Per cent means out of a hundred

'Mega Sale: up to 50% OFF!' 'Hiya scored 83% in her board exams.' Your phone says 79% battery. What does that little symbol actually mean?

It's read per cent, from the Latin per centum: 'by the hundred', or 'out of a hundred'. So 25 per cent means 25 out of every 100: 25 people out of 100, 25 rupees out of 100 rupees, 25 marks out of 100 marks.

Work out what that does to a quantity. 50% of s means 50 lots of one-hundredth of s: 50 × (1/100) × s = (50/100)s = ½s.

So percentages are nothing new. They're simply fractions with 100 underneath. 20% = 20/100 = 1/5. 33% = 33/100. (And two worth learning by heart: 1/3 = 33.33% and 2/3 = 66.66%.)

Which raises the obvious question: can any fraction be written as a percentage? Surya mixes paint for a sunset, and red makes up ¾ of the mixture. What percentage is red?

One way is to climb through equivalent fractions until the bottom is 100: ¾ = 6/8 = 30/40 = 75/100. That's 75%.

A quicker way: say ¾ = x/100 and multiply both sides by 100, giving x = ¾ × 100 = 75. Same answer.

That gives the rule. A fraction is a part of one whole; a percentage is a part per 100. So to turn a fraction into a percentage, multiply it by 100. (Multiplying by 100% changes nothing, since 100% is just 100/100 = 1; it only changes the form.)

Going back is even easier: 24% is 24/100, and so also 12/50, 6/25 or 48/200. Any fraction equal to z/100 is z%.