Fractions Decimals and Percents Worksheets - Math Monks - Free Printable

Let's solve each part of this Fraction, Decimal, and Percent Conversion worksheet 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. $\frac{46}{100} = 0.46$
→ Since the denominator is 100, just move the decimal two places left: $46 \div 100 = 0.46$

b. $\frac{6}{100} = 0.06$
→ $6 \div 100 = 0.06$

c. $\frac{292}{1000} = 0.292$
→ Divide by 1000 → move decimal three places left: $292 \div 1000 = 0.292$

d. $\frac{46}{100} = 0.46$
→ Same as (a): $46 \div 100 = 0.46$

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

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② Convert each decimal into fraction.

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

a. $0.07 = \frac{7}{100}$
→ 7 hundredths → already simplified.

b. $0.67 = \frac{67}{100}$
→ 67 hundredths → already simplified.

c. $9.37 = \frac{937}{100}$
→ Write as improper fraction: $9.37 = \frac{937}{100}$
→ Can also write as mixed number: $9\frac{37}{100}$
But since it says "fraction", either is acceptable; we'll use improper: $\frac{937}{100}$

d. $27.17 = \frac{2717}{100}$
→ 27.17 = 2717 hundredths → $\frac{2717}{100}$
→ Simplify? Check GCF of 2717 and 100.
Since 2717 ÷ 100 = 27.17, and no common factors (100 = 2²×5², 2717 not divisible by 2 or 5), so it’s already simplified.

✔ Answers:
a. $\frac{7}{100}$
b. $\frac{67}{100}$
c. $\frac{937}{100}$
d. $\frac{2717}{100}$

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③ Convert each fraction into percent.

To convert a fraction to a percent:
- Divide numerator by denominator → get decimal
- Multiply by 100 → get percent

a. $\frac{2}{7} \approx ?$
→ $2 \div 7 \approx 0.2857$ → $0.2857 \times 100 = 28.57\%$
→ So, $\boxed{28.57\%}$ (approximately)

b. $\frac{11}{12} \approx ?$
→ $11 \div 12 \approx 0.9167$ → $0.9167 \times 100 = 91.67\%$
→ So, $\boxed{91.67\%}$ (approximately)

c. $\frac{100}{113} \approx ?$
→ $100 \div 113 \approx 0.8849$ → $0.8849 \times 100 = 88.49\%$
→ So, $\boxed{88.49\%}$ (approximately)

d. $\frac{20}{27} \approx ?$
→ $20 \div 27 \approx 0.7407$ → $0.7407 \times 100 = 74.07\%$
→ So, $\boxed{74.07\%}$ (approximately)

✔ Answers:
a. 28.57%
b. 91.67%
c. 88.49%
d. 74.07%

> Note: These are approximations. You can round to nearest hundredth unless otherwise specified.

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④ Convert each percent into fraction.

To convert percent to fraction:
- Write percent over 100
- Simplify

a. $37.17\% = \frac{37.17}{100}$
→ To eliminate decimals, multiply numerator and denominator by 100:
$\frac{37.17 \times 100}{100 \times 100} = \frac{3717}{10000}$
→ Now check if reducible.
GCF of 3717 and 10000? Let's see:
3717 ÷ 3 = 1239 → divisible by 3
10000 ÷ 3? No → so only factor is 1?
Actually, check:
3717 ÷ 3 = 1239 → 1+2+3+9=15 → divisible by 3 → yes
But 10000 not divisible by 3 → so GCF is 1 → already simplified
So: $\boxed{\frac{3717}{10000}}$

b. $805.11\% = \frac{805.11}{100}$
→ Multiply numerator and denominator by 100:
$\frac{80511}{10000}$
Check if reducible:
Try dividing by 3: 8+0+5+1+1=15 → divisible by 3
80511 ÷ 3 = 26837
10000 ÷ 3? No → not divisible
So GCF is 1 → $\boxed{\frac{80511}{10000}}$

c. $6394.37\% = \frac{6394.37}{100}$
→ Multiply by 100: $\frac{639437}{10000}$
Check GCF:
639437 → sum digits: 6+3+9+4+3+7=42 → divisible by 3
10000 not divisible by 3 → GCF = 1 → $\boxed{\frac{639437}{10000}}$

d. $0.09\% = \frac{0.09}{100} = \frac{9}{10000}$
→ Because 0.09 = 9/100, so:
$\frac{9}{100} \div 100 = \frac{9}{10000}$
→ Already simplified → $\boxed{\frac{9}{10000}}$

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

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⑤ Convert each percent into decimal.

Divide percent by 100 (move decimal two places left).

a. $11.33\% = 0.1133$
→ Move decimal two places left: $11.33 \div 100 = 0.1133$

b. $77\frac{1}{3}\% = ?$
First, convert mixed number to improper:
$77\frac{1}{3} = \frac{232}{3}\%$
Now divide by 100:
$\frac{232}{3} \div 100 = \frac{232}{300} = \frac{58}{75} \approx 0.7733$
Or: $77\frac{1}{3} \div 100 = 0.7733...$
So: $\boxed{0.77\overline{3}}$ or approximately $0.7733$

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

d. $80.3\% = 0.803$
→ Move decimal two places left: $80.3 \div 100 = 0.803$

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

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⑥ Convert each decimal into percent.

Multiply decimal by 100 (move decimal two places right).

a. $0.37 = 37\%$
→ $0.37 \times 100 = 37\%$

b. $0.22 = 22\%$
→ $0.22 \times 100 = 22\%$

c. $0.99 = 99\%$
→ $0.99 \times 100 = 99\%$

d. $0.01 = 1\%$
→ $0.01 \times 100 = 1\%$

✔ 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. $\frac{937}{100}$
d. $\frac{2717}{100}$

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. 0.7733 (or $0.77\overline{3}$)
c. 0.905
d. 0.803

⑥ Decimal → Percent

a. 37%
b. 22%
c. 99%
d. 1%

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