Worksheet for converting decimals to fractions, including examples and practice problems.

Problem Overview:

The task is to convert given decimal numbers into fractions. Some of these fractions can be simplified. The worksheet provides an example: \(0.35\) can be written as \(\frac{35}{100}\), which can be simplified further.

Solution Approach:

1. Convert Decimals to Fractions:
- Each decimal number can be expressed as a fraction by placing the decimal digits over a denominator that is a power of 10 (e.g., \(0.27 = \frac{27}{100}\)).

2. Simplify the Fractions:
- Simplify the fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Step-by-Step Solution:

#### 1. \(0.27\)
- Decimal: \(0.27\)
- Fraction: \(\frac{27}{100}\)
- Simplify: The GCD of 27 and 100 is 1, so the fraction is already in its simplest form.
- Answer: \(\frac{27}{100}\)

#### 2. \(0.45\)
- Decimal: \(0.45\)
- Fraction: \(\frac{45}{100}\)
- Simplify: The GCD of 45 and 100 is 5. Divide both numerator and denominator by 5.
\[
\frac{45 \div 5}{100 \div 5} = \frac{9}{20}
\]
- Answer: \(\frac{9}{20}\)

#### 3. \(0.72\)
- Decimal: \(0.72\)
- Fraction: \(\frac{72}{100}\)
- Simplify: The GCD of 72 and 100 is 4. Divide both numerator and denominator by 4.
\[
\frac{72 \div 4}{100 \div 4} = \frac{18}{25}
\]
- Answer: \(\frac{18}{25}\)

#### 4. \(0.5\)
- Decimal: \(0.5\)
- Fraction: \(\frac{5}{10}\)
- Simplify: The GCD of 5 and 10 is 5. Divide both numerator and denominator by 5.
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
- Answer: \(\frac{1}{2}\)

#### 5. \(0.67\)
- Decimal: \(0.67\)
- Fraction: \(\frac{67}{100}\)
- Simplify: The GCD of 67 and 100 is 1, so the fraction is already in its simplest form.
- Answer: \(\frac{67}{100}\)

#### 6. \(0.80\)
- Decimal: \(0.80\)
- Fraction: \(\frac{80}{100}\)
- Simplify: The GCD of 80 and 100 is 20. Divide both numerator and denominator by 20.
\[
\frac{80 \div 20}{100 \div 20} = \frac{4}{5}
\]
- Answer: \(\frac{4}{5}\)

#### 7. \(0.77\)
- Decimal: \(0.77\)
- Fraction: \(\frac{77}{100}\)
- Simplify: The GCD of 77 and 100 is 1, so the fraction is already in its simplest form.
- Answer: \(\frac{77}{100}\)

#### 8. \(0.25\)
- Decimal: \(0.25\)
- Fraction: \(\frac{25}{100}\)
- Simplify: The GCD of 25 and 100 is 25. Divide both numerator and denominator by 25.
\[
\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
\]
- Answer: \(\frac{1}{4}\)

#### 9. \(0.60\)
- Decimal: \(0.60\)
- Fraction: \(\frac{60}{100}\)
- Simplify: The GCD of 60 and 100 is 20. Divide both numerator and denominator by 20.
\[
\frac{60 \div 20}{100 \div 20} = \frac{3}{5}
\]
- Answer: \(\frac{3}{5}\)

#### 10. \(0.99\)
- Decimal: \(0.99\)
- Fraction: \(\frac{99}{100}\)
- Simplify: The GCD of 99 and 100 is 1, so the fraction is already in its simplest form.
- Answer: \(\frac{99}{100}\)

#### 11. \(0.13\)
- Decimal: \(0.13\)
- Fraction: \(\frac{13}{100}\)
- Simplify: The GCD of 13 and 100 is 1, so the fraction is already in its simplest form.
- Answer: \(\frac{13}{100}\)

#### 12. \(0.1\)
- Decimal: \(0.1\)
- Fraction: \(\frac{1}{10}\)
- Simplify: The fraction is already in its simplest form.
- Answer: \(\frac{1}{10}\)

Final Answers:

\[
\boxed{
\begin{array}{ccc}
1. & \frac{27}{100} & 2. & \frac{9}{20} & 3. & \frac{18}{25} \\
4. & \frac{1}{2} & 5. & \frac{67}{100} & 6. & \frac{4}{5} \\
7. & \frac{77}{100} & 8. & \frac{1}{4} & 9. & \frac{3}{5} \\
10. & \frac{99}{100} & 11. & \frac{13}{100} & 12. & \frac{1}{10}
\end{array}
}
\]