What a percentage is

Percentages are a tool we use every day — from shop discounts to statistical data. Before treating them rigorously, let us clarify their meaning: saying "$60\%$" is the same as saying ”$60$ hundredths”, that is, the fraction $\frac{60}{100}$. But of what?

Definition — Percentage

A percentage is always a percentage of something (or relative to something). Computing it means multiplying that quantity by the corresponding fraction: $\text{the } 60\%\text{ of }3000 = 3000\cdot\frac{60}{100} = 1800.$

The symbol $\%$ has no meaning on its own: it always indicates a ratio with a reference. Keeping in mind relative to what a percentage is computed is the key to avoiding mistakes with discounts, VAT and interest.

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Topics: Percentages
Concepts: Percentage
Skills: Calculating