Convert decimals to fractions worksheet with 20 practice problems.
Worksheet for converting decimals to fractions with 20 problems listed in two columns.
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Step-by-step solution for: Convert decimals to fractions - Exercise 4 | Math fractions ...
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Show Answer Key & Explanations
Step-by-step solution for: Convert decimals to fractions - Exercise 4 | Math fractions ...
To solve the problem of converting decimals to fractions, we need to follow these steps:
1. Understand the decimal: Each decimal represents a number that can be expressed as a fraction.
2. Convert the decimal to a fraction:
- Write the decimal as a fraction with the decimal number as the numerator and a denominator that is a power of 10 (based on the number of decimal places).
- Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by the GCD.
Let's solve each problem step by step:
---
- Decimal: 0.7
- Fraction: \( \frac{7}{10} \)
- Simplified: \( \frac{7}{10} \) (already in simplest form)
Answer: \( \frac{7}{10} \)
---
- Decimal: 0.78
- Fraction: \( \frac{78}{100} \)
- Simplify: The GCD of 78 and 100 is 2.
\[
\frac{78 \div 2}{100 \div 2} = \frac{39}{50}
\]
Answer: \( \frac{39}{50} \)
---
- Decimal: 0.57
- Fraction: \( \frac{57}{100} \)
- Simplify: The GCD of 57 and 100 is 1.
\[
\frac{57}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{57}{100} \)
---
- Decimal: 0.9
- Fraction: \( \frac{9}{10} \)
- Simplified: \( \frac{9}{10} \) (already in simplest form)
Answer: \( \frac{9}{10} \)
---
- Decimal: 0.76
- Fraction: \( \frac{76}{100} \)
- Simplify: The GCD of 76 and 100 is 4.
\[
\frac{76 \div 4}{100 \div 4} = \frac{19}{25}
\]
Answer: \( \frac{19}{25} \)
---
- Decimal: 0.85
- Fraction: \( \frac{85}{100} \)
- Simplify: The GCD of 85 and 100 is 5.
\[
\frac{85 \div 5}{100 \div 5} = \frac{17}{20}
\]
Answer: \( \frac{17}{20} \)
---
- Decimal: 0.48
- Fraction: \( \frac{48}{100} \)
- Simplify: The GCD of 48 and 100 is 4.
\[
\frac{48 \div 4}{100 \div 4} = \frac{12}{25}
\]
Answer: \( \frac{12}{25} \)
---
- Decimal: 0.77
- Fraction: \( \frac{77}{100} \)
- Simplify: The GCD of 77 and 100 is 1.
\[
\frac{77}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{77}{100} \)
---
- Decimal: 0.53
- Fraction: \( \frac{53}{100} \)
- Simplify: The GCD of 53 and 100 is 1.
\[
\frac{53}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{53}{100} \)
---
- Decimal: 0.37
- Fraction: \( \frac{37}{100} \)
- Simplify: The GCD of 37 and 100 is 1.
\[
\frac{37}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{37}{100} \)
---
- Decimal: 0.5
- Fraction: \( \frac{5}{10} \)
- Simplify: The GCD of 5 and 10 is 5.
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
Answer: \( \frac{1}{2} \)
---
- Decimal: 0.42
- Fraction: \( \frac{42}{100} \)
- Simplify: The GCD of 42 and 100 is 2.
\[
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
\]
Answer: \( \frac{21}{50} \)
---
- Decimal: 0.36
- Fraction: \( \frac{36}{100} \)
- Simplify: The GCD of 36 and 100 is 4.
\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\]
Answer: \( \frac{9}{25} \)
---
- Decimal: 0.38
- Fraction: \( \frac{38}{100} \)
- Simplify: The GCD of 38 and 100 is 2.
\[
\frac{38 \div 2}{100 \div 2} = \frac{19}{50}
\]
Answer: \( \frac{19}{50} \)
---
- Decimal: 0.7
- Fraction: \( \frac{7}{10} \)
- Simplified: \( \frac{7}{10} \) (already in simplest form)
Answer: \( \frac{7}{10} \)
---
- Decimal: 0.36
- Fraction: \( \frac{36}{100} \)
- Simplify: The GCD of 36 and 100 is 4.
