Conversions between Fractions, Decimals and Percentages

Learn to convert between these three forms!

1. Converting Fractions to Percentages

Two Methods

Method 1: Multiply by 100%

Express $\frac{3}{5}$ as a percentage:

$\frac{3}{5} \times 100\%$

= $\frac{3 \times 100}{5}\%$

= $\frac{300}{5}\%$

= 60%

Method 2: Equivalent Fractions

Convert to denominator 100:

$\frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100}$

= 60%

Example: Express $\frac{16}{200}$ as a percentage

Method 1:

$\frac{16}{200} \times 100\% = \frac{16 \times 100}{200}\% = \frac{1600}{200}\% = 8\%$

Method 2:

$\frac{16}{200} = \frac{16 \div 2}{200 \div 2} = \frac{8}{100} = 8\%$

2. Converting Decimals to Percentages

Rule: Multiply the decimal by 100% to get the percentage, e.g. 0.15 × 100% = 15%

Or: Convert decimal to fraction with denominator 100

Example (a): 0.05 as a percentage

0.05 = $\frac{5}{100}$ = 5%

Example (b): 0.15 as a percentage

0.15 = $\frac{15}{100}$ = 15%

Example (c): 0.3 as a percentage

0.3 = $\frac{3}{10} = \frac{30}{100}$ = 30%

3. Converting Percentages to Decimals

Rule: Drop the % sign and divide the number by 100 to get the decimal

99% as a decimal:

99% = $\frac{99}{100}$ = 0.99

7% as a decimal:

7% = $\frac{7}{100}$ = 0.07

4. Converting Percentages to Fractions

Rule: Write as fraction over 100, then simplify to lowest terms

75% as a fraction:

75% = $\frac{75}{100}$

= $\frac{75 \div 25}{100 \div 25}$

= $\mathbf{\frac{3}{4}}$

80% as a fraction:

80% = $\frac{80}{100}$

= $\frac{80 \div 20}{100 \div 20}$

= $\mathbf{\frac{4}{5}}$

6% as a fraction:

6% = $\frac{6}{100}$

= $\frac{6 \div 2}{100 \div 2}$

= $\mathbf{\frac{3}{50}}$

📌 Conversion Summary

From	To	Method
Fraction	Percentage	× 100% OR equivalent fraction /100
Decimal	Percentage	× 100%
Percentage	Decimal	drop %, then ÷ 100
Percentage	Fraction	Write as /100, simplify

Practice Problems

Practice 1: Fraction to Percentage

Express $\frac{9}{20}$ as a percentage.

ShowHide solution

$\frac{9}{20} \times 100\% = \frac{9 \times 100}{20}\% = \frac{900}{20}\% =$ 45%

Or: $\frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} = 45\%$

Practice 2: Decimal to Percentage

Express 0.72 as a percentage.

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0.72 = $\frac{72}{100}$ = 72%

Practice 3: Percentage to Decimal

Express 45% as a decimal.

ShowHide solution

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

Practice 4: Percentage to Fraction

Express 40% as a fraction in its simplest form.

ShowHide solution

40% = $\frac{40}{100} = \frac{40 \div 20}{100 \div 20} =$ $\mathbf{\frac{2}{5}}$

Key Takeaways

Fraction → Percentage: Multiply by 100% OR make denominator 100
Decimal → Percentage: Multiply by 100% (move the decimal point 2 places to the right)
Percentage → Decimal: Drop the % sign and divide by 100 (move the decimal point 2 places to the left)
Percentage → Fraction: Write over 100, then simplify
Remember: 100% = 1 whole = $\frac{100}{100}$ = 1.00