Converting Decimals to Fractions Worksheet Download - Free Printable

Problem Overview:

The task involves converting decimals to fractions. The worksheet provides examples and a set of problems for practice. Each decimal is to be converted into its fractional form, simplified if possible.

Key Concepts:

1. Understanding Place Values:
- Decimals are based on place values (tenths, hundredths, thousandths, etc.).
- For example:
- \(0.9\) is in the tenths place.
- \(0.63\) is in the hundredths place.

2. Converting to Fractions:
- Write the decimal as a fraction with the denominator corresponding to the place value.
- Simplify the fraction if possible.

Solution Explanation:

#### Example Provided:
- Example 1: Convert \(0.9\) to a fraction.
- \(0.9\) is in the tenths place.
- Write it as \(\frac{9}{10}\).
- This fraction is already in simplest form.

- Example 2: Convert \(0.63\) to a fraction.
- \(0.63\) is in the hundredths place.
- Write it as \(\frac{63}{100}\).
- This fraction cannot be simplified further.

#### General Steps:
1. Identify the place value of the decimal.
2. Write the decimal as a fraction with the denominator matching the place value.
3. Simplify the fraction if possible.

Solving the Problems:

#### Problem 1: \(0.78\)
- Place value: Hundredths.
- Fraction: \(\frac{78}{100}\).
- Simplify: \(\frac{78}{100} = \frac{39}{50}\) (dividing numerator and denominator by 2).

#### Problem 2: \(0.97\)
- Place value: Hundredths.
- Fraction: \(\frac{97}{100}\).
- This fraction is already in simplest form.

#### Problem 3: \(0.8\)
- Place value: Tenths.
- Fraction: \(\frac{8}{10}\).
- Simplify: \(\frac{8}{10} = \frac{4}{5}\) (dividing numerator and denominator by 2).

#### Problem 4: \(0.25\)
- Place value: Hundredths.
- Fraction: \(\frac{25}{100}\).
- Simplify: \(\frac{25}{100} = \frac{1}{4}\) (dividing numerator and denominator by 25).

#### Problem 5: \(0.82\)
- Place value: Hundredths.
- Fraction: \(\frac{82}{100}\).
- Simplify: \(\frac{82}{100} = \frac{41}{50}\) (dividing numerator and denominator by 2).

#### Problem 6: \(0.5\)
- Place value: Tenths.
- Fraction: \(\frac{5}{10}\).
- Simplify: \(\frac{5}{10} = \frac{1}{2}\) (dividing numerator and denominator by 5).

#### Problem 7: \(0.06\)
- Place value: Hundredths.
- Fraction: \(\frac{6}{100}\).
- Simplify: \(\frac{6}{100} = \frac{3}{50}\) (dividing numerator and denominator by 2).

#### Problem 8: \(0.03\)
- Place value: Hundredths.
- Fraction: \(\frac{3}{100}\).
- This fraction is already in simplest form.

#### Problem 9: \(0.4\)
- Place value: Tenths.
- Fraction: \(\frac{4}{10}\).
- Simplify: \(\frac{4}{10} = \frac{2}{5}\) (dividing numerator and denominator by 2).

#### Problem 10: \(0.33\)
- Place value: Hundredths.
- Fraction: \(\frac{33}{100}\).
- This fraction is already in simplest form.

#### Problem 11: \(0.2\)
- Place value: Tenths.
- Fraction: \(\frac{2}{10}\).
- Simplify: \(\frac{2}{10} = \frac{1}{5}\) (dividing numerator and denominator by 2).

#### Problem 12: \(0.95\)
- Place value: Hundredths.
- Fraction: \(\frac{95}{100}\).
- Simplify: \(\frac{95}{100} = \frac{19}{20}\) (dividing numerator and denominator by 5).

#### Problem 13: \(0.07\)
- Place value: Hundredths.
- Fraction: \(\frac{7}{100}\).
- This fraction is already in simplest form.

#### Problem 14: \(0.1\)
- Place value: Tenths.
- Fraction: \(\frac{1}{10}\).
- This fraction is already in simplest form.

#### Problem 15: \(0.9\)
- Place value: Tenths.
- Fraction: \(\frac{9}{10}\).
- This fraction is already in simplest form.

#### Problem 16: \(0.09\)
- Place value: Hundredths.
- Fraction: \(\frac{9}{100}\).
- This fraction is already in simplest form.

#### Problem 17: \(0.01\)
- Place value: Hundredths.
- Fraction: \(\frac{1}{100}\).
- This fraction is already in simplest form.

#### Problem 18: \(0.17\)
- Place value: Hundredths.
- Fraction: \(\frac{17}{100}\).
- This fraction is already in simplest form.

#### Problem 19: \(0.08\)
- Place value: Hundredths.
- Fraction: \(\frac{8}{100}\).
- Simplify: \(\frac{8}{100} = \frac{2}{25}\) (dividing numerator and denominator by 4).

#### Problem 20: \(0.94\)
- Place value: Hundredths.
- Fraction: \(\frac{94}{100}\).
- Simplify: \(\frac{94}{100} = \frac{47}{50}\) (dividing numerator and denominator by 2).

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & \frac{39}{50} \\
2) & \frac{97}{100} \\
3) & \frac{4}{5} \\
4) & \frac{1}{4} \\
5) & \frac{41}{50} \\
6) & \frac{1}{2} \\
7) & \frac{3}{50} \\
8) & \frac{3}{100} \\
9) & \frac{2}{5} \\
10) & \frac{33}{100} \\
11) & \frac{1}{5} \\
12) & \frac{19}{20} \\
13) & \frac{7}{100} \\
14) & \frac{1}{10} \\
15) & \frac{9}{10} \\
16) & \frac{9}{100} \\
17) & \frac{1}{100} \\
18) & \frac{17}{100} \\
19) & \frac{2}{25} \\
20) & \frac{47}{50} \\
\end{array}
}
\]