\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\]
Answer: \( \frac{9}{25} \)
---
- Decimal: 0.57
- Fraction: \( \frac{57}{100} \)
- Simplify: The GCD of 57 and 100 is 1.
\[
\frac{57}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{57}{100} \)
---
- Decimal: 0.1
- Fraction: \( \frac{1}{10} \)
- Simplified: \( \frac{1}{10} \) (already in simplest form)
Answer: \( \frac{1}{10} \)
---
- Decimal: 0.46
- Fraction: \( \frac{46}{100} \)
- Simplify: The GCD of 46 and 100 is 2.
\[
\frac{46 \div 2}{100 \div 2} = \frac{23}{50}
\]
Answer: \( \frac{23}{50} \)
---
- Decimal: 0.16
- Fraction: \( \frac{16}{100} \)
- Simplify: The GCD of 16 and 100 is 4.
\[
\frac{16 \div 4}{100 \div 4} = \frac{4}{25}
\]
Answer: \( \frac{4}{25} \)
---
\[
\boxed{
\begin{array}{ll}
1. & \frac{7}{10} \\
2. & \frac{39}{50} \\
3. & \frac{57}{100} \\
4. & \frac{9}{10} \\
5. & \frac{19}{25} \\
6. & \frac{17}{20} \\
7. & \frac{12}{25} \\
8. & \frac{77}{100} \\
9. & \frac{53}{100} \\
10. & \frac{37}{100} \\
11. & \frac{1}{2} \\
12. & \frac{21}{50} \\
13. & \frac{9}{25} \\
14. & \frac{19}{50} \\
15. & \frac{7}{10} \\
16. & \frac{9}{25} \\
17. & \frac{57}{100} \\
18. & \frac{1}{10} \\
19. & \frac{23}{50} \\
20. & \frac{4}{25} \\
\end{array}
}
\]
1. Understand the decimal: Each decimal represents a number that can be expressed as a fraction.
2. Convert the decimal to a fraction:
- Write the decimal as a fraction with the decimal number as the numerator and a denominator that is a power of 10 (based on the number of decimal places).
- Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by the GCD.
Let's solve each problem step by step:
---
Problem 1: 0.7
- Decimal: 0.7
- Fraction: \( \frac{7}{10} \)
- Simplified: \( \frac{7}{10} \) (already in simplest form)
Answer: \( \frac{7}{10} \)
---
Problem 2: 0.78
- Decimal: 0.78
- Fraction: \( \frac{78}{100} \)
- Simplify: The GCD of 78 and 100 is 2.
\[
\frac{78 \div 2}{100 \div 2} = \frac{39}{50}
\]
Answer: \( \frac{39}{50} \)
---
Problem 3: 0.57
- Decimal: 0.57
- Fraction: \( \frac{57}{100} \)
- Simplify: The GCD of 57 and 100 is 1.
\[
\frac{57}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{57}{100} \)
---
Problem 4: 0.9
- Decimal: 0.9
- Fraction: \( \frac{9}{10} \)
- Simplified: \( \frac{9}{10} \) (already in simplest form)
Answer: \( \frac{9}{10} \)
---
Problem 5: 0.76
- Decimal: 0.76
- Fraction: \( \frac{76}{100} \)
- Simplify: The GCD of 76 and 100 is 4.
\[
\frac{76 \div 4}{100 \div 4} = \frac{19}{25}
\]
Answer: \( \frac{19}{25} \)
---
Problem 6: 0.85
- Decimal: 0.85
- Fraction: \( \frac{85}{100} \)
- Simplify: The GCD of 85 and 100 is 5.
\[
\frac{85 \div 5}{100 \div 5} = \frac{17}{20}
\]
Answer: \( \frac{17}{20} \)
---
Problem 7: 0.48
- Decimal: 0.48
- Fraction: \( \frac{48}{100} \)
- Simplify: The GCD of 48 and 100 is 4.
