Grade 5 worksheet for converting decimals to fractions.

Problem:

The task is to convert the given decimal numbers into fractions. Here are the decimals provided:

1. 0.83
2. 0.4
3. 0.24
4. 0.96
5. 0.6
6. 0.2
7. 0.7
8. 0.19
9. 0.95
10. 0.1
11. 0.23
12. 0.68
13. 0.2
14. 0.97
15. 0.94
16. 0.5

Solution Approach:

To convert a decimal to a fraction, follow these steps:
1. Identify the place value of the decimal: Determine how many digits are after the decimal point.
2. Write the decimal as a fraction:
- The numerator is the decimal number without the decimal point.
- The denominator is a power of 10 corresponding to the number of decimal places.
3. Simplify the fraction: Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Step-by-Step Conversion:

#### 1. 0.83
- Decimal: 0.83
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{83}{100} \)
- Simplify: 83 and 100 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{83}{100} \)

#### 2. 0.4
- Decimal: 0.4
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{4}{10} \)
- Simplify: GCD of 4 and 10 is 2. Divide both by 2.
\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\]
- Result: \( \frac{2}{5} \)

#### 3. 0.24
- Decimal: 0.24
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{24}{100} \)
- Simplify: GCD of 24 and 100 is 4. Divide both by 4.
\[
\frac{24 \div 4}{100 \div 4} = \frac{6}{25}
\]
- Result: \( \frac{6}{25} \)

#### 4. 0.96
- Decimal: 0.96
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{96}{100} \)
- Simplify: GCD of 96 and 100 is 4. Divide both by 4.
\[
\frac{96 \div 4}{100 \div 4} = \frac{24}{25}
\]
- Result: \( \frac{24}{25} \)

#### 5. 0.6
- Decimal: 0.6
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{6}{10} \)
- Simplify: GCD of 6 and 10 is 2. Divide both by 2.
\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
- Result: \( \frac{3}{5} \)

#### 6. 0.2
- Decimal: 0.2
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{2}{10} \)
- Simplify: GCD of 2 and 10 is 2. Divide both by 2.
\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\]
- Result: \( \frac{1}{5} \)

#### 7. 0.7
- Decimal: 0.7
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{7}{10} \)
- Simplify: 7 and 10 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{7}{10} \)

#### 8. 0.19
- Decimal: 0.19
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{19}{100} \)
- Simplify: 19 and 100 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{19}{100} \)

#### 9. 0.95
- Decimal: 0.95
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{95}{100} \)
- Simplify: GCD of 95 and 100 is 5. Divide both by 5.
\[
\frac{95 \div 5}{100 \div 5} = \frac{19}{20}
\]
- Result: \( \frac{19}{20} \)

#### 10. 0.1
- Decimal: 0.1
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{1}{10} \)
- Simplify: 1 and 10 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{1}{10} \)

#### 11. 0.23
- Decimal: 0.23
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{23}{100} \)
- Simplify: 23 and 100 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{23}{100} \)

#### 12. 0.68
- Decimal: 0.68
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{68}{100} \)
- Simplify: GCD of 68 and 100 is 4. Divide both by 4.
\[
\frac{68 \div 4}{100 \div 4} = \frac{17}{25}
\]
- Result: \( \frac{17}{25} \)

#### 13. 0.2
- Decimal: 0.2
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{2}{10} \)
- Simplify: GCD of 2 and 10 is 2. Divide both by 2.
\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\]
- Result: \( \frac{1}{5} \)

#### 14. 0.97
- Decimal: 0.97
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{97}{100} \)
- Simplify: 97 and 100 have no common factors other than 1, so the fraction is already in simplest form.
- Result: \( \frac{97}{100} \)

#### 15. 0.94
- Decimal: 0.94
- Place value: 2 decimal places → Denominator = 100
- Fraction: \( \frac{94}{100} \)
- Simplify: GCD of 94 and 100 is 2. Divide both by 2.
\[
\frac{94 \div 2}{100 \div 2} = \frac{47}{50}
\]
- Result: \( \frac{47}{50} \)

#### 16. 0.5
- Decimal: 0.5
- Place value: 1 decimal place → Denominator = 10
- Fraction: \( \frac{5}{10} \)
- Simplify: GCD of 5 and 10 is 5. Divide both by 5.
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
- Result: \( \frac{1}{2} \)

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \frac{83}{100} \\
2. & \frac{2}{5} \\
3. & \frac{6}{25} \\
4. & \frac{24}{25} \\
5. & \frac{3}{5} \\
6. & \frac{1}{5} \\
7. & \frac{7}{10} \\
8. & \frac{19}{100} \\
9. & \frac{19}{20} \\
10. & \frac{1}{10} \\
11. & \frac{23}{100} \\
12. & \frac{17}{25} \\
13. & \frac{1}{5} \\
14. & \frac{97}{100} \\
15. & \frac{47}{50} \\
16. & \frac{1}{2} \\
\end{array}
}
\]