# 2.21: Conversions of Length, Mass, Capacity in Metric Units

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

**Practice**Conversions of Length, Mass, Capacity in Metric Units

While Kara was at the exhibit on the solar system, she also noticed that the exhibit listed distances in metric units as well as standard units.

The distance from Earth to Saturn is 1,427,000,000 km.

Can you convert this measure to meters?

**This Concept is about converting among metric units of measure. You will know how to solve this dilemma by the end of it.**

### Guidance

**As we have seen, the metric system of measurement is based on powers of 10. When you have a measurement in one unit, we convert it to another unit by either multiplying or dividing by some power of 10.**

To get from kilometers to meters, multiply by 1,000. Working backwards, to get from kilometers to meters, *divide* by 1,000. To get from kilometers to millimeters, we divide by \begin{align*}1,000,000 \ (1,000 \times 1,000)\end{align*}. When converting among measurements, use prefixes as a guide in multiplying or dividing by powers of 10.

**Then you can ask yourself, “Am I moving from a smaller unit to a larger unit, or from a larger unit to a smaller unit?”**

**If the units you’re converting to are smaller,** *multiply***.**

**If the units you’re converting to are larger,** *divide***.**

**Now try to do some conversions without using the conversion chart. If you remember the rules of moving the decimal point, you should be able to do these quite easily. Keep in mind the relationship between the powers of 10 and moving the decimal point to the right or left.**

**Dividing by 1,000, for instance, has the same effect as moving the decimal point three places to the left. Similarly, multiplying by 1,000 has the same effect as moving the decimal point three places to the right.**

**Here is one to look at.**

Convert the following measurements to centimeters, 525 meters

**There are 100 centimeters in a meter, so to go from meters to centimeters, we multiply by 100 or move the decimal point two places to the right.**

**The answer is 52,500 cm.**

**Let's look at another one.**

Convert the following measurements into kilograms, 95231 milligrams

**To move from milligrams to kilograms, we divide by 1,000,000 (1,000 milligrams in a gram \begin{align*}\times\end{align*} 1,000 grams in a kilogram), or move the decimal point six places to the left.**

**Our answer is .095231 kg.**

Now it is time to practice what you have learned. Here is a table to help you.

\begin{align*}&\text{KM to M} && \times 1000\\ &\text{M to CM} && \times 100\\ &\text{CM to MM} && \times 10\\ &\text{MM to CM} && \div 10\\ &\text{CM to M} && \div 100\\ &\text{M to KM} && \div 1000\end{align*}

Practice converting the following units by moving the decimal point.

#### Example A

500 m =_____ cm

**Solution: \begin{align*}50,000\end{align*}**

#### Example B

120 m = _____ km

**Solution: \begin{align*}.12\end{align*}**

#### Example C

50 cm = _____m

**Solution: \begin{align*}.5\end{align*}**

Here is the original problem once again.

While Kara was at the exhibit on the solar system, she also noticed that the exhibit listed distances in metric units as well as standard units.

The distance from Earth to Saturn is 1,427,000,000 km.

Can you convert this measure to meters?

To convert from kilometers to meters, we multiply by 1000.

\begin{align*}1,427,000,000 \times 1000 = 1,427,000,000,000\end{align*}

Wow! That is a lot of zeros.

Let's write the value in scientific notation.

\begin{align*}1.427000 \times 10^9\end{align*}

**This is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Metric System
- a system of measurement developed by the French. Some units include meters, grams and liters.

- Customary System
- a system of measurement common in the United States. Some units include feet, pounds and gallons.

- Estimate
- to find an approximate measurement, useful in figuring out a reasonable number and not an exact one.

- Equivalence
- means equal.

### Guided Practice

Here is one for you to try on your own.

Convert 150 m to cm.

**Answer**

To convert these units, we are going from a larger unit to a smaller unit.

When we convert from meters to centimeters, we multiply by 100.

\begin{align*}150 \times 100 = 15,000\end{align*}

**This is our answer.**

### Video Review

Here is a video for review.

- This is a James Sousa video on converting between metric units of measure.

### Practice

Directions: Convert the following metric units of length.

1. 10 cm to millimeters

2. 100 kilometers to meters

3. 453 meters to kilometers

4. 1,567 kilometers to meters

5. 6700 centimeters to meters

6. 7.8 meters to centimeters

Directions: Convert the following measurements into milliliters.

7. 65.57 liters

8. 28.203 centiliters

9. 0.009761 kiloliters

Directions: Convert the following measurements into centigrams.

10. 29.467 grams

11. 0.0562 milligrams

12. .0450584 kilograms

Directions: Convert the following measurements into kiloliters.

13. 89.96 liters

14. 45,217 milliliters

15. 3,120,700 centiliters

### Image Attributions

Here you'll learn to convert among metric units of measure using powers of 10.