Definition
A percentage is a ratio rescaled to a common denominator of 100. The word literally means "per hundred", from the Latin per centum. Converting a fraction or decimal to a percentage requires only multiplication by 100: the fraction 3/4 becomes 75%, the decimal 0.27 becomes 27%. The transformation does not change the underlying value — it changes the scale on which the value is read.
That rescaling is the whole point. Raw counts depend on the size of the group: 12 successes out of 40 attempts and 30 successes out of 100 attempts are not obviously comparable until both are converted to the same denominator. As percentages — 30% and 30% — the comparison is immediate.
Why it matters
How it works
To convert between a percentage and its underlying ratio, divide by 100 to get a decimal, multiply by 100 to get a percentage. The decimal form is what you use for arithmetic — to find 23% of 800, compute 0.23 * 800 = 184. Compound operations always work cleanly on the decimal: a 10% increase followed by a 10% decrease is 1.10 * 0.90 = 0.99, not the intuitively-expected return to the original. Percentages do not commute additively the way many readers expect.
The most common source of confusion is conflating percentage point differences with percentage differences. If an unemployment rate moves from 5% to 7%, that is a two-percentage-point rise, but a 40% relative rise (2/5 = 0.4). Headlines that report the larger relative figure without naming the base can mislead readers about magnitude. The discipline is simple: name the base explicitly whenever you quote a percentage change. Percentages are also the natural language of probability — a 25% chance of rain and the fraction 1/4 are the same statement, dressed differently. Switching between the two representations fluently is the first practical skill in elementary statistics.