Dividing Decimals by Powers of Ten - Math worksheet with 16 practice problems.

To solve the problems involving dividing decimals by powers of ten, we need to understand how moving the decimal point affects the result. Dividing by a power of ten (e.g., 0.1, 0.01, 10, 100) involves shifting the decimal point in the dividend either to the left or to the right.

General Rules:

1. Dividing by a number less than 1 (e.g., 0.1, 0.01):
- Move the decimal point in the dividend to the right by the number of places equal to the number of zeros after the decimal plus one.
- For example, dividing by 0.1 moves the decimal point one place to the right, and dividing by 0.01 moves it two places to the right.

2. Dividing by a number greater than 1 (e.g., 10, 100):
- Move the decimal point in the dividend to the left by the number of zeros in the divisor.
- For example, dividing by 10 moves the decimal point one place to the left, and dividing by 100 moves it two places to the left.

Now, let's solve each problem step by step:

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Problem 1: \( 883.9 \div 0.1 \)

- Dividing by 0.1 means moving the decimal point one place to the right.
- \( 883.9 \rightarrow 8839 \).
- Answer: \( 8839 \).

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Problem 2: \( 9.8 \div 0.01 \)

- Dividing by 0.01 means moving the decimal point two places to the right.
- \( 9.8 \rightarrow 980 \).
- Answer: \( 980 \).

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Problem 3: \( 2.1 \div 0.001 \)

- Dividing by 0.001 means moving the decimal point three places to the right.
- \( 2.1 \rightarrow 2100 \).
- Answer: \( 2100 \).

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Problem 4: \( 1.38 \div 0.1 \)

- Dividing by 0.1 means moving the decimal point one place to the right.
- \( 1.38 \rightarrow 13.8 \).
- Answer: \( 13.8 \).

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Problem 5: \( 6.19 \div 100 \)

- Dividing by 100 means moving the decimal point two places to the left.
- \( 6.19 \rightarrow 0.0619 \).
- Answer: \( 0.0619 \).

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Problem 6: \( 462.7 \div 0.001 \)

- Dividing by 0.001 means moving the decimal point three places to the right.
- \( 462.7 \rightarrow 462700 \).
- Answer: \( 462700 \).

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Problem 7: \( 30.01 \div 0.01 \)

- Dividing by 0.01 means moving the decimal point two places to the right.
- \( 30.01 \rightarrow 3001 \).
- Answer: \( 3001 \).

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Problem 8: \( 7.5 \div 0.1 \)

- Dividing by 0.1 means moving the decimal point one place to the right.
- \( 7.5 \rightarrow 75 \).
- Answer: \( 75 \).

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Problem 9: \( 6.05 \div 1000 \)

- Dividing by 1000 means moving the decimal point three places to the left.
- \( 6.05 \rightarrow 0.00605 \).
- Answer: \( 0.00605 \).

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Problem 10: \( 36.46 \div 0.01 \)

- Dividing by 0.01 means moving the decimal point two places to the right.
- \( 36.46 \rightarrow 3646 \).
- Answer: \( 3646 \).

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Problem 11: \( 10.3 \div 0.1 \)

- Dividing by 0.1 means moving the decimal point one place to the right.
- \( 10.3 \rightarrow 103 \).
- Answer: \( 103 \).

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Problem 12: \( 18.2 \div 0.001 \)

- Dividing by 0.001 means moving the decimal point three places to the right.
- \( 18.2 \rightarrow 18200 \).
- Answer: \( 18200 \).

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Problem 13: \( 594.2 \div 100 \)

- Dividing by 100 means moving the decimal point two places to the left.
- \( 594.2 \rightarrow 5.942 \).
- Answer: \( 5.942 \).

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Problem 14: \( 0.7 \div 10 \)

- Dividing by 10 means moving the decimal point one place to the left.
- \( 0.7 \rightarrow 0.07 \).
- Answer: \( 0.07 \).

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Problem 15: \( 11.4 \div 10 \)

- Dividing by 10 means moving the decimal point one place to the left.
- \( 11.4 \rightarrow 1.14 \).
- Answer: \( 1.14 \).

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Problem 16: \( 10.3 \div 1000 \)

- Dividing by 1000 means moving the decimal point three places to the left.
- \( 10.3 \rightarrow 0.0103 \).
- Answer: \( 0.0103 \).

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 8839 \\
2) & 980 \\
3) & 2100 \\
4) & 13.8 \\
5) & 0.0619 \\
6) & 462700 \\
7) & 3001 \\
8) & 75 \\
9) & 0.00605 \\
10) & 3646 \\
11) & 103 \\
12) & 18200 \\
13) & 5.942 \\
14) & 0.07 \\
15) & 1.14 \\
16) & 0.0103 \\
\end{array}
}
\]