Converting Decimals to Fractions Worksheet - Free Printable

To solve the problem of converting mixed decimals to fractions, we need to follow these steps:

Steps to Convert a Decimal to a Fraction:

1. Identify the whole number part and the decimal part.
2. Convert the decimal part to a fraction:
- The decimal part is written as a fraction with the denominator being a power of 10 (e.g., 0.6 becomes \( \frac{6}{10} \)).
3. Combine the whole number part with the fractional part to form a mixed fraction.
4. Convert the mixed fraction to an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the result to the numerator.
- Write the new numerator over the original denominator.

Detailed Solutions:

#### Example: Convert \( 2.6 \) to a fraction
- Whole number part: 2
- Decimal part: 0.6
- Fraction form of decimal part: \( \frac{6}{10} \)
- Mixed fraction: \( 2 \frac{6}{10} \)
- Improper fraction:
\[
2 \times 10 + 6 = 20 + 6 = 26 \quad \text{so} \quad \frac{26}{10}
\]

#### Now, let's solve all the problems step-by-step:

---

Problem 1: \( 2.6 \)

- Mixed: \( 2 \frac{6}{10} \)
- Improper: \( \frac{26}{10} \)

---

Problem 2: \( 1.3 \)

- Mixed: \( 1 \frac{3}{10} \)
- Improper: \( \frac{13}{10} \)

---

Problem 3: \( 3.1 \)

- Mixed: \( 3 \frac{1}{10} \)
- Improper: \( \frac{31}{10} \)

---

Problem 4: \( 0.9 \)

- Mixed: \( 0 \frac{9}{10} \) (or simply \( \frac{9}{10} \))
- Improper: \( \frac{9}{10} \)

---

Problem 5: \( 4.8 \)

- Mixed: \( 4 \frac{8}{10} \)
- Improper: \( \frac{48}{10} \)

---

Problem 6: \( 0.34 \)

- Mixed: \( 0 \frac{34}{100} \) (or simply \( \frac{34}{100} \))
- Improper: \( \frac{34}{100} \)

---

Problem 7: \( 1.58 \)

- Mixed: \( 1 \frac{58}{100} \)
- Improper: \( \frac{158}{100} \)

---

Problem 8: \( 4.81 \)

- Mixed: \( 4 \frac{81}{100} \)
- Improper: \( \frac{481}{100} \)

---

Problem 9: \( 1.43 \)

- Mixed: \( 1 \frac{43}{100} \)
- Improper: \( \frac{143}{100} \)

---

Problem 10: \( 0.85 \)

- Mixed: \( 0 \frac{85}{100} \) (or simply \( \frac{85}{100} \))
- Improper: \( \frac{85}{100} \)

---

Problem 11: \( 3.78 \)

- Mixed: \( 3 \frac{78}{100} \)
- Improper: \( \frac{378}{100} \)

---

Problem 12: \( 2.34 \)

- Mixed: \( 2 \frac{34}{100} \)
- Improper: \( \frac{234}{100} \)

---

Problem 13: \( 8.2 \)

- Mixed: \( 8 \frac{2}{10} \)
- Improper: \( \frac{82}{10} \)

---

Problem 14: \( 0.81 \)

- Mixed: \( 0 \frac{81}{100} \) (or simply \( \frac{81}{100} \))
- Improper: \( \frac{81}{100} \)

---

Problem 15: \( 4.7 \)

- Mixed: \( 4 \frac{7}{10} \)
- Improper: \( \frac{47}{10} \)

---

Problem 16: \( 2.35 \)

- Mixed: \( 2 \frac{35}{100} \)
- Improper: \( \frac{235}{100} \)

---

Problem 17: \( 1.29 \)

- Mixed: \( 1 \frac{29}{100} \)
- Improper: \( \frac{129}{100} \)

---

Problem 18: \( 6.45 \)

- Mixed: \( 6 \frac{45}{100} \)
- Improper: \( \frac{645}{100} \)

---

Problem 19: \( 5.03 \)

- Mixed: \( 5 \frac{3}{100} \)
- Improper: \( \frac{503}{100} \)

---

Problem 20: \( 8.6 \)

- Mixed: \( 8 \frac{6}{10} \)
- Improper: \( \frac{86}{10} \)

---

Problem 21: \( 1.09 \)

- Mixed: \( 1 \frac{9}{100} \)
- Improper: \( \frac{109}{100} \)

---

Problem 22: \( 7.36 \)

- Mixed: \( 7 \frac{36}{100} \)
- Improper: \( \frac{736}{100} \)

---

Final Answer:

\[
\boxed{
\begin{array}{c|c|c|c}
\text{Decimal} & \text{Mixed} & \text{Improper} \\
\hline
2.6 & 2 \frac{6}{10} & \frac{26}{10} \\
1.3 & 1 \frac{3}{10} & \frac{13}{10} \\
3.1 & 3 \frac{1}{10} & \frac{31}{10} \\
0.9 & 0 \frac{9}{10} & \frac{9}{10} \\
4.8 & 4 \frac{8}{10} & \frac{48}{10} \\
0.34 & 0 \frac{34}{100} & \frac{34}{100} \\
1.58 & 1 \frac{58}{100} & \frac{158}{100} \\
4.81 & 4 \frac{81}{100} & \frac{481}{100} \\
1.43 & 1 \frac{43}{100} & \frac{143}{100} \\
0.85 & 0 \frac{85}{100} & \frac{85}{100} \\
3.78 & 3 \frac{78}{100} & \frac{378}{100} \\
2.34 & 2 \frac{34}{100} & \frac{234}{100} \\
8.2 & 8 \frac{2}{10} & \frac{82}{10} \\
0.81 & 0 \frac{81}{100} & \frac{81}{100} \\
4.7 & 4 \frac{7}{10} & \frac{47}{10} \\
2.35 & 2 \frac{35}{100} & \frac{235}{100} \\
1.29 & 1 \frac{29}{100} & \frac{129}{100} \\
6.45 & 6 \frac{45}{100} & \frac{645}{100} \\
5.03 & 5 \frac{3}{100} & \frac{503}{100} \\
8.6 & 8 \frac{6}{10} & \frac{86}{10} \\
1.09 & 1 \frac{9}{100} & \frac{109}{100} \\
7.36 & 7 \frac{36}{100} & \frac{736}{100} \\
\end{array}
}
\]