# 3.5: Equivalent Metric Units of Length

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

**Practice**Equivalent Metric Units of Length

Have you ever had to measure distances in metrics? Have you ever made a map?

Well, Julie is working on math that shows the distance from the local high school to the ice cream stand. She began by going to the town hall to look at maps and distances of her town. She figured out that it is 6500 meters from the ice cream stand to the high school.

Julie thinks that meters is a strange way to write this measurement. She would much rather use kilometers.

How can she do this? Is it possible?

**This is where you come in. This Concept is all about equivalent metric units of length. Pay attention and you will be able to help Julie at the end of the Concept.**

### Guidance

This Concept focuses on metric units of measurements.

**What are the metric units for measuring length?**

When measuring ** length**, we are measuring how long something is, or you could say we are measuring from one end to the other end. That is the length of the item.

**Here are the common metric units of length from the smallest unit to the largest unit.**

*Millimeter*

*Centimeter*

*Meter*

*Kilometer*

A ** millimeter** is the smallest unit. Millimeters are most useful when measuring really tiny things. You can find millimeters on some rulers.

A ** centimeter** is the next smallest unit. Centimeters can also be found on a ruler.

A ** meter** is a little more than 3 feet. A meter is a unit that would be very helpful to a carpenter or to someone working in construction.

A ** kilometer** is used to measure longer distances. You often hear the word kilometer mentioned when talking about a road race that is 5k (or 5 kilometers) long.

**How can we convert metric units of length?**

When working with the customary units of length: inches, feet, etc., we know that we can convert them from one to another to change the units we are working with. For example, if you have 24 inches, it might make more sense to say that we have 2 feet. We can do the same thing when working with metric units. Here is a chart to help us with the conversions.

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

Now that you know the conversions, we can change one unit to another unit.

5 km = ____ m

Here we are converting kilometers to meters.

**How can we convert larger units to smaller units?**

We can convert larger units to smaller units by multiplying. There are 1000 meters in one kilometer.

\begin{align*}5 \ km &= \underline{\;\;\;\;\;\;\;\;\;\;} \ m\\ 5 \times 1000 &= 5000 \ m\end{align*}

**Our answer is 5000 m.**

600 cm = ______ m

Here we are converting smaller units to larger units.

**How can we convert smaller units to larger units?**

We can convert smaller units to larger units by dividing. There are 100 cm in one meter.

600 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} 6

**Our answer is 6.**

Now let's practice. Find each equivalent unit.

#### Example A

**2000 mm = ______ cm**

**Solution: 200**

#### Example B

**3 km = ______ m**

**Solution: 3000**

#### Example C

**4000 cm = ______ m**

**Solution: 40**

Do you know how to help Julie with her measurement? Let's go back and look at the original problem.

Well, Julie is working on math that shows the distance from the local high school to the ice cream stand. She began by going to the town hall to look at maps and distances of her town. She figured out that it is 6500 meters from the ice cream stand to the high school.

Julie thinks that meters is a strange way to write this measurement. She would much rather use kilometers.

How can she do this? Is it possible?

First, let's think about the measurement that Julie knows. She knows that it is 6500 meters from the ice cream stand to the high school. Julie wants to convert this measurement into kilometers.

To do this, let's write down the equivalent measure from meters to kilometers.

**There are 1000 meters in 1 kilometer.**

Next, we can convert 6500 meters into kilometers. When we convert from a small unit to a larger unit, we divide.

We can divide 6500 by 1000.

**Our answer is \begin{align*}6.5\end{align*}.**

**It is \begin{align*}6.5\end{align*} kilometers from the ice cream stand to the high school.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Metric System
- a system of measurement

- Length
- the measurement of a object or distance from one end to the other

- Millimeter
- the smallest common metric unit of measuring length, found on a ruler

- Centimeter
- a small unit of measuring length, found on a ruler

- Meter
- approximately 3 feet, measured using a meter stick

- Kilometer
- a measurement used to measure longer distances, the largest common metric unit of measuring length

### Guided Practice

Here is one for you to try on your own.

Mark has measured his walkway using a meter stick. Mark has measured that his walkway is 6 meters long. How many centimeters is Mark's walkway? How many millimeters?

**Answer**

There are two answers to this problem. Let's begin by thinking about the equivalent units.

1 meter = 100 cm

1 cm = 10 mm

Let's convert from meters to centimeters first. When you convert from a larger unit to a smaller unit, we multiply.

\begin{align*}6 \times 100 = 600\end{align*}

**Mark's walkway is 600 centimeters.**

Now we can convert from centimeters to millimeters.

\begin{align*}600 \times 10 = 6000\end{align*}

**Mark's walkway is 6000 millimeters.**

### Video Review

Here are two videos for review.

James Sousa, Converting Between Metric Units

Other Videos:

- http://www.mathplayground.com/howto_Metric.html – This video expands on the basic information of the metric system. It also begins working with metric conversions.

### Practice

Directions: Complete the following metric equivalents.

1. 6 km = ______ m

2. 5 m = ______ cm

3. 100 cm = ______ m

4. 400 cm = ______ m

5. 9 km = ______ m

6. 2000 m = ______ km

7. 20 mm = ______ cm

8. 8 cm = ______ mm

9. 900 cm = ______ m

10. 12 m = ______ cm

11. 10 cm = ______ mm

12. 100 cm = _____ mm

13. 6700 m = ______ km

14. 8200 m = ______ km

15. 12,500 m = ______ km

Centimeter

A centimeter is a very small unit of metric measure. A centimeter is one hundredth of one meter.Kilometer

A kilometer is a common metric unit of length that is equal to 1,000 meters.Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.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.Millimeter

A millimeter is the smallest common metric unit of length.### Image Attributions

Here you'll learn to identify equivalent metric units of length.

## Concept Nodes:

Centimeter

A centimeter is a very small unit of metric measure. A centimeter is one hundredth of one meter.Kilometer

A kilometer is a common metric unit of length that is equal to 1,000 meters.Length

Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles.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.Millimeter

A millimeter is the smallest common metric unit of length.