To solve the problems involving multiplication by powers of 10, we need to understand how multiplying by powers of 10 affects the placement of the decimal point. Specifically:
- Multiplying by \(10^n\) (where \(n\) is a positive integer) means moving the decimal point \(n\) places to the right.
- If there is no explicit decimal point, it is assumed to be at the end of the number.
Let's solve each problem step by step.
Problem 1: \(9 \times 10^3\)
- \(10^3 = 1000\)
- \(9 \times 1000 = 9000\)
-
Answer: \(9000\)
Problem 2: \(720 \times 10^2\)
- \(10^2 = 100\)
- \(720 \times 100 = 72000\)
-
Answer: \(72000\)
Problem 3: \(4 \times 10^2\)
- \(10^2 = 100\)
- \(4 \times 100 = 400\)
-
Answer: \(400\)
Problem 4: \(200 \times 10^2\)
- \(10^2 = 100\)
- \(200 \times 100 = 20000\)
-
Answer: \(20000\)
Problem 5: \(39 \times 10^4\)
- \(10^4 = 10000\)
- \(39 \times 10000 = 390000\)
-
Answer: \(390000\)
Problem 6: \(70 \times 10^3\)
- \(10^3 = 1000\)
- \(70 \times 1000 = 70000\)
-
Answer: \(70000\)
Problem 7: \(25 \times 10^3\)
- \(10^3 = 1000\)
- \(25 \times 1000 = 25000\)
-
Answer: \(25000\)
Problem 8: \(64 \times 10^4\)
- \(10^4 = 10000\)
- \(64 \times 10000 = 640000\)
-
Answer: \(640000\)
Problem 9: \(40 \times 10^4\)
- \(10^4 = 10000\)
- \(40 \times 10000 = 400000\)
-
Answer: \(400000\)
Problem 10: \(450 \times 10^2\)
- \(10^2 = 100\)
- \(450 \times 100 = 45000\)
-
Answer: \(45000\)
Problem 11: \(705 \times 10^3\)
- \(10^3 = 1000\)
- \(705 \times 1000 = 705000\)
-
Answer: \(705000\)
Problem 12: \(99 \times 10^4\)
- \(10^4 = 10000\)
- \(99 \times 10000 = 990000\)
-
Answer: \(990000\)
Final Answer:
\[
\boxed{
\begin{array}{ll}
9 \times 10^3 = 9000 & 720 \times 10^2 = 72000 \\
4 \times 10^2 = 400 & 200 \times 10^2 = 20000 \\
39 \times 10^4 = 390000 & 70 \times 10^3 = 70000 \\
25 \times 10^3 = 25000 & 64 \times 10^4 = 640000 \\
40 \times 10^4 = 400000 & 450 \times 10^2 = 45000 \\
705 \times 10^3 = 705000 & 99 \times 10^4 = 990000 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of power and exponents worksheets.
