Grade 6 Math Worksheets: Long division of decimals (2-digits) | Worsheets library... - Free Printable

Problem: Long Division of Decimals by Decimals

The task is to solve the given division problems involving decimals and round the answers to 6 decimal places. Here are the steps to solve each problem:

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#### Problem 1: \( 0.01 \div 37.43 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.01) and the dividend (37.43) two places to the right.
- Divisor: \( 0.01 \rightarrow 1 \)
- Dividend: \( 37.43 \rightarrow 3743 \)

2. Perform the division:
- Divide \( 3743 \div 1 \):
\[
3743 \div 1 = 3743
\]

3. Round to 6 decimal places:
- Since the result is an integer, it remains \( 3743.000000 \).

Answer for Problem 1:
\[
\boxed{3743.000000}
\]

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#### Problem 2: \( 0.6 \div 350.2 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.6) and the dividend (350.2) one place to the right.
- Divisor: \( 0.6 \rightarrow 6 \)
- Dividend: \( 350.2 \rightarrow 3502 \)

2. Perform the division:
- Divide \( 3502 \div 6 \):
\[
3502 \div 6 = 583.666666\ldots
\]

3. Round to 6 decimal places:
- The repeating decimal \( 583.666666\ldots \) rounds to \( 583.666667 \).

Answer for Problem 2:
\[
\boxed{583.666667}
\]

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#### Problem 3: \( 0.4 \div 588.5 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.4) and the dividend (588.5) one place to the right.
- Divisor: \( 0.4 \rightarrow 4 \)
- Dividend: \( 588.5 \rightarrow 5885 \)

2. Perform the division:
- Divide \( 5885 \div 4 \):
\[
5885 \div 4 = 1471.25
\]

3. Round to 6 decimal places:
- The result \( 1471.25 \) can be written as \( 1471.250000 \).

Answer for Problem 3:
\[
\boxed{1471.250000}
\]

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#### Problem 4: \( 0.2 \div 628.3 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.2) and the dividend (628.3) one place to the right.
- Divisor: \( 0.2 \rightarrow 2 \)
- Dividend: \( 628.3 \rightarrow 6283 \)

2. Perform the division:
- Divide \( 6283 \div 2 \):
\[
6283 \div 2 = 3141.5
\]

3. Round to 6 decimal places:
- The result \( 3141.5 \) can be written as \( 3141.500000 \).

Answer for Problem 4:
\[
\boxed{3141.500000}
\]

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#### Problem 5: \( 0.3 \div 13.82 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.3) and the dividend (13.82) one place to the right.
- Divisor: \( 0.3 \rightarrow 3 \)
- Dividend: \( 13.82 \rightarrow 138.2 \)

2. Perform the division:
- Divide \( 138.2 \div 3 \):
\[
138.2 \div 3 = 46.066666\ldots
\]

3. Round to 6 decimal places:
- The repeating decimal \( 46.066666\ldots \) rounds to \( 46.066667 \).

Answer for Problem 5:
\[
\boxed{46.066667}
\]

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#### Problem 6: \( 0.2 \div 863.1 \)

1. Adjust the divisor to a whole number:
- Move the decimal point in both the divisor (0.2) and the dividend (863.1) one place to the right.
- Divisor: \( 0.2 \rightarrow 2 \)
- Dividend: \( 863.1 \rightarrow 8631 \)

2. Perform the division:
- Divide \( 8631 \div 2 \):
\[
8631 \div 2 = 4315.5
\]

3. Round to 6 decimal places:
- The result \( 4315.5 \) can be written as \( 4315.500000 \).

Answer for Problem 6:
\[
\boxed{4315.500000}
\]

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Final Answers:

1. \( \boxed{3743.000000} \)
2. \( \boxed{583.666667} \)
3. \( \boxed{1471.250000} \)
4. \( \boxed{3141.500000} \)
5. \( \boxed{46.066667} \)
6. \( \boxed{4315.500000} \)