8.1 A Number in Disguise

What does % mean?

Banners shouting “Festive Sale, flat 40% off!” or a report card noting that “Ananya scored 91%” are everywhere. That small symbol % is read per cent, from the Latin per centum, which means “by the hundred” or “out of a hundred.”

So 25% is shorthand for 25 in every 100: 25 children out of 100, 25 rupees out of every 100 rupees, 25 marks out of a possible 100.

If we ask for 50\% of some quantity s, we are asking for 50 copies of the unit fraction \tfrac{1}{100} of s:

50\% \text{ of } s = 50 \times \tfrac{1}{100}\times s = \tfrac{50}{100}\times s = \tfrac{1}{2}\,s.

A percentage, then, is just a fraction whose denominator is fixed at 100:

20\% = \tfrac{20}{100} = \tfrac{2}{10} = \tfrac{1}{5}, \qquad 33\% = \tfrac{33}{100}.

That is the whole disguise. Underneath every percentage sits a perfectly ordinary fraction.

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