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Mental Math to Divide by Whole Number Powers of Ten

Find quotients of powers mentally.

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Mental Math to Divide by Whole Number Powers of Ten

Introduction

Hailey has an astronomy question about earth. It is going to involve dividing by whole number powers of ten. Take a look.

What would the diameter of the earth be if it were 100 times smaller?

The diameter of the earth is 12,756.3 km. Hailey knows that she will need to divide, and she thinks that she can use mental math to do it. Do you think that she is right? Pay close attention during this Concept and you will understand how Hailey can solve this problem.

Guided Learning

In the last few Concepts, you learned how to use mental math when multiplying, you can use mental math to divide by whole number powers of ten too.

See if you can see the pattern.

\begin{align*}2.5 \div 10 & = .25\\ 2.5 \div 100 & = .025\\ 2.5 \div 1000 & = .0025\end{align*}

What is the pattern?

When you divide by a power of ten, you move the decimal point to the left according to the number of zeros that are in the power of ten that you are dividing by.

Once you have learned and memorized this rule, you will be able to divide using mental math.

Notice that division is the opposite of multiplication. When we multiplied by a power of ten we moved the decimal point to the right. When we divide by a power of ten, we move the decimal point to the left.

Now it is your turn to practice. Use mental math to divide the following decimals by using powers of ten.

Example A

4.5 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} _____

Solution: _____

Example B

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

Solution: _____

Example C

87.4 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} _____

Solution: _____

Now you are ready to help Hailey with her problem about shrinking the earth.

Hailey’s question asks if what the diameter of the earth would be if it were 100 times smaller. To complete this problem, Hailey needs to divide the diameter of the earth by 100. She will move the decimal point two places to the left.

12,756.3 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} ________

Wow! The earth went from being in the ten-thousands to being in the hundreds. Think about how much smaller that is!

Here is one for you to try on your own.

67.89 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

To divide by a power of ten, we will need to move the decimal point in the dividend. Here we are dividing by 1000, so we move the decimal point three places to the left.

Video Review

Here is a video for review.

Practice Set

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

1. 3.4 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} ______

2. .67 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} _____

3. 8.91 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} _____

4. 12.34 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} _____

5. 67.89 \begin{align*}\div\end{align*} 10 \begin{align*}=\end{align*} _____

6. 67.89 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} ______

7. 32.10 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} ______

8. .568 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} _____

9. 45 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} ______

10. 235 \begin{align*}\div\end{align*} 100 \begin{align*}=\end{align*} ______

11. 67.9 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

12. 4.545 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

13. .457 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

14. 44.57 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

15. 1234.5 \begin{align*}\div\end{align*} 1000 \begin{align*}=\end{align*} _____

16.

 482 ÷  10 = 482 ÷  100 = 482 ÷  1000 =

17.

 40 ÷     10 = 40 ÷     100 = 40 ÷     1000 =

18.

 369.3 ÷     10 = 369.3 ÷     100 = 369.3 ÷     1000 =

Review

• When you divide by a power of ten, you move the decimal point to the left according to the number of zeros that are in the power of ten that you are dividing by.
• Notice that division is the opposite of multiplication. When we multiplied by a power of ten we moved the decimal point to the right. When we divide by a power of ten, we move the decimal point to the left.

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