The task involves converting fractions into decimals using the
long division method. The provided image shows a worksheet with several fractions and their corresponding decimal equivalents. Below, I will explain how to solve one of these conversions step by step as an example, and then summarize the process.
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Example Problem: Convert \( \frac{3}{20} \) to a decimal
#### Step 1: Set up the long division
- The fraction \( \frac{3}{20} \) means we need to divide 3 by 20.
- Write it as \( 3 \div 20 \).
#### Step 2: Add a decimal point and zeros
- Since 3 is less than 20, we cannot divide 3 by 20 directly. Instead, we add a decimal point and zeros to 3, making it 3.000 (or more zeros if needed).
#### Step 3: Perform the division
1. Divide 30 (from 3.0) by 20:
- 20 goes into 30 once (1 × 20 = 20).
- Subtract 20 from 30 to get a remainder of 10.
2. Bring down the next zero, making the remainder 100.
- Divide 100 by 20:
- 20 goes into 100 five times (5 × 20 = 100).
- Subtract 100 from 100 to get a remainder of 0.
#### Step 4: Write the result
- The quotient is 0.15, so \( \frac{3}{20} = 0.15 \).
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General Process for Converting Fractions to Decimals Using Long Division
1.
Set up the division: Write the numerator as the dividend and the denominator as the divisor.
2.
Add a decimal point and zeros: If the numerator is smaller than the denominator, add a decimal point and zeros to the numerator.
3.
Perform the division: Divide the numerator by the denominator, bringing down zeros as needed until the division is complete or a repeating pattern emerges.
4.
Write the result: The quotient is the decimal equivalent of the fraction.
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Summary of the Worksheet Answers
The worksheet provides the following conversions:
1. \( \frac{18}{20} = 0.90 \)
2. \( \frac{2}{20} = 0.10 \)
3. \( \frac{7}{20} = 0.35 \)
4. \( \frac{0.8}{20} = 0.04 \)
5. \( \frac{0.5}{20} = 0.025 \)
6. \( \frac{0.1}{20} = 0.005 \)
7. \( \frac{0.9}{20} = 0.045 \)
8. \( \frac{0.55}{20} = 0.0275 \)
9. \( \frac{0.15}{20} = 0.0075 \)
Each of these conversions follows the same long division process described above.
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Final Answer:
\[
\boxed{0.15}
\] (for \( \frac{3}{20} \))
Parent Tip: Review the logic above to help your child master the concept of long division decimals worksheet.
