Converting Between Fractions, Decimals, and Percents

Fractions, decimals, and percents are three ways of writing the same value. Being able to convert between them fluently is one of the most useful arithmetic skills — it comes up in shopping, cooking, test-taking, and every trade. This page covers all six conversion directions with a clear method for each.

The Big Picture

$\frac{3}{4} = 0.75 = 75\%$

These three expressions all represent the same amount: three-quarters of a whole. The table below shows the conversion paths:

Fraction → Decimal

Method: Divide the numerator by the denominator.

$\frac{a}{b} = a \div b$

Example 1: Convert $\frac{3}{8}$ to a decimal

$3 \div 8 = 0.375$

Example 2: Convert $\frac{2}{3}$ to a decimal

$2 \div 3 = 0.666... = 0.\overline{6}$

The bar over the 6 means the digit repeats forever. In practice, round to the precision you need: $0.667$ (to three decimal places).

Common Fractions to Decimals Reference

Decimal → Fraction

Method:

1. Read the decimal using place value
2. Write it as a fraction over the appropriate power of 10
3. Simplify to lowest terms

Example 3: Convert $0.45$ to a fraction

$0.45$ is “forty-five hundredths”:

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

Simplify (GCF of 45 and 100 is 5):

$\frac{45}{100} = \frac{9}{20}$

Answer: $\frac{9}{20}$

Example 4: Convert $0.6$ to a fraction

$0.6$ is “six tenths”:

$0.6 = \frac{6}{10} = \frac{3}{5}$

Answer: $\frac{3}{5}$

Example 5: Convert $0.125$ to a fraction

$0.125$ is “one hundred twenty-five thousandths”:

$0.125 = \frac{125}{1000} = \frac{1}{8}$

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

Fraction → Percent

Method: Convert the fraction to a decimal, then multiply by 100.

$\frac{a}{b} \times 100\%$

Example 6: Convert $\frac{4}{5}$ to a percent

$\frac{4}{5} = 0.8 = 80\%$

Example 7: Convert $\frac{7}{8}$ to a percent

$\frac{7}{8} = 0.875 = 87.5\%$

Percent → Fraction

Method: Write the percent over 100 and simplify.

Example 8: Convert $35\%$ to a fraction

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

Example 9: Convert $12.5\%$ to a fraction

$12.5\% = \frac{12.5}{100} = \frac{125}{1000} = \frac{1}{8}$

Decimal → Percent

Method: Multiply by 100, which moves the decimal point two places to the right.

Example 10: Convert $0.72$ to a percent

$0.72 = 72\%$

Example 11: Convert $0.035$ to a percent

$0.035 = 3.5\%$

Percent → Decimal

Method: Divide by 100, which moves the decimal point two places to the left.

Example 12: Convert $45\%$ to a decimal

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

Example 13: Convert $6.5\%$ to a decimal

$6.5\% = \frac{6.5}{100} = 0.065$

Common Equivalents to Memorize

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Fraction → Decimal: divide numerator by denominator
• Decimal → Fraction: write over the place value (10, 100, 1000…) and simplify
• To get a percent: multiply the decimal by 100
• From a percent: divide by 100 to get a decimal, or write over 100 to get a fraction
• Memorize common equivalents (halves, thirds, quarters, fifths, eighths) — they come up constantly

Return to Arithmetic for more foundational math topics.