Let's solve each problem on this 8th-grade math worksheet. The task is to
multiply a decimal number by a power of 10 (like $10^2$, $10^3$, etc.).
🔍 Key Concept:
When you multiply a number by $10^n$, you move the decimal point
n places to the right.
- If $n$ is positive, move the decimal
right.
- If $n$ is negative, move the decimal
left.
---
Now let’s go through each problem:
---
Left Column:
1.
$.8 \times 10^2 = ?$
$10^2 = 100$
Move decimal 2 places right:
$.8 \to 8.\to 80.$
→
80
2.
$1.24 \times 10^3 = ?$
$10^3 = 1000$
Move decimal 3 places right:
$1.24 \to 12.4 \to 124. \to 1240.$
→
1240
3.
$.6 \times 10^2 = ?$
Move decimal 2 places right:
$.6 \to 6. \to 60.$
→
60
4.
$.89 \times 10^4 = ?$
$10^4 = 10,000$
Move decimal 4 places right:
$.89 \to 8.9 \to 89. \to 890. \to 8900.$
→
8900
5.
$13.7 \times 10^2 = ?$
Move decimal 2 places right:
$13.7 \to 137. \to 1370.$
→
1370
6.
$20.8 \times 10^4 = ?$
Move decimal 4 places right:
$20.8 \to 208. \to 2080. \to 20800. \to 208000.$
→
208,000
---
Right Column:
1.
$.67 \times 10^3 = ?$
$10^3 = 1000$
Move decimal 3 places right:
$.67 \to 6.7 \to 67. \to 670.$
→
670
2.
$300.2 \times 10^2 = ?$
Move decimal 2 places right:
$300.2 \to 3002. \to 30020.$
→
30,020
3.
$9.61 \times 10^6 = ?$
$10^6 = 1,000,000$
Move decimal 6 places right:
$9.61 \to 96.1 \to 961. \to 9610. \to 96100. \to 961000. \to 9,610,000$
→
9,610,000
4.
$80.6 \times 10^4 = ?$
Move decimal 4 places right:
$80.6 \to 806. \to 8060. \to 80600. \to 806000.$
→
806,000
5.
$.54 \times 10^2 = ?$
Move decimal 2 places right:
$.54 \to 5.4 \to 54.$
→
54
6.
$12.89 \times 10^1 = ?$
$10^1 = 10$
Move decimal 1 place right:
$12.89 \to 128.9$
→
128.9
---
✔ Final Answers:
#### Left Column:
1. $ .8 \times 10^2 = 80 $
2. $ 1.24 \times 10^3 = 1240 $
3. $ .6 \times 10^2 = 60 $
4. $ .89 \times 10^4 = 8900 $
5. $ 13.7 \times 10^2 = 1370 $
6. $ 20.8 \times 10^4 = 208,000 $
#### Right Column:
1. $ .67 \times 10^3 = 670 $
2. $ 300.2 \times 10^2 = 30,020 $
3. $ 9.61 \times 10^6 = 9,610,000 $
4. $ 80.6 \times 10^4 = 806,000 $
5. $ .54 \times 10^2 = 54 $
6. $ 12.89 \times 10^1 = 128.9 $
---
📝 Summary Tip:
To multiply by $10^n$:
👉 Just
move the decimal point n places to the right.
Add zeros if needed.
This is a fundamental skill for working with scientific notation and large/small numbers!
Parent Tip: Review the logic above to help your child master the concept of 8th grade math worksheet algebra.
