Decimals to Fractions Worksheets - Free Printable

Problem:

The task is to convert the given decimal numbers into fractions. The worksheet provides the following decimals:

1. \( 0.75 \)
2. \( 0.333 \)
3. \( 0.833 \)
4. \( 0.375 \)
5. \( 0.2 \)
6. \( 0.4 \)
7. \( 0.5 \)
8. \( 0.8 \)
9. \( 0.75 \)
10. \( 0.5 \)

Solution:

We will convert each decimal into a fraction step by step.

---

#### 1. \( 0.75 \)
- Write \( 0.75 \) as a fraction: \( \frac{75}{100} \).
- Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 25:
\[
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
\]
- Answer: \( \frac{3}{4} \)

---

#### 2. \( 0.333 \)
- Recognize that \( 0.333 \) is approximately \( \frac{1}{3} \). To confirm:
- Write \( 0.333 \) as \( \frac{333}{1000} \).
- Since \( 0.333 \) is a repeating decimal, it is more accurately represented as \( \frac{1}{3} \).
- Answer: \( \frac{1}{3} \)

---

#### 3. \( 0.833 \)
- Recognize that \( 0.833 \) is approximately \( \frac{5}{6} \). To confirm:
- Write \( 0.833 \) as \( \frac{833}{1000} \).
- Since \( 0.833 \) is a repeating decimal, it is more accurately represented as \( \frac{5}{6} \).
- Answer: \( \frac{5}{6} \)

---

#### 4. \( 0.375 \)
- Write \( 0.375 \) as a fraction: \( \frac{375}{1000} \).
- Simplify the fraction by dividing both numerator and denominator by their GCD, which is 125:
\[
\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}
\]
- Answer: \( \frac{3}{8} \)

---

#### 5. \( 0.2 \)
- Write \( 0.2 \) as a fraction: \( \frac{2}{10} \).
- Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\]
- Answer: \( \frac{1}{5} \)

---

#### 6. \( 0.4 \)
- Write \( 0.4 \) as a fraction: \( \frac{4}{10} \).
- Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\]
- Answer: \( \frac{2}{5} \)

---

#### 7. \( 0.5 \)
- Write \( 0.5 \) as a fraction: \( \frac{5}{10} \).
- Simplify the fraction by dividing both numerator and denominator by their GCD, which is 5:
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
- Answer: \( \frac{1}{2} \)

---

#### 8. \( 0.8 \)
- Write \( 0.8 \) as a fraction: \( \frac{8}{10} \).
- Simplify the fraction by dividing both numerator and denominator by their GCD, which is 2:
\[
\frac{8 \div 2}{10 \div 2} = \frac{4}{5}
\]
- Answer: \( \frac{4}{5} \)

---

#### 9. \( 0.75 \)
- This is the same as the first problem.
- Answer: \( \frac{3}{4} \)

---

#### 10. \( 0.5 \)
- This is the same as the seventh problem.
- Answer: \( \frac{1}{2} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad \frac{3}{4} \\
2. & \quad \frac{1}{3} \\
3. & \quad \frac{5}{6} \\
4. & \quad \frac{3}{8} \\
5. & \quad \frac{1}{5} \\
6. & \quad \frac{2}{5} \\
7. & \quad \frac{1}{2} \\
8. & \quad \frac{4}{5} \\
9. & \quad \frac{3}{4} \\
10. & \quad \frac{1}{2}
\end{aligned}
}
\]