Remember Julie and the ice cream stand in the Identify Equivalence of Metric Units of Length Concept?

Julie was very excited to realize that the ice cream stand was so close to the high school.

"It is a little more than a 5k race," Julie told Jose as he looked at his science book. "What are you looking at?"

"Well, this is an organism from the ocean that is 5 mm in size," Jose said showing her the book.

Julie looked at the book at the magnified picture of the organism. She began to think and wonder how many centimeters the organism would be if it were measured in centimeters instead of millimeters.

Have you ever wondered anything like this? Maybe or maybe not. Either way, that is the task ahead of you.

**This Concept will show you how to find equivalent measures like this one.**

### Guidance

Sometimes when we convert metric units we don’t have a whole number answer. In the last Concept you saw this a little bit when Julie was measuring from meters to kilometers. We ended up with a decimal answer of 6.5 kilometers. This can happen quite often.

2000 mm = 200 cm

These are both whole numbers.

**What happens when we convert smaller units to larger units and they don’t end up as a whole number?**

When this happens, we end up with an answer that is a decimal. If we remember our rules for working with decimals and place value, we can be very successful at converting these small units of measurement to larger units.

1 mm = ______ cm

Here we are converting a smaller unit to a larger unit, because of this we know that we are going to divide. There are 10 mm in one centimeter, so we are going to divide 1 by 10. Think about this, we are dividing 1 whole into 10 parts-our answer is definitely going to be a decimal.

1 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} .1 (one-tenth)

**Our answer is that 1 mm = .1 cm.**

**We can also round our answer to the nearest tenth.**

What if we had a problem where we wanted to convert 1.5 mm to cm?

1.5 mm = ______ cm

Once again, we are going to be dividing by 10. When we divide by 10 in this example we end up with an answer of .15

**1.5 mm = .15 cm**

**We can round this answer to the nearest tenth.**

**.15 rounds to .2**

**We can say that .2 is the closest tenth of a cm to 1.5 mm.** **Just as we were able to round whole numbers, we can round decimal measurements too.**

Now let's practice.

#### Example A

**2 m = ______ km**

**Solution: .002**

#### Example B

**8 mm = ______ cm**

**Solution: .8**

#### Example C

**4 cm = ______ m**

**Solution: .04**

Remember the organism? Well, here is the original problem once again. You should now have a good idea how to solve it.

Julie was very excited to realize that the ice cream stand was so close to the high school.

"It is a little more than a 5k race," Julie told Jose as he looked at his science book. "What are you looking at?"

"Well, this is an organism from the ocean that is 5 mm in size," Jose said showing her the book.

Julie looked at the book at the magnified picture of the organism. She began to think and wonder how many centimeters the organism would be if it were measured in centimeters instead of millimeters.

To solve this, we need to convert 5 mm into centimeters. There are 10 mm in one centimeter.

We can start by dividing 5 mm by 10.

**Our answer is \begin{align*}0.5\end{align*} centimeters.**

### Vocabulary

- 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.

1 m = ______ km

**Answer**

Here we are converting a smaller unit to a larger unit. There are 1000 meters in one kilometer. We divide by 1000.

**1 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} .001**

**Here our answer is one-thousandth of a kilometer.**

### Video 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.
- http://www.teachertube.com/viewVideo.php?video_id=8896 – The Metric System song to “Arms Wide Open” by Creed this is sung by two science teachers.

### Practice

Directions: Write each decimal conversion. Round to the nearest hundredth when necessary.

1. 1 mm = ______ cm

2. 5 mm = ______ cm

3. 10 mm = ______ cm

4. 15 mm = ______ cm

5. 8 cm = ______ m

6. 9 cm = ______ m

7. 11 cm = ______ m

8. 22 cm = ______ m

9. 12 m = ______ km

10. 8 m = ______ km

11. 22 mm = ______ cm

12. 225 mm = ______ cm

13. 543 mm = ______ cm

14. 987 mm = ______ cm

15. 1234 mm = ______ cm