Percentages and Decimals: Guides and Calculator

Free guides to percentages and decimals: how to calculate a percentage, convert fractions to decimals and percents, plus a percentage calculator with steps.

What Are Percentages and Decimals?

A percentage is a number out of 100, so 25% means 25 out of every 100. A decimal shows the same amount in base ten, so 25% = 0.25 = 1/4. Fractions, decimals and percents are three ways of writing one value, and you switch between them by dividing or multiplying by 100. To calculate a percentage of a total, divide the part by the whole and multiply by 100.

In short: Percent means per hundred. Decimal to percent: multiply by 100. Percent to decimal: divide by 100. Fraction to decimal: divide the top by the bottom.

Your Percentages Learning Path

  1. Learn how to calculate a percentage: the formula, percent of a number, what percent one number is of another, and percentage change.
  2. Convert simple fractions such as 1/2, 1/4 and 3/4 to decimals and percents.
  3. Work with repeating decimals such as 1/3, 5/6 and 6/7.
  4. Check your answers with the free percentage calculator, which shows every step.

Common Fractions as Decimals and Percents

Select a fraction to see both conversions step by step, with a diagram, examples and practice problems.

Fraction Decimal Percent
1/8 0.125 12.5%
1/5 0.2 20%
1/4 0.25 25%
1/3 0.333… 33⅓% (≈ 33.33%)
1/2 0.5 50%
3/5 0.6 60%
5/8 0.625 62.5%
7/10 0.7 70%
3/4 0.75 75%
5/6 0.833… 83⅓% (≈ 83.33%)
6/7 0.857142… ≈ 85.71%
7/8 0.875 87.5%

How to Convert Between Fractions, Decimals and Percents

  • Fraction to decimal: divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375.
  • Decimal to percent: multiply by 100. 0.375 × 100 = 37.5%.
  • Percent to decimal: divide by 100. 37.5% ÷ 100 = 0.375.
  • Decimal to fraction: write it over 10, 100 or 1000 and simplify. 0.375 = 375/1000 = 3/8.

A fraction in simplest form gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. Fractions such as 1/3 and 6/7 give repeating decimals.

In short: Divide to go from fraction to decimal, then shift the decimal point two places right for the percent. Reverse the steps to go back.

Percentages and Decimals: Frequently Asked Questions

How do I calculate a percentage?

Divide the part by the whole and multiply by 100. For example, 18 out of 72 is 18 ÷ 72 × 100 = 25%.

How do you convert a fraction to a percent?

Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 5/8 = 0.625, and 0.625 × 100 = 62.5%.

Why do some fractions give repeating decimals?

A fraction in simplest form has a terminating decimal only if its denominator’s prime factors are 2s and 5s. Any other prime factor, such as 3 or 7, makes the digits repeat forever, as in 1/3 = 0.333… and 6/7 = 0.857142857….