Training Percents Percent–Fraction–Decimal Conversions
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Percent–Fraction–Decimal Conversions

20 min Percents

What Is a Percent?

The word "percent" literally means "per hundred." When you say that a test score is 85 percent, you mean 85 out of every 100 — a standardized way to express a proportion that makes comparisons easy across different contexts.

Every percent can be written as a fraction with a denominator of 100, and every such fraction can be converted to a decimal by dividing by 100. This three-way connection — percent, fraction, decimal — is the central idea of this lesson.

Mastering these conversions is essential because real-world problems freely mix all three forms. A store might advertise a 25% discount, your calculator shows 0.25, and the math requires the fraction one-fourth.

Percent means "per hundred." The symbol % represents division by 100:

$$45\% = \frac{45}{100} = 0.45$$
Definition

A percent is a ratio that compares a number to 100. The word comes from the Latin per centum — "for each hundred."

Conversion Rules

Conversions
FromToMethodExample
PercentDecimalMove decimal 2 places left (÷ 100)$72\% = 0.72$
DecimalPercentMove decimal 2 places right (× 100)$0.035 = 3.5\%$
PercentFractionWrite over 100, simplify$25\% = \dfrac{25}{100} = \dfrac{1}{4}$
FractionPercentDivide, then × 100$\dfrac{3}{8} = 0.375 = 37.5\%$

Common Equivalents Worth Memorizing

FractionDecimalPercent
$\dfrac{1}{2}$$0.5$$50\%$
$\dfrac{1}{3}$$0.\overline{3}$$33.\overline{3}\%$
$\dfrac{1}{4}$$0.25$$25\%$
$\dfrac{1}{5}$$0.2$$20\%$
$\dfrac{1}{8}$$0.125$$12.5\%$
$\dfrac{2}{3}$$0.\overline{6}$$66.\overline{6}\%$
$\dfrac{3}{4}$$0.75$$75\%$
Example 1

Convert $135\%$ to a decimal and a fraction.

Decimal: $135\% = 1.35$

Fraction: $\dfrac{135}{100} = \dfrac{27}{20} = 1\dfrac{7}{20}$

Example 2

Convert $0.004$ to a percent.

$0.004 \times 100 = 0.4\%$

Example 3

Convert $\dfrac{5}{6}$ to a percent.

$5 \div 6 = 0.8\overline{3}$, so $\dfrac{5}{6} = 83.\overline{3}\%$

Example 4

Write $0.5\%$ as a fraction.

$$0.5\% = \frac{0.5}{100} = \frac{5}{1000} = \frac{1}{200}$$

Example 5

Convert $\dfrac{7}{20}$ to a percent.

$\dfrac{7}{20} = \dfrac{35}{100} = 35\%$

Practice Problems

1. Convert $60\%$ to a decimal.
2. Convert $0.85$ to a percent.
3. Convert $40\%$ to a fraction (lowest terms).
4. Convert $\dfrac{3}{5}$ to a percent.
5. Convert $250\%$ to a decimal.
6. Convert $0.003$ to a percent.
7. Convert $\dfrac{7}{8}$ to a percent.
8. Convert $16.5\%$ to a decimal.
9. Convert $\dfrac{11}{25}$ to a percent.
10. Write $0.75\%$ as a fraction.
11. Convert $6\%$ to a fraction (lowest terms).
12. Convert $\dfrac{1}{6}$ to a percent (round to nearest tenth).
13. Convert $1.05$ to a percent.
14. Write $33\dfrac{1}{3}\%$ as a fraction.
15. Convert $\dfrac{9}{4}$ to a percent.
Show Answer Key

1. $0.60$

2. $85\%$

3. $\dfrac{2}{5}$

4. $60\%$

5. $2.50$

6. $0.3\%$

7. $87.5\%$

8. $0.165$

9. $44\%$

10. $\dfrac{3}{400}$

11. $\dfrac{3}{50}$

12. $16.7\%$

13. $105\%$

14. $\dfrac{1}{3}$

15. $225\%$

Solving Percent Problems