Converting Decimals to Fractions Worksheet - Free Printable

To solve the problem of converting mixed decimals to fractions, we need to follow a systematic approach. Let's go through each step and convert the given decimal numbers into fractions.

General Steps:

1. Identify the whole number part (if any) and the decimal part.
2. Convert the decimal part to a fraction by placing the decimal digits over a power of 10.
3. Simplify the fraction if possible.
4. Combine the whole number part with the fractional part (if there is a whole number part).

Let's solve each problem step by step:

---

Problem 1: $2.25$

- Whole number part: $2$
- Decimal part: $0.25$
- Convert $0.25$ to a fraction:
$$
0.25 = \frac{25}{100} = \frac{1}{4}
$$
- Combine the whole number and the fraction:
$$
2 + \frac{1}{4} = 2\frac{1}{4}
$$

Answer: $2\frac{1}{4}$

---

Problem 2: $1.75$

- Whole number part: $1$
- Decimal part: $0.75$
- Convert $0.75$ to a fraction:
$$
0.75 = \frac{75}{100} = \frac{3}{4}
$$
- Combine the whole number and the fraction:
$$
1 + \frac{3}{4} = 1\frac{3}{4}
$$

Answer: $1\frac{3}{4}$

---

Problem 3: $0.75$

- Whole number part: $0$
- Decimal part: $0.75$
- Convert $0.75$ to a fraction:
$$
0.75 = \frac{75}{100} = \frac{3}{4}
$$

Answer: $\frac{3}{4}$

---

Problem 4: $0.333$

- Whole number part: $0$
- Decimal part: $0.333$
- Recognize that $0.333$ is approximately $\frac{1}{3}$ (since $0.333 \approx \frac{1}{3}$).
- Convert $0.333$ to a fraction:
$$
0.333 \approx \frac{1}{3}
$$

Answer: $\frac{1}{3}$

---

Problem 5: $4.32$

- Whole number part: $4$
- Decimal part: $0.32$
- Convert $0.32$ to a fraction:
$$
0.32 = \frac{32}{100} = \frac{8}{25}
$$
- Combine the whole number and the fraction:
$$
4 + \frac{8}{25} = 4\frac{8}{25}
$$

Answer: $4\frac{8}{25}$

---

Problem 6: $2.35$

- Whole number part: $2$
- Decimal part: $0.35$
- Convert $0.35$ to a fraction:
$$
0.35 = \frac{35}{100} = \frac{7}{20}
$$
- Combine the whole number and the fraction:
$$
2 + \frac{7}{20} = 2\frac{7}{20}
$$

Answer: $2\frac{7}{20}$

---

Problem 7: $1.348$

- Whole number part: $1$
- Decimal part: $0.348$
- Convert $0.348$ to a fraction:
$$
0.348 = \frac{348}{1000} = \frac{87}{250}
$$
- Combine the whole number and the fraction:
$$
1 + \frac{87}{250} = 1\frac{87}{250}
$$

Answer: $1\frac{87}{250}$

---

Problem 8: $9.012$

- Whole number part: $9$
- Decimal part: $0.012$
- Convert $0.012$ to a fraction:
$$
0.012 = \frac{12}{1000} = \frac{3}{250}
$$
- Combine the whole number and the fraction:
$$
9 + \frac{3}{250} = 9\frac{3}{250}
$$

Answer: $9\frac{3}{250}$

---

Problem 9: $2.81$

- Whole number part: $2$
- Decimal part: $0.81$
- Convert $0.81$ to a fraction:
$$
0.81 = \frac{81}{100}
$$
- Combine the whole number and the fraction:
$$
2 + \frac{81}{100} = 2\frac{81}{100}
$$

Answer: $2\frac{81}{100}$

---

Problem 10: $5.662$

- Whole number part: $5$
- Decimal part: $0.662$
- Convert $0.662$ to a fraction:
$$
0.662 = \frac{662}{1000} = \frac{331}{500}
$$
- Combine the whole number and the fraction:
$$
5 + \frac{331}{500} = 5\frac{331}{500}
$$

Answer: $5\frac{331}{500}$

---

Problem 11: $1.667$

- Whole number part: $1$
- Decimal part: $0.667$
- Recognize that $0.667$ is approximately $\frac{2}{3}$ (since $0.667 \approx \frac{2}{3}$).
- Convert $0.667$ to a fraction:
$$
0.667 \approx \frac{2}{3}
$$
- Combine the whole number and the fraction:
$$
1 + \frac{2}{3} = 1\frac{2}{3}
$$

Answer: $1\frac{2}{3}$

---

Problem 12: $8.5$

- Whole number part: $8$
- Decimal part: $0.5$
- Convert $0.5$ to a fraction:
$$
0.5 = \frac{5}{10} = \frac{1}{2}
$$
- Combine the whole number and the fraction:
$$
8 + \frac{1}{2} = 8\frac{1}{2}
$$

Answer: $8\frac{1}{2}$

---

Problem 13: $2.338$

- Whole number part: $2$
- Decimal part: $0.338$
- Convert $0.338$ to a fraction:
$$
0.338 = \frac{338}{1000} = \frac{169}{500}
$$
- Combine the whole number and the fraction:
$$
2 + \frac{169}{500} = 2\frac{169}{500}
$$

Answer: $2\frac{169}{500}$

---

Problem 14: $0.375$

- Whole number part: $0$
- Decimal part: $0.375$
- Convert $0.375$ to a fraction:
$$
0.375 = \frac{375}{1000} = \frac{3}{8}
$$

Answer: $\frac{3}{8}$

---

Final Answers:

$$
\boxed{
\begin{array}{ll}
\text{a)} & 2\frac{1}{4} \\
\text{b)} & 1\frac{3}{4} \\
\text{c)} & \frac{3}{4} \\
\text{d)} & \frac{1}{3} \\
\text{e)} & 4\frac{8}{25} \\
\text{f)} & 2\frac{7}{20} \\
\text{g)} & 1\frac{87}{250} \\
\text{h)} & 9\frac{3}{250} \\
\text{i)} & 2\frac{81}{100} \\
\text{j)} & 5\frac{331}{500} \\
\text{k)} & 1\frac{2}{3} \\
\text{l)} & 8\frac{1}{2} \\
\text{m)} & 2\frac{169}{500} \\
\text{n)} & \frac{3}{8} \\
\end{array}
}
$$