Multiplying Decimals | kellyfrindell - Free Printable

Problem: Multiplying Decimals

The task is to multiply the given pairs of numbers and correctly place the decimal point in the final answer by counting the total number of decimal places in the factors.

Solution Approach:

1. Multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both factors.
3. Place the decimal point in the product so that the total number of decimal places in the product matches the sum of the decimal places in the factors.

Let's solve each multiplication step by step.

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#### Row 1:
1. 68.2 × 8.4
- Multiply: \( 682 \times 84 = 57288 \)
- Decimal places: \( 68.2 \) has 1 decimal place, and \( 8.4 \) has 1 decimal place. Total = 2.
- Result: \( 572.88 \)

2. 630 × 1.2
- Multiply: \( 630 \times 12 = 7560 \)
- Decimal places: \( 630 \) has 0 decimal places, and \( 1.2 \) has 1 decimal place. Total = 1.
- Result: \( 756.0 \) or simply \( 756 \)

3. 16.0 × 36
- Multiply: \( 160 \times 36 = 5760 \)
- Decimal places: \( 16.0 \) has 1 decimal place, and \( 36 \) has 0 decimal places. Total = 1.
- Result: \( 576.0 \) or simply \( 576 \)

4. 5.52 × 0.25
- Multiply: \( 552 \times 25 = 13800 \)
- Decimal places: \( 5.52 \) has 2 decimal places, and \( 0.25 \) has 2 decimal places. Total = 4.
- Result: \( 1.3800 \) or simply \( 1.38 \)

5. 32.3 × 26
- Multiply: \( 323 \times 26 = 8398 \)
- Decimal places: \( 32.3 \) has 1 decimal place, and \( 26 \) has 0 decimal places. Total = 1.
- Result: \( 839.8 \)

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#### Row 2:
1. 7.91 × 0.19
- Multiply: \( 791 \times 19 = 15029 \)
- Decimal places: \( 7.91 \) has 2 decimal places, and \( 0.19 \) has 2 decimal places. Total = 4.
- Result: \( 1.5029 \)

2. 26.3 × 7.8
- Multiply: \( 263 \times 78 = 20514 \)
- Decimal places: \( 26.3 \) has 1 decimal place, and \( 7.8 \) has 1 decimal place. Total = 2.
- Result: \( 205.14 \)

3. 3.07 × 19
- Multiply: \( 307 \times 19 = 5833 \)
- Decimal places: \( 3.07 \) has 2 decimal places, and \( 19 \) has 0 decimal places. Total = 2.
- Result: \( 58.33 \)

4. 63.2 × 8.5
- Multiply: \( 632 \times 85 = 53720 \)
- Decimal places: \( 63.2 \) has 1 decimal place, and \( 8.5 \) has 1 decimal place. Total = 2.
- Result: \( 537.20 \) or simply \( 537.2 \)

5. 0.394 × 70
- Multiply: \( 394 \times 70 = 27580 \)
- Decimal places: \( 0.394 \) has 3 decimal places, and \( 70 \) has 0 decimal places. Total = 3.
- Result: \( 27.580 \) or simply \( 27.58 \)

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#### Row 3:
1. 55.8 × 9.4
- Multiply: \( 558 \times 94 = 52452 \)
- Decimal places: \( 55.8 \) has 1 decimal place, and \( 9.4 \) has 1 decimal place. Total = 2.
- Result: \( 524.52 \)

2. 596 × 3.6
- Multiply: \( 596 \times 36 = 21456 \)
- Decimal places: \( 596 \) has 0 decimal places, and \( 3.6 \) has 1 decimal place. Total = 1.
- Result: \( 2145.6 \)

3. 940 × 8.2
- Multiply: \( 940 \times 82 = 77080 \)
- Decimal places: \( 940 \) has 0 decimal places, and \( 8.2 \) has 1 decimal place. Total = 1.
- Result: \( 7708.0 \) or simply \( 7708 \)

4. 203 × 42
- Multiply: \( 203 \times 42 = 8526 \)
- Decimal places: \( 203 \) has 0 decimal places, and \( 42 \) has 0 decimal places. Total = 0.
- Result: \( 8526 \)

5. 0.707 × 0.97
- Multiply: \( 707 \times 97 = 68479 \)
- Decimal places: \( 0.707 \) has 3 decimal places, and \( 0.97 \) has 2 decimal places. Total = 5.
- Result: \( 0.68479 \)

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#### Row 4:
1. 906 × 64
- Multiply: \( 906 \times 64 = 57984 \)
- Decimal places: \( 906 \) has 0 decimal places, and \( 64 \) has 0 decimal places. Total = 0.
- Result: \( 57984 \)

2. 310 × 1.8
- Multiply: \( 310 \times 18 = 5580 \)
- Decimal places: \( 310 \) has 0 decimal places, and \( 1.8 \) has 1 decimal place. Total = 1.
- Result: \( 558.0 \) or simply \( 558 \)

3. 520 × 0.92
- Multiply: \( 520 \times 92 = 47840 \)
- Decimal places: \( 520 \) has 0 decimal places, and \( 0.92 \) has 2 decimal places. Total = 2.
- Result: \( 478.40 \) or simply \( 478.4 \)

4. 131 × 0.41
- Multiply: \( 131 \times 41 = 5371 \)
- Decimal places: \( 131 \) has 0 decimal places, and \( 0.41 \) has 2 decimal places. Total = 2.
- Result: \( 53.71 \)

5. 6.00 × 5.1
- Multiply: \( 600 \times 51 = 30600 \)
- Decimal places: \( 6.00 \) has 2 decimal places, and \( 5.1 \) has 1 decimal place. Total = 3.
- Result: \( 30.600 \) or simply \( 30.6 \)

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#### Row 5:
1. 0.913 × 56
- Multiply: \( 913 \times 56 = 51128 \)
- Decimal places: \( 0.913 \) has 3 decimal places, and \( 56 \) has 0 decimal places. Total = 3.
- Result: \( 51.128 \)

2. 12.8 × 3.8
- Multiply: \( 128 \times 38 = 4864 \)
- Decimal places: \( 12.8 \) has 1 decimal place, and \( 3.8 \) has 1 decimal place. Total = 2.
- Result: \( 48.64 \)

3. 52.2 × 2.3
- Multiply: \( 522 \times 23 = 11906 \)
- Decimal places: \( 52.2 \) has 1 decimal place, and \( 2.3 \) has 1 decimal place. Total = 2.
- Result: \( 119.06 \)

4. 0.394 × 76
- Multiply: \( 394 \times 76 = 29984 \)
- Decimal places: \( 0.394 \) has 3 decimal places, and \( 76 \) has 0 decimal places. Total = 3.
- Result: \( 29.984 \)

5. 0.411 × 0.35
- Multiply: \( 411 \times 35 = 14385 \)
- Decimal places: \( 0.411 \) has 3 decimal places, and \( 0.35 \) has 2 decimal places. Total = 5.
- Result: \( 0.14385 \)

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Final Answers:

\[
\boxed{
\begin{array}{ccccc}
572.88 & 756 & 576 & 1.38 & 839.8 \\
1.5029 & 205.14 & 58.33 & 537.2 & 27.58 \\
524.52 & 2145.6 & 7708 & 8526 & 0.68479 \\
57984 & 558 & 478.4 & 53.71 & 30.6 \\
51.128 & 48.64 & 119.06 & 29.984 & 0.14385 \\
\end{array}
}
\]