Decimals to Fractions Worksheets - Free Printable

Problem:

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

1. \( 0.833 \)
2. \( 0.4 \)
3. \( 0.333 \)
4. \( 0.75 \)
5. \( 0.167 \)
6. \( 0.25 \)
7. \( 0.667 \)
8. \( 0.875 \)
9. \( 0.667 \)
10. \( 0.75 \)

Solution:

#### Step 1: Understand the process of converting decimals to fractions
To convert a decimal to a fraction:
1. Write the decimal as a fraction with the decimal number as the numerator and a power of 10 as the denominator (based on the number of decimal places).
2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

#### Step 2: Solve each problem

1. \( 0.833 \)
- Write as \( \frac{833}{1000} \).
- This fraction cannot be simplified further because 833 and 1000 have no common factors other than 1.
- Answer: \( \frac{833}{1000} \)

2. \( 0.4 \)
- Write as \( \frac{4}{10} \).
- Simplify by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\]
- Answer: \( \frac{2}{5} \)

3. \( 0.333 \)
- Write as \( \frac{333}{1000} \).
- This fraction cannot be simplified further because 333 and 1000 have no common factors other than 1.
- Answer: \( \frac{333}{1000} \)

4. \( 0.75 \)
- Write as \( \frac{75}{100} \).
- Simplify by dividing both numerator and denominator by their GCD, which is 25:
\[
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
\]
- Answer: \( \frac{3}{4} \)

5. \( 0.167 \)
- Write as \( \frac{167}{1000} \).
- This fraction cannot be simplified further because 167 and 1000 have no common factors other than 1.
- Answer: \( \frac{167}{1000} \)

6. \( 0.25 \)
- Write as \( \frac{25}{100} \).
- Simplify by dividing both numerator and denominator by their GCD, which is 25:
\[
\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
\]
- Answer: \( \frac{1}{4} \)

7. \( 0.667 \)
- Write as \( \frac{667}{1000} \).
- This fraction cannot be simplified further because 667 and 1000 have no common factors other than 1.
- Answer: \( \frac{667}{1000} \)

8. \( 0.875 \)
- Write as \( \frac{875}{1000} \).
- Simplify by dividing both numerator and denominator by their GCD, which is 125:
\[
\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}
\]
- Answer: \( \frac{7}{8} \)

9. \( 0.667 \)
- Same as problem 7.
- Answer: \( \frac{667}{1000} \)

10. \( 0.75 \)
- Same as problem 4.
- Answer: \( \frac{3}{4} \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{833}{1000} \\
2. & \frac{2}{5} \\
3. & \frac{333}{1000} \\
4. & \frac{3}{4} \\
5. & \frac{167}{1000} \\
6. & \frac{1}{4} \\
7. & \frac{667}{1000} \\
8. & \frac{7}{8} \\
9. & \frac{667}{1000} \\
10. & \frac{3}{4} \\
\end{array}
}
\]