Grade 5 Decimals Worksheet: Long Division with Decimals

Problem: Long Division with Decimals

The task is to solve the given long division problems involving decimals. The instructions specify that we should find the quotient and round it to 3 decimal places if necessary.

#### Steps to Solve:
1. Understand the Structure: Each problem involves dividing a number (dividend) by another number (divisor). The divisor or dividend may contain decimals.
2. Adjust for Decimals: To simplify the division, multiply both the divisor and the dividend by a power of 10 to eliminate the decimal in the divisor.
3. Perform Long Division: Carry out the division as usual.
4. Round the Quotient: If the quotient has more than 3 decimal places, round it to 3 decimal places.

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Solutions:

#### Problem 1: \( 0.7 \div 792 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 10:
\( 0.7 \times 10 = 7 \)
\( 792 \times 10 = 7920 \)
- New problem: \( 7 \div 7920 \).

- Step 2: Perform the division.
- \( 7 \div 7920 = 0.00088386 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.00088386 \ldots \approx 0.001 \)

Answer: \( 0.001 \)

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#### Problem 2: \( 0.03 \div 0.35 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 100:
\( 0.03 \times 100 = 3 \)
\( 0.35 \times 100 = 35 \)
- New problem: \( 3 \div 35 \).

- Step 2: Perform the division.
- \( 3 \div 35 = 0.085714 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.085714 \ldots \approx 0.086 \)

Answer: \( 0.086 \)

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#### Problem 3: \( 0.5 \div 63 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 10:
\( 0.5 \times 10 = 5 \)
\( 63 \times 10 = 630 \)
- New problem: \( 5 \div 630 \).

- Step 2: Perform the division.
- \( 5 \div 630 = 0.0079365 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.0079365 \ldots \approx 0.008 \)

Answer: \( 0.008 \)

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#### Problem 4: \( 0.05 \div 0.20 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 100:
\( 0.05 \times 100 = 5 \)
\( 0.20 \times 100 = 20 \)
- New problem: \( 5 \div 20 \).

- Step 2: Perform the division.
- \( 5 \div 20 = 0.25 \)

- Step 3: No rounding needed since it already has fewer than 3 decimal places.

Answer: \( 0.250 \) (Note: We can write it as 0.250 to match the format.)

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#### Problem 5: \( 0.06 \div 62 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 100:
\( 0.06 \times 100 = 6 \)
\( 62 \times 100 = 6200 \)
- New problem: \( 6 \div 6200 \).

- Step 2: Perform the division.
- \( 6 \div 6200 = 0.0009677 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.0009677 \ldots \approx 0.001 \)

Answer: \( 0.001 \)

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#### Problem 6: \( 0.03 \div 77.4 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 10:
\( 0.03 \times 10 = 0.3 \)
\( 77.4 \times 10 = 774 \)
- New problem: \( 0.3 \div 774 \).

- Step 2: Adjust further to eliminate the decimal in the dividend.
- Multiply both the divisor and the dividend by 10:
\( 0.3 \times 10 = 3 \)
\( 774 \times 10 = 7740 \)
- New problem: \( 3 \div 7740 \).

- Step 3: Perform the division.
- \( 3 \div 7740 = 0.0003875 \ldots \)

- Step 4: Round to 3 decimal places.
- \( 0.0003875 \ldots \approx 0.000 \)

Answer: \( 0.000 \)

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#### Problem 7: \( 0.7 \div 4.4 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 10:
\( 0.7 \times 10 = 7 \)
\( 4.4 \times 10 = 44 \)
- New problem: \( 7 \div 44 \).

- Step 2: Perform the division.
- \( 7 \div 44 = 0.159090 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.159090 \ldots \approx 0.159 \)

Answer: \( 0.159 \)

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#### Problem 8: \( 0.4 \div 5.1 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 10:
\( 0.4 \times 10 = 4 \)
\( 5.1 \times 10 = 51 \)
- New problem: \( 4 \div 51 \).

- Step 2: Perform the division.
- \( 4 \div 51 = 0.078431 \ldots \)

- Step 3: Round to 3 decimal places.
- \( 0.078431 \ldots \approx 0.078 \)

Answer: \( 0.078 \)

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#### Problem 9: \( 0.08 \div 50 \)

- Step 1: Adjust for the decimal in the divisor.
- Multiply both the divisor and the dividend by 100:
\( 0.08 \times 100 = 8 \)
\( 50 \times 100 = 5000 \)
- New problem: \( 8 \div 5000 \).

- Step 2: Perform the division.
- \( 8 \div 5000 = 0.0016 \)

- Step 3: Round to 3 decimal places.
- \( 0.0016 \approx 0.002 \)

Answer: \( 0.002 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 0.001 \\
2. & 0.086 \\
3. & 0.008 \\
4. & 0.250 \\
5. & 0.001 \\
6. & 0.000 \\
7. & 0.159 \\
8. & 0.078 \\
9. & 0.002 \\
\end{array}
}
\]