Do you remember Kailey and the astronomy question about earth? This was presented in Use Mental Math to Multiply Whole Number Powers of Ten Concept. When Kailey finished with her first astronomy dilemma, she was on to the next one. This one 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. Kailey 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 Kailey can solve this problem.

### Guidance

Previously we worked on 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: .45**

#### Example B

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

**Solution: .00678**

#### Example C

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

**Solution: .874**

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

Kailey’s question asks if what the diameter of the earth would be if it were 100 times smaller. To complete this problem, Kailey 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*} 127.563**

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

### Vocabulary

- 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.

### Guided Practice

Here is one for you to try on your own.

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

**Answer**

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.

**Our answer is \begin{align*}.06789\end{align*}.**

### Video Review

James Sousa Dividing by Powers of Ten

### Practice

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*} _____