Multiply Decimals and 2-Digit Numbers: Vertical Multiplication - Free Printable

Problem: Multiply Decimals by Powers of 10

The task involves multiplying decimal numbers by powers of 10. When multiplying a number by a power of 10, the decimal point is moved to the right by the number of places equal to the exponent of 10.

#### General Rule:
- If you multiply a number by \(10^n\), move the decimal point \(n\) places to the right.
- If \(n\) is positive, the decimal point moves to the right.
- If \(n\) is negative, the decimal point moves to the left (though this case is not present in the given problem).

Let's solve each problem step by step.

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Left Column:

1. \(3.1 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(3.1\) two places to the right: \(3.1 \rightarrow 310\).
- Answer: \(310\).

2. \(3.15 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(3.15\) two places to the right: \(3.15 \rightarrow 315\).
- Answer: \(315\).

3. \(3.157 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(3.157\) two places to the right: \(3.157 \rightarrow 315.7\).
- Answer: \(315.7\).

4. \(4 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(4\) three places to the right: \(4 \rightarrow 4000\).
- Answer: \(4000\).

5. \(4.2 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(4.2\) three places to the right: \(4.2 \rightarrow 4200\).
- Answer: \(4200\).

6. \(4.28 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(4.28\) three places to the right: \(4.28 \rightarrow 4280\).
- Answer: \(4280\).

7. \(4.283 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(4.283\) three places to the right: \(4.283 \rightarrow 4283\).
- Answer: \(4283\).

8. \(5 \times 10^4\):
- \(10^4 = 10000\).
- Move the decimal point in \(5\) four places to the right: \(5 \rightarrow 50000\).
- Answer: \(50000\).

9. \(5.7 \times 10^4\):
- \(10^4 = 10000\).
- Move the decimal point in \(5.7\) four places to the right: \(5.7 \rightarrow 57000\).
- Answer: \(57000\).

10. \(5.73 \times 10^4\):
- \(10^4 = 10000\).
- Move the decimal point in \(5.73\) four places to the right: \(5.73 \rightarrow 57300\).
- Answer: \(57300\).

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Right Column:

1. \(24 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(24\) two places to the right: \(24 \rightarrow 2400\).
- Answer: \(2400\).

2. \(24.7 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(24.7\) two places to the right: \(24.7 \rightarrow 2470\).
- Answer: \(2470\).

3. \(24.07 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(24.07\) two places to the right: \(24.07 \rightarrow 2407\).
- Answer: \(2407\).

4. \(24.007 \times 10^2\):
- \(10^2 = 100\).
- Move the decimal point in \(24.007\) two places to the right: \(24.007 \rightarrow 2400.7\).
- Answer: \(2400.7\).

5. \(53 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(53\) three places to the right: \(53 \rightarrow 53000\).
- Answer: \(53000\).

6. \(53.8 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(53.8\) three places to the right: \(53.8 \rightarrow 53800\).
- Answer: \(53800\).

7. \(53.08 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(53.08\) three places to the right: \(53.08 \rightarrow 53080\).
- Answer: \(53080\).

8. \(53.082 \times 10^3\):
- \(10^3 = 1000\).
- Move the decimal point in \(53.082\) three places to the right: \(53.082 \rightarrow 53082\).
- Answer: \(53082\).

9. \(9.1 \times 10^4\):
- \(10^4 = 10000\).
- Move the decimal point in \(9.1\) four places to the right: \(9.1 \rightarrow 91000\).
- Answer: \(91000\).

10. \(91.4 \times 10^4\):
- \(10^4 = 10000\).
- Move the decimal point in \(91.4\) four places to the right: \(91.4 \rightarrow 914000\).
- Answer: \(914000\).

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Final Answers:

\[
\begin{array}{ll}
3.1 \times 10^2 = 310 & 24 \times 10^2 = 2400 \\
3.15 \times 10^2 = 315 & 24.7 \times 10^2 = 2470 \\
3.157 \times 10^2 = 315.7 & 24.07 \times 10^2 = 2407 \\
4 \times 10^3 = 4000 & 24.007 \times 10^2 = 2400.7 \\
4.2 \times 10^3 = 4200 & 53 \times 10^3 = 53000 \\
4.28 \times 10^3 = 4280 & 53.8 \times 10^3 = 53800 \\
4.283 \times 10^3 = 4283 & 53.08 \times 10^3 = 53080 \\
5 \times 10^4 = 50000 & 53.082 \times 10^3 = 53082 \\
5.7 \times 10^4 = 57000 & 9.1 \times 10^4 = 91000 \\
5.73 \times 10^4 = 57300 & 91.4 \times 10^4 = 914000 \\
\end{array}
\]

\boxed{
\begin{array}{ll}
310 & 2400 \\
315 & 2470 \\
315.7 & 2407 \\
4000 & 2400.7 \\
4200 & 53000 \\
4280 & 53800 \\
4283 & 53080 \\
50000 & 53082 \\
57000 & 91000 \\
57300 & 914000 \\
\end{array}
}