# 4.20: Equivalent Metric Units of Mass

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

**Practice**Equivalent Metric Units of Mass

Have you ever been to a metric playground? Can you imagine the types of metric problems that would be there?

Mrs. Andersen and her class are about to visit one at the science museum.

Mrs. Andersen’s class is having a great time at the science museum. Sam and Olivia are very excited when the group comes upon the metric playground. This playground has been built inside the museum and combines playground toys with metrics. The first one that they try is the metric seesaw. Sam sits on one side of the seesaw and Olivia sits on the other side. Since they weigh about the same, it is easy to keep the seesaw balanced. Under Sam, there is a digital scale. Under Olivia there is the same scale with a key pad. Sam’s weight shows up under the scale. Sam weighs 37 kg. “Next, we have to convert kilograms to grams and punch it in so both of our scales will have the same reading,” Sam tells Olivia.

Olivia pauses, she can’t remember how to do this.

**In this Concept, you will learn to work with equivalent metric units of mass. Then you'll know how Olivia and Sam can solve this dilemma.**

### Guidance

When people work with topics in science they use a system called the ** Metric system**. In the metric system we use different standard units to measure mass or weight.

This text box lists the units of measuring mass from the largest unit, the kilogram, to the smallest unit, the milligram. If you think back to when you learned about measuring length, the prefix “milli” indicated a very small unit. That is the same here as we measure mass.

**How can we find equivalent metric units of mass?**

The word ** equivalent** means equal. We can compare different units of measuring mass with kilograms, grams and milligrams. To do this, we need to know how many grams equal one kilogram, how many milligrams equal one gram, etc. Here is a chart to help us understand equivalent units.

Here you can see that when we convert **kilograms to grams you multiply by 1000.**

When you convert **grams to milligrams, you multiply by 1000.**

**To convert from a large unit to a small unit, we multiply.**

**To convert from a small unit to a large unit, we divide.**

5 kg = _____ g

When we go from kilograms to grams, we multiply by 1000.

5 kg = 5000 g

These two values are equivalent.

2000 mg = _____ g

When we go from milligrams to grams, we divide.

2000 mg = 2 g

These two values are equivalent.

Now it is your turn to practice. Convert each metric unit of mass to its equivalent.

#### Example A

6 kg = _____ g

**Solution: 6000**

#### Example B

3000 g = _____ kg

**Solution: 3**

#### Example C

4 g = _____ mg

**Solution: 4000**

Remember back to the metric park? Well, now you are ready to help Sam and Olivia with those conversions.

To solve this problem, Sam and Olivia need to convert 37 kg into grams. There are 1000 grams in 1 kilogram, so there are 37,000 grams in 37 kilograms.

Sam and Olivia need to multiply the number of kilograms, 37 by the number of grams in 1 kilogram, 1000 to get their answer.

**You can see why it makes so much more sense to measure someone’s weight in kilograms versus grams.**

### Vocabulary

Here are the vocabulary words found in this Concept.

- Customary System
- The system of measurement common in the United States, uses feet, inches, pounds, cups, gallons, etc.

- Mass
- the weight of an object

### Guided Practice

Here is one for you to try on your own.

How many grams are in 18 kilograms?

**Answer**

To figure this out, we have to use the equivalents presented in the Concept.

There are 1000 grams in 1 kilogram.

We can multiply \begin{align*}18 \times 1000\end{align*}.

**Our answer is 18,000 grams.**

### Video Review

Here are videos for review.

Khan Academy Conversion Between Metric Units

James Sousa Metric Unit Conversions

### Practice

Directions: Convert to an equivalent unit for each given unit of mass.

1. 5 kg = ______ g

2. 2000 g = ______ kg

3. 2500 g = ______ kg

4. 10 kg = ______ g

5. 2000 mg = ______ g

6. 30 g = ______ mg

7. 4500 mg = ______ g

8. 6.7 g = ______ mg

9. 9 kg = ______ g

10. 10 g = ______ kg

11. 1 kg = ______ mg

12. 5000 mg = ______ g

13. 7500 g = ______ kg

14. 8200 g = ______ kg

15. 15 kg = ______ g

16. 1600 g = ______ mg

### Image Attributions

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