A percentage expresses a quantity as parts per one hundred and is normally written with the percent sign (%). Saying 40% is the same as saying 40 out of 100, or 0.40 when expressed as a decimal. Percentages allow values with different totals to be compared on a common scale.

Basic meaning and notation

The core idea is scaling a ratio to a base of 100. A fraction, ratio or decimal can be converted into a percentage so that the magnitude is easier to read and compare. The percent sign follows the number, for example 75% reads “seventy-five percent.” You can also write percentages as fractions (75/100) or decimals (0.75). For more on ratios see related material about ratios.

How to convert and calculate

Conversion between forms is straightforward: to convert a decimal to a percent, multiply by 100 and add %; to convert a fraction, divide numerator by denominator then multiply by 100. To turn a percent into a decimal, divide by 100. Common calculations include finding X% of a quantity (“30% of 200 = 200 × 0.30 = 60”) and solving for the original value given a percent.

Examples and percent change

Example: a bowl contains 3 apples and 1 orange; apples are 3 out of 4, which is 0.75 or 75%. Percent change describes increase or decrease: if a value rises from 50 to 75 the change is 25 on a base of 50, so the increase is (25/50)×100 = 50% increase. Note the difference between percentage points and percent: a rise from 10% to 12% is a 2 percentage point increase, but a 20% relative increase.

Common uses and practical notes

Percentages appear in many fields: interest rates and yield in finance, data summaries and margins in statistics, discounts in retail, vote shares in elections, and composition in demographics. They provide an intuitive way to express proportions but can be misleading with small sample sizes or when absolute numbers are omitted — context matters.

Distinctive facts and cautions

  • Percent vs percentage point: percent describes relative change; percentage point describes absolute difference between percentages.
  • Formatting: some languages place the percent sign before the number, but the symbol % is widely used internationally.
  • Always clarify the base when reporting percent changes (change relative to what?).

Understanding percentages makes it easier to compare and interpret data across different contexts, and basic conversion rules let you move between fractions, decimals, and percent form reliably.