Multiplying Decimals - Tenths | Decimal Worksheets - Free Printable
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Step-by-step solution for: Multiplying Decimals - Tenths | Decimal Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Multiplying Decimals - Tenths | Decimal Worksheets
The task involves multiplying decimals. To solve each problem, we need to follow these steps:
1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both numbers being multiplied.
3. Place the decimal point in the product so that the total number of decimal places in the product equals the sum of the decimal places in the original numbers.
Let's solve each problem step by step.
---
1. Multiply as whole numbers:
\( 409 \times 21 = 8589 \)
2. Count decimal places:
- \( 40.9 \) has 1 decimal place.
- \( 2.1 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 8589 \).
Result: \( 85.89 \).
Answer: \( 85.89 \)
---
1. Multiply as whole numbers:
\( 659 \times 264 = 174696 \)
2. Count decimal places:
- \( 65.9 \) has 1 decimal place.
- \( 26.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 174696 \).
Result: \( 1746.96 \).
Answer: \( 1746.96 \)
---
1. Multiply as whole numbers:
\( 856 \times 805 = 689380 \)
2. Count decimal places:
- \( 85.6 \) has 1 decimal place.
- \( 80.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 689380 \).
Result: \( 6893.80 \) or simply \( 6893.8 \).
Answer: \( 6893.8 \)
---
1. Multiply as whole numbers:
\( 886 \times 25 = 22150 \)
2. Count decimal places:
- \( 88.6 \) has 1 decimal place.
- \( 2.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 22150 \).
Result: \( 221.50 \) or simply \( 221.5 \).
Answer: \( 221.5 \)
---
1. Multiply as whole numbers:
\( 925 \times 808 = 747100 \)
2. Count decimal places:
- \( 92.5 \) has 1 decimal place.
- \( 80.8 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 747100 \).
Result: \( 7471.00 \) or simply \( 7471.0 \).
Answer: \( 7471.0 \)
---
1. Multiply as whole numbers:
\( 591 \times 14 = 8274 \)
2. Count decimal places:
- \( 59.1 \) has 1 decimal place.
- \( 1.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 8274 \).
Result: \( 82.74 \).
Answer: \( 82.74 \)
---
1. Multiply as whole numbers:
\( 458 \times 413 = 188754 \)
2. Count decimal places:
- \( 45.8 \) has 1 decimal place.
- \( 41.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 188754 \).
Result: \( 1887.54 \).
Answer: \( 1887.54 \)
---
1. Multiply as whole numbers:
\( 350 \times 78 = 27300 \)
2. Count decimal places:
- \( 35.0 \) has 1 decimal place.
- \( 7.8 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 27300 \).
Result: \( 273.00 \) or simply \( 273.0 \).
Answer: \( 273.0 \)
---
1. Multiply as whole numbers:
\( 849 \times 23 = 19527 \)
2. Count decimal places:
- \( 84.9 \) has 1 decimal place.
- \( 2.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 19527 \).
Result: \( 195.27 \).
Answer: \( 195.27 \)
---
1. Multiply as whole numbers:
\( 335 \times 44 = 14740 \)
2. Count decimal places:
- \( 33.5 \) has 1 decimal place.
- \( 4.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 14740 \).
Result: \( 147.40 \) or simply \( 147.4 \).
Answer: \( 147.4 \)
---
1. Multiply as whole numbers:
\( 254 \times 155 = 39470 \)
2. Count decimal places:
- \( 25.4 \) has 1 decimal place.
- \( 15.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 39470 \).
Result: \( 394.70 \) or simply \( 394.7 \).
Answer: \( 394.7 \)
---
1. Multiply as whole numbers:
\( 861 \times 867 = 746387 \)
2. Count decimal places:
- \( 86.1 \) has 1 decimal place.
- \( 86.7 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 746387 \).
Result: \( 7463.87 \).
Answer: \( 7463.87 \)
---
1. Multiply as whole numbers:
\( 522 \times 343 = 179046 \)
2. Count decimal places:
- \( 52.2 \) has 1 decimal place.
- \( 34.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 179046 \).
Result: \( 1790.46 \).
Answer: \( 1790.46 \)
---
1. Multiply as whole numbers:
\( 625 \times 353 = 220375 \)
2. Count decimal places:
- \( 62.5 \) has 1 decimal place.
- \( 35.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 220375 \).
Result: \( 2203.75 \).
Answer: \( 2203.75 \)
---
1. Multiply as whole numbers:
\( 201 \times 60 = 12060 \)
2. Count decimal places:
- \( 20.1 \) has 1 decimal place.
- \( 6.0 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 12060 \).
Result: \( 120.60 \) or simply \( 120.6 \).
Answer: \( 120.6 \)
---
\[
\boxed{
\begin{array}{ll}
1.) & 85.89 \\
2.) & 1746.96 \\
3.) & 6893.8 \\
4.) & 221.5 \\
5.) & 7471.0 \\
6.) & 82.74 \\
7.) & 1887.54 \\
8.) & 273.0 \\
9.) & 195.27 \\
10.) & 147.4 \\
11.) & 394.7 \\
12.) & 7463.87 \\
13.) & 1790.46 \\
14.) & 2203.75 \\
15.) & 120.6 \\
\end{array}
}
\]
1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both numbers being multiplied.
3. Place the decimal point in the product so that the total number of decimal places in the product equals the sum of the decimal places in the original numbers.
Let's solve each problem step by step.
---
Problem 1: \( 40.9 \times 2.1 \)
1. Multiply as whole numbers:
\( 409 \times 21 = 8589 \)
2. Count decimal places:
- \( 40.9 \) has 1 decimal place.
