Problem: Solve the given problems involving multiplication of exponents.
The worksheet involves multiplying numbers by powers of 10. The general rule for multiplying a number by \(10^n\) is to move the decimal point \(n\) places to the right if \(n\) is positive, or \(n\) places to the left if \(n\) is negative.
Let's solve each problem step by step:
---
####
1. \(0.8 \times 10^2\)
- \(10^2 = 100\)
- Multiply \(0.8\) by \(100\):
\[
0.8 \times 100 = 80
\]
Answer: \(80\)
---
####
2. \(0.67 \times 10^3\)
- \(10^3 = 1000\)
- Multiply \(0.67\) by \(1000\):
\[
0.67 \times 1000 = 670
\]
Answer: \(670\)
---
####
3. \(1.24 \times 10^3\)
- \(10^3 = 1000\)
- Multiply \(1.24\) by \(1000\):
\[
1.24 \times 1000 = 1240
\]
Answer: \(1240\)
---
####
4. \(300.2 \times 10^2\)
- \(10^2 = 100\)
- Multiply \(300.2\) by \(100\):
\[
300.2 \times 100 = 30020
\]
Answer: \(30020\)
---
####
5. \(0.6 \times 10^2\)
- \(10^2 = 100\)
- Multiply \(0.6\) by \(100\):
\[
0.6 \times 100 = 60
\]
Answer: \(60\)
---
####
6. \(9.61 \times 10^6\)
- \(10^6 = 1,000,000\)
- Multiply \(9.61\) by \(1,000,000\):
\[
9.61 \times 1,000,000 = 9,610,000
\]
Answer: \(9,610,000\)
---
####
7. \(0.89 \times 10^4\)
- \(10^4 = 10,000\)
- Multiply \(0.89\) by \(10,000\):
\[
0.89 \times 10,000 = 8900
\]
Answer: \(8900\)
---
####
8. \(80.6 \times 10^4\)
- \(10^4 = 10,000\)
- Multiply \(80.6\) by \(10,000\):
\[
80.6 \times 10,000 = 806,000
\]
Answer: \(806,000\)
---
####
9. \(13.7 \times 10^2\)
- \(10^2 = 100\)
- Multiply \(13.7\) by \(100\):
\[
13.7 \times 100 = 1370
\]
Answer: \(1370\)
---
####
10. \(0.54 \times 10^2\)
- \(10^2 = 100\)
- Multiply \(0.54\) by \(100\):
\[
0.54 \times 100 = 54
\]
Answer: \(54\)
---
####
11. \(20.8 \times 10^4\)
- \(10^4 = 10,000\)
- Multiply \(20.8\) by \(10,000\):
\[
20.8 \times 10,000 = 208,000
\]
Answer: \(208,000\)
---
####
12. \(12.89 \times 10^1\)
- \(10^1 = 10\)
- Multiply \(12.89\) by \(10\):
\[
12.89 \times 10 = 128.9
\]
Answer: \(128.9\)
---
Final Answers:
\[
\boxed{
\begin{aligned}
&0.8 \times 10^2 = 80 \\
&0.67 \times 10^3 = 670 \\
&1.24 \times 10^3 = 1240 \\
&300.2 \times 10^2 = 30020 \\
&0.6 \times 10^2 = 60 \\
&9.61 \times 10^6 = 9,610,000 \\
&0.89 \times 10^4 = 8900 \\
&80.6 \times 10^4 = 806,000 \\
&13.7 \times 10^2 = 1370 \\
&0.54 \times 10^2 = 54 \\
&20.8 \times 10^4 = 208,000 \\
&12.89 \times 10^1 = 128.9
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of printable math worksheets for grade 8.
