# 4.16: Mental Math to Divide by Decimal Powers of Ten

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

**Practice**Mental Math to Divide by Decimal Powers of Ten

Have you ever had to do math homework on the bus? Well it isn't the best place for it, but Kelsey is trying to do just that. Take a look.

On the morning after the trip to the museum, Kelsey realized that she had forgotten to do her math homework. She took out her math notebook on the bus. Everything was going fine until she saw this problem.

\begin{align*}.3456 \div .1000\end{align*}

Kelsey isn't sure how to solve this problem, but she is sure that she can solve it in her head. Do you know?

**This Concept will teach you how to use mental math to divide by decimal powers of ten. Then we'll come back to the homework.**

### Guidance

You have already learned how to multiply by what appears to be a power of ten after a decimal place. Remember that all powers of ten that you see written to the right of a decimal point are equal.

.10 = .100 = .1000 = .10000

**When we multiply by this power of ten to the right a decimal point, we move the decimal point one place to the left.**

**When we divide by a power of ten to the right a decimal point, we are going to move the decimal point one place to the right.**

If you think about this it makes perfect sense. The powers of ten written to the right of a decimal point are all equal. It doesn’t matter if you are multiplying or dividing by .10 or .100 or .1000. Division is the opposite of multiplication so you move the decimal point one place to the right.

\begin{align*}5.2 \div .10 & = 52\\ 5.2 \div .100 & = 52\\ 5.2 \div .1000 & = 52\end{align*}

**Once you have learned the rule, you can use mental math to complete the division of decimals by a power of ten.**

Practice using mental math to divide these decimals.

#### Example A

.67 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} _____

**Solution: 6.7**

#### Example B

12.3 \begin{align*}\div\end{align*} .100 \begin{align*}=\end{align*} _____

**Solution: 123**

#### Example C

4.567 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} _____

**Solution: 45.67**

Now back to the math homework. Here is the original problem once again.

On the morning after the trip to the museum, Kelsey realized that she had forgotten to do her math homework. She took out her math notebook on the bus. Everything was going fine until she saw this problem.

\begin{align*}.3456 \div .1000\end{align*}

Kelsey isn't sure how to solve this problem, but she is sure that she can solve it in her head.

Kelsey is right. She can solve it by simply moving the decimal point.

\begin{align*}.3456 \div .1000 = 3.456\end{align*}

**This is the answer.**

### Vocabulary

Here are the vocabulary words found in this Concept.

- Power of ten
- 10, 100, 1000, 10,000 - you can think of them as multiples of ten.

- Scientific notation
- a way to write decimals and numbers by writing a number sentence that shows a power of ten using an exponent.

**Remember:**

Multiplying by a power of ten with a positive exponent means the decimal point was moved to the right.

Multiplying by a power of ten with a negative exponent means the decimal point was moved to the left.

### Guided Practice

Here is one for you to try on your own.

.7893 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} _____

**Answer**

To complete this problem, we move the decimal point one place to the right.

**Our answer is \begin{align*}7.893\end{align*}.**

### Video Review

Here are a few videos for review.

James Sousa Dividing by Powers of Ten

Other Videos:

http://www.mathplayground.com/howto_dividedecimalspower10.html – Good basic video on how to divide decimals by a power of ten

### Practice

Directions: Use mental math to divide each decimal by a decimal power of ten.

1. 6.7 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

2. .654 \begin{align*}\div\end{align*} .100 \begin{align*}=\end{align*} ______

3. 2.1 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

4. 4.32 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} ______

5. .98765 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

6. .987 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

7. .045 \begin{align*}\div\end{align*} .100 \begin{align*}=\end{align*} ______

8. .00098 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

9. .000987 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} ______

10. 6.73 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

11. 12.3 \begin{align*}\div\end{align*} .100 \begin{align*}=\end{align*} ______

12. 456 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} ______

13. 67 \begin{align*}\div\end{align*} .10 \begin{align*}=\end{align*} ______

14. 770 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} ______

15. 234 \begin{align*}\div\end{align*} .100 \begin{align*}=\end{align*} ______

16. 1899 \begin{align*}\div\end{align*} .1000 \begin{align*}=\end{align*} ______

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Powers of ten

The powers of ten are 10, 100, 1000, 10,000, etc. They are ten to the first power, ten to the second power, ten to the third power, etc.Scientific Notation

Scientific notation is a means of representing a number as a product of a number that is at least 1 but less than 10 and a power of 10.### Image Attributions

Here you'll learn how to divide by decimal powers of ten.