percentage

A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol percent (%). The word comes from Latin per centum, meaning by the hundred. Percentages are used to describe proportions, rates, and comparisons in many contexts.

Percentages appear in finance, science, and daily life. They describe interest rates, discounts, test scores, population shares, and other measures that compare a part to a whole. They are also useful for communicating changes, such as increases or decreases in value or frequency.

Calculation and conversion: percentage = (part / whole) × 100. Conversely, part = (percentage / 100) × whole. To determine the whole when given part and percentage, use whole = part × 100 / percentage. Converting between decimals and percentages is straightforward: a decimal number d corresponds to d × 100 percent, while p percent equals p/100 as a decimal.

Common terms and pitfalls: the difference between a percentage and a percentage point is important. A change of 1 percentage point is a fixed difference in percentage terms (for example, from 5% to 6%), whereas a relative change (such as from 5% to 6%) is a 20% increase. The term percentage refers to a portion expressed as a fraction of 100, while percentage points describe absolute changes between percentages.

Related concepts include proportion, rate, and ratio, all of which are related to comparing parts to a whole. Percentages provide a concise way to convey such comparisons across disciplines.