefore we divide by 10.

80 \begin{align*}\div\end{align*} 10 = 8

Kiddie Cone 1 = 8 cm

Kiddie Cone 2 = 6 cm

8 > 6

**Kiddie Cone 1 is greater than Kiddie Cone 2.**

### Vocabulary

Here are the vocabulary words that are used in this Concept.

- Equivalent
- means equal

- Comparing
- using greater than, less than or equal to so that we can compare numbers

### Guided Practice

Here is one for you to try on your own.

Which is greater 12 meters or 1000 millimeters?

**Answer**

To figure this out, we first have to think about equivalent metric units.

There are 1000 millimeters in 1 meter, so 12 meters is definitely greater than 1000 millimeters.

\begin{align*}12 m > 1000 mm\end{align*}

**This is our answer.**

### Video Review

Here is a video for review.

James Sousa: Metric Unit Conversion

### Practice

Directions: Compare metric lengths using <, >, or =

1. 6 cm ______ 60 mm

2. 8 cm ______ 90 mm

3. 10 mm ______ 4 cm

4. 40 mm ______ 6 cm

5. 5 km ______ 4000 m

6. 7 km ______ 7500 m

7. 11 m ______ 1200 cm

8. 9 km ______ 9000 m

9. 100 mm ______ 750 cm

10. 18 km ______ 1500 m

11. 1000 m ______ 19 km

12. 10 m ______ 100 cm

13. .25 m _______ 1 km

14. 6 km ______ 6000 m

15. 7 km ______ 8000 m

### Image Attributions

Here you'll learn how to compare metric lengths.