Multiplying and dividing by powers of 10 worksheets for 5th grade - Free Printable

To solve these problems, we use the rule for multiplying by powers of 10.

The Rule:
When you multiply a number by $10^n$ (where $n$ is the exponent), you move the decimal point $n$ places to the right. If there are no digits left, you add zeros.

Let's solve each problem step-by-step:

1. $4 \times 10^1$
* The exponent is 1. Move the decimal in 4 one place to the right.
* $4 \rightarrow 40$
* Answer: 40

2. $17 \times 10^3$
* The exponent is 3. Move the decimal in 17 three places to the right.
* $17 \rightarrow 170 \rightarrow 1,700 \rightarrow 17,000$
* Answer: 17,000

3. $51 \times 10^5$
* The exponent is 5. Move the decimal in 51 five places to the right.
* $51 \rightarrow 510 \rightarrow 5,100 \rightarrow 51,000 \rightarrow 510,000 \rightarrow 5,100,000$
* Answer: 5,100,000

4. $216 \times 10^4$
* The exponent is 4. Move the decimal in 216 four places to the right.
* $216 \rightarrow 2,160 \rightarrow 21,600 \rightarrow 216,000 \rightarrow 2,160,000$
* Answer: 2,160,000

5. $11 \times 10^8$
* The exponent is 8. Move the decimal in 11 eight places to the right.
* Start with 11, then add 8 zeros.
* Answer: 1,100,000,000

6. $34 \times 10^2$
* The exponent is 2. Move the decimal in 34 two places to the right.
* $34 \rightarrow 340 \rightarrow 3,400$
* Answer: 3,400

7. $301 \times 10^2$
* The exponent is 2. Move the decimal in 301 two places to the right.
* $301 \rightarrow 3,010 \rightarrow 30,100$
* Answer: 30,100

8. $103 \times 10^2$
* The exponent is 2. Move the decimal in 103 two places to the right.
* $103 \rightarrow 1,030 \rightarrow 10,300$
* Answer: 10,300

9. $8 \times 10^7$
* The exponent is 7. Move the decimal in 8 seven places to the right.
* Start with 8, then add 7 zeros.
* Answer: 80,000,000

10. $16 \times 10^2$
* The exponent is 2. Move the decimal in 16 two places to the right.
* $16 \rightarrow 160 \rightarrow 1,600$
* Answer: 1,600

11. $62 \times 10^5$
* The exponent is 5. Move the decimal in 62 five places to the right.
* Start with 62, then add 5 zeros.
* Answer: 6,200,000

12. $1 \times 10^7$
* The exponent is 7. Move the decimal in 1 seven places to the right.
* Start with 1, then add 7 zeros.
* Answer: 10,000,000

13. $10 \times 10^6$
* The exponent is 6. Move the decimal in 10 six places to the right.
* $10 \rightarrow 100 \rightarrow 1,000 \rightarrow 10,000 \rightarrow 100,000 \rightarrow 1,000,000 \rightarrow 10,000,000$
* Alternatively: $10^1 \times 10^6 = 10^{(1+6)} = 10^7$.
* Answer: 10,000,000

14. $17 \times 10^3$
* The exponent is 3. Move the decimal in 17 three places to the right.
* $17 \rightarrow 170 \rightarrow 1,700 \rightarrow 17,000$
* Answer: 17,000

Final Answer:
1. 40
2. 17,000
3. 5,100,000
4. 2,160,000
5. 1,100,000,000
6. 3,400
7. 30,100
8. 10,300
9. 80,000,000
10. 1,600
11. 6,200,000
12. 10,000,000
13. 10,000,000
14. 17,000