\[
\frac{48 \div 4}{100 \div 4} = \frac{12}{25}
\]
Answer: \( \frac{12}{25} \)
---
Problem 8: 0.77
- Decimal: 0.77
- Fraction: \( \frac{77}{100} \)
- Simplify: The GCD of 77 and 100 is 1.
\[
\frac{77}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{77}{100} \)
---
Problem 9: 0.53
- Decimal: 0.53
- Fraction: \( \frac{53}{100} \)
- Simplify: The GCD of 53 and 100 is 1.
\[
\frac{53}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{53}{100} \)
---
Problem 10: 0.37
- Decimal: 0.37
- Fraction: \( \frac{37}{100} \)
- Simplify: The GCD of 37 and 100 is 1.
\[
\frac{37}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{37}{100} \)
---
Problem 11: 0.5
- Decimal: 0.5
- Fraction: \( \frac{5}{10} \)
- Simplify: The GCD of 5 and 10 is 5.
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
Answer: \( \frac{1}{2} \)
---
Problem 12: 0.42
- Decimal: 0.42
- Fraction: \( \frac{42}{100} \)
- Simplify: The GCD of 42 and 100 is 2.
\[
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
\]
Answer: \( \frac{21}{50} \)
---
Problem 13: 0.36
- Decimal: 0.36
- Fraction: \( \frac{36}{100} \)
- Simplify: The GCD of 36 and 100 is 4.
\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\]
Answer: \( \frac{9}{25} \)
---
Problem 14: 0.38
- Decimal: 0.38
- Fraction: \( \frac{38}{100} \)
- Simplify: The GCD of 38 and 100 is 2.
\[
\frac{38 \div 2}{100 \div 2} = \frac{19}{50}
\]
Answer: \( \frac{19}{50} \)
---
Problem 15: 0.7
- Decimal: 0.7
- Fraction: \( \frac{7}{10} \)
- Simplified: \( \frac{7}{10} \) (already in simplest form)
Answer: \( \frac{7}{10} \)
---
Problem 16: 0.36
- Decimal: 0.36
- Fraction: \( \frac{36}{100} \)
- Simplify: The GCD of 36 and 100 is 4.
\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\]
Answer: \( \frac{9}{25} \)
---
Problem 17: 0.57
- Decimal: 0.57
- Fraction: \( \frac{57}{100} \)
- Simplify: The GCD of 57 and 100 is 1.
\[
\frac{57}{100} \text{ (already in simplest form)}
\]
Answer: \( \frac{57}{100} \)
---
Problem 18: 0.1
- Decimal: 0.1
- Fraction: \( \frac{1}{10} \)
- Simplified: \( \frac{1}{10} \) (already in simplest form)
Answer: \( \frac{1}{10} \)
---
Problem 19: 0.46
- Decimal: 0.46
- Fraction: \( \frac{46}{100} \)
- Simplify: The GCD of 46 and 100 is 2.
\[
\frac{46 \div 2}{100 \div 2} = \frac{23}{50}
\]
Answer: \( \frac{23}{50} \)
---
Problem 20: 0.16
- Decimal: 0.16
- Fraction: \( \frac{16}{100} \)
- Simplify: The GCD of 16 and 100 is 4.
\[
\frac{16 \div 4}{100 \div 4} = \frac{4}{25}
\]
Answer: \( \frac{4}{25} \)
---
Final Answers
\[
\boxed{
\begin{array}{ll}
1. & \frac{7}{10} \\
2. & \frac{39}{50} \\
3. & \frac{57}{100} \\
4. & \frac{9}{10} \\
5. & \frac{19}{25} \\
6. & \frac{17}{20} \\
7. & \frac{12}{25} \\
8. & \frac{77}{100} \\
9. & \frac{53}{100} \\
10. & \frac{37}{100} \\
11. & \frac{1}{2} \\
12. & \frac{21}{50} \\
13. & \frac{9}{25} \\
14. & \frac{19}{50} \\
15. & \frac{7}{10} \\
16. & \frac{9}{25} \\
17. & \frac{57}{100} \\
18. & \frac{1}{10} \\
19. & \frac{23}{50} \\
20. & \frac{4}{25} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of decimal to fraction worksheet printable.
