Fractions Decimals and Percents Worksheets - Math Monks - Free Printable

Let's solve each problem step by step with clear explanations.

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① Convert each fraction into decimal.

To convert a fraction to a decimal, divide the numerator by the denominator.

a.
$$
\frac{46}{100} = 0.46
$$
*Explanation:* Since the denominator is 100, just move the decimal point two places left: 46 → 0.46

b.
$$
\frac{6}{100} = 0.06
$$
*Explanation:* 6 divided by 100 = 0.06

c.
$$
\frac{292}{1000} = 0.292
$$
*Explanation:* Denominator is 1000 → move decimal three places left: 292 → 0.292

d.
$$
\frac{46}{100} = 0.46
$$
*Same as part (a)*

✔ Answers:
- a. 0.46
- b. 0.06
- c. 0.292
- d. 0.46

---

② Convert each decimal into fraction.

Write the decimal as a fraction over its place value, then simplify.

a.
$$
0.07 = \frac{7}{100}
$$
*Explanation:* 0.07 is 7 hundredths → $\frac{7}{100}$, already simplified.

b.
$$
0.67 = \frac{67}{100}
$$
*Explanation:* 67 hundredths → $\frac{67}{100}$, simplified.

c.
$$
9.37 = \frac{937}{100}
$$
*Explanation:* 9.37 = 9 + 0.37 = $\frac{937}{100}$ (since 0.37 = 37/100)
You can write it as a mixed number: $9\frac{37}{100}$, but improper fraction is acceptable.

d.
$$
27.17 = \frac{2717}{100}
$$
*Explanation:* 27.17 = 27 + 0.17 = $\frac{2717}{100}$

✔ Answers:
- a. $\frac{7}{100}$
- b. $\frac{67}{100}$
- c. $\frac{937}{100}$ or $9\frac{37}{100}$
- d. $\frac{2717}{100}$ or $27\frac{17}{100}$

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③ Convert each fraction into percent.

To convert a fraction to a percent: divide numerator by denominator, then multiply by 100.

a.
$$
\frac{2}{7} \approx ?
$$
Divide: $2 ÷ 7 ≈ 0.2857$ → $0.2857 × 100 ≈ 28.57\%$

b.
$$
\frac{11}{12} ≈ ?
$$
$11 ÷ 12 ≈ 0.9167$ → $0.9167 × 100 ≈ 91.67\%$

c.
$$
\frac{100}{113} ≈ ?
$$
$100 ÷ 113 ≈ 0.8849$ → $0.8849 × 100 ≈ 88.49\%$

d.
$$
\frac{20}{27} ≈ ?
$$
$20 ÷ 27 ≈ 0.7407$ → $0.7407 × 100 ≈ 74.07\%$

✔ Answers (rounded to two decimal places):
- a. 28.57%
- b. 91.67%
- c. 88.49%
- d. 74.07%

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④ Convert each percent into fraction.

Remove % sign, write over 100, then simplify.

a.
$$
37.17\% = \frac{37.17}{100} = \frac{3717}{10000}
$$
*Explanation:* Multiply numerator and denominator by 100 to eliminate decimal:
$\frac{37.17}{100} = \frac{3717}{10000}$ → already in simplest form (check GCF of 3717 and 10000 — no common factors).

b.
$$
805.11\% = \frac{805.11}{100} = \frac{80511}{10000}
$$
Multiply numerator and denominator by 100:
→ $\frac{80511}{10000}$ (no simplification possible)

c.
$$
6394.37\% = \frac{6394.37}{100} = \frac{639437}{10000}
$$
Again, multiply numerator and denominator by 100 → $\frac{639437}{10000}$

d.
$$
0.09\% = \frac{0.09}{100} = \frac{9}{10000}
$$
*Explanation:* $0.09 ÷ 100 = 0.0009$, but better:
$\frac{0.09}{100} = \frac{9}{10000}$ (multiply numerator and denominator by 100)

✔ Answers:
- a. $\frac{3717}{10000}$
- b. $\frac{80511}{10000}$
- c. $\frac{639437}{10000}$
- d. $\frac{9}{10000}$

---

⑤ Convert each percent into decimal.

Divide by 100 (move decimal two places left).

a.
$$
11.33\% = \frac{11.33}{100} = 0.1133
$$

b.
$$
77\frac{1}{3}\% = 77.\overline{3}\%
$$
First convert $77\frac{1}{3} = 77 + \frac{1}{3} = \frac{232}{3}$
Now divide by 100: $\frac{232}{3} ÷ 100 = \frac{232}{300} = \frac{58}{75} ≈ 0.7733$

But directly:
$77.\overline{3}\% = 0.7733...$ → $0.77\overline{3}$

So:
$$
77\frac{1}{3}\% = 0.77\overline{3}
$$

c.
$$
90\frac{1}{2}\% = 90.5\% = \frac{90.5}{100} = 0.905
$$

d.
$$
80.3\% = \frac{80.3}{100} = 0.803
$$

✔ Answers:
- a. 0.1133
- b. $0.77\overline{3}$ or approximately 0.7733
- c. 0.905
- d. 0.803

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⑥ Convert each decimal into percent.

Multiply by 100 (move decimal two places right).

a.
$$
0.37 = 37\%
$$

b.
$$
0.22 = 22\%
$$

c.
$$
0.99 = 99\%
$$

d.
$$
0.01 = 1\%
$$

✔ Answers:
- a. 37%
- b. 22%
- c. 99%
- d. 1%

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✔ Final Answer Summary:

#### ① Fraction → Decimal
a. 0.46
b. 0.06
c. 0.292
d. 0.46

#### ② Decimal → Fraction
a. $\frac{7}{100}$
b. $\frac{67}{100}$
c. $\frac{937}{100}$ or $9\frac{37}{100}$
d. $\frac{2717}{100}$ or $27\frac{17}{100}$

#### ③ Fraction → Percent
a. 28.57%
b. 91.67%
c. 88.49%
d. 74.07%

#### ④ Percent → Fraction
a. $\frac{3717}{10000}$
b. $\frac{80511}{10000}$
c. $\frac{639437}{10000}$
d. $\frac{9}{10000}$

#### ⑤ Percent → Decimal
a. 0.1133
b. $0.77\overline{3}$
c. 0.905
d. 0.803

#### ⑥ Decimal → Percent
a. 37%
b. 22%
c. 99%
d. 1%

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