- \( 2.1 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 8589 \).
Result: \( 85.89 \).
Answer: \( 85.89 \)
---
Problem 2: \( 65.9 \times 26.4 \)
1. Multiply as whole numbers:
\( 659 \times 264 = 174696 \)
2. Count decimal places:
- \( 65.9 \) has 1 decimal place.
- \( 26.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 174696 \).
Result: \( 1746.96 \).
Answer: \( 1746.96 \)
---
Problem 3: \( 85.6 \times 80.5 \)
1. Multiply as whole numbers:
\( 856 \times 805 = 689380 \)
2. Count decimal places:
- \( 85.6 \) has 1 decimal place.
- \( 80.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 689380 \).
Result: \( 6893.80 \) or simply \( 6893.8 \).
Answer: \( 6893.8 \)
---
Problem 4: \( 88.6 \times 2.5 \)
1. Multiply as whole numbers:
\( 886 \times 25 = 22150 \)
2. Count decimal places:
- \( 88.6 \) has 1 decimal place.
- \( 2.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 22150 \).
Result: \( 221.50 \) or simply \( 221.5 \).
Answer: \( 221.5 \)
---
Problem 5: \( 92.5 \times 80.8 \)
1. Multiply as whole numbers:
\( 925 \times 808 = 747100 \)
2. Count decimal places:
- \( 92.5 \) has 1 decimal place.
- \( 80.8 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 747100 \).
Result: \( 7471.00 \) or simply \( 7471.0 \).
Answer: \( 7471.0 \)
---
Problem 6: \( 59.1 \times 1.4 \)
1. Multiply as whole numbers:
\( 591 \times 14 = 8274 \)
2. Count decimal places:
- \( 59.1 \) has 1 decimal place.
- \( 1.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 8274 \).
Result: \( 82.74 \).
Answer: \( 82.74 \)
---
Problem 7: \( 45.8 \times 41.3 \)
1. Multiply as whole numbers:
\( 458 \times 413 = 188754 \)
2. Count decimal places:
- \( 45.8 \) has 1 decimal place.
- \( 41.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 188754 \).
Result: \( 1887.54 \).
Answer: \( 1887.54 \)
---
Problem 8: \( 35.0 \times 7.8 \)
1. Multiply as whole numbers:
\( 350 \times 78 = 27300 \)
2. Count decimal places:
- \( 35.0 \) has 1 decimal place.
- \( 7.8 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 27300 \).
Result: \( 273.00 \) or simply \( 273.0 \).
Answer: \( 273.0 \)
---
Problem 9: \( 84.9 \times 2.3 \)
1. Multiply as whole numbers:
\( 849 \times 23 = 19527 \)
2. Count decimal places:
- \( 84.9 \) has 1 decimal place.
- \( 2.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 19527 \).
Result: \( 195.27 \).
Answer: \( 195.27 \)
---
Problem 10: \( 33.5 \times 4.4 \)
1. Multiply as whole numbers:
\( 335 \times 44 = 14740 \)
2. Count decimal places:
- \( 33.5 \) has 1 decimal place.
- \( 4.4 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 14740 \).
Result: \( 147.40 \) or simply \( 147.4 \).
Answer: \( 147.4 \)
---
Problem 11: \( 25.4 \times 15.5 \)
1. Multiply as whole numbers:
\( 254 \times 155 = 39470 \)
2. Count decimal places:
- \( 25.4 \) has 1 decimal place.
- \( 15.5 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 39470 \).
Result: \( 394.70 \) or simply \( 394.7 \).
Answer: \( 394.7 \)
---
Problem 12: \( 86.1 \times 86.7 \)
1. Multiply as whole numbers:
\( 861 \times 867 = 746387 \)
2. Count decimal places:
- \( 86.1 \) has 1 decimal place.
- \( 86.7 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 746387 \).
Result: \( 7463.87 \).
Answer: \( 7463.87 \)
---
Problem 13: \( 52.2 \times 34.3 \)
1. Multiply as whole numbers:
\( 522 \times 343 = 179046 \)
2. Count decimal places:
- \( 52.2 \) has 1 decimal place.
- \( 34.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 179046 \).
Result: \( 1790.46 \).
Answer: \( 1790.46 \)
---
Problem 14: \( 62.5 \times 35.3 \)
1. Multiply as whole numbers:
\( 625 \times 353 = 220375 \)
2. Count decimal places:
- \( 62.5 \) has 1 decimal place.
- \( 35.3 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 220375 \).
Result: \( 2203.75 \).
Answer: \( 2203.75 \)
---
Problem 15: \( 20.1 \times 6.0 \)
1. Multiply as whole numbers:
\( 201 \times 60 = 12060 \)
2. Count decimal places:
- \( 20.1 \) has 1 decimal place.
- \( 6.0 \) has 1 decimal place.
- Total decimal places: \( 1 + 1 = 2 \).
3. Place the decimal point:
Move the decimal point 2 places to the left in \( 12060 \).
Result: \( 120.60 \) or simply \( 120.6 \).
Answer: \( 120.6 \)
---
Final Answers
\[
\boxed{
\begin{array}{ll}
1.) & 85.89 \\
2.) & 1746.96 \\
3.) & 6893.8 \\
4.) & 221.5 \\
5.) & 7471.0 \\
6.) & 82.74 \\
7.) & 1887.54 \\
8.) & 273.0 \\
9.) & 195.27 \\
10.) & 147.4 \\
11.) & 394.7 \\
12.) & 7463.87 \\
13.) & 1790.46 \\
14.) & 2203.75 \\
15.) & 120.6 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of decimal multiplication worksheets.
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