Here is a quiet but powerful idea: the same amount can be written in three different outfits. A fraction, a decimal, and a percentage can all name one and the same quantity — they just dress it up differently.

Take a half. We can write it three ways, and they are exactly equal:

A percentage is simply "out of a hundred" — the sign \% means "per cent", per hundred. So 50\% means \tfrac{50}{100}, which is the same as a half.

A few more turn up so often it is worth knowing them by heart. Split a whole into four equal parts and the quarters line up neatly:

And one tenth, the first step into decimals:

See it on a hundred grid

A square of one hundred little cells is the perfect picture. Shade some cells and read off all three names at once: how many cells out of 100 (the percentage), the same as a decimal, and the same as a fraction. Step through it. Reload to see a different amount.

How to convert

You do not have to memorise every case — two small moves get you anywhere.

Fraction to decimal: divide the top by the bottom. A fraction is a division, so \tfrac{3}{4} is just 3 \div 4 = 0.75.

Decimal to percentage: multiply by 100 (which slides the point two places right) and add the \% sign. So 0.75 \times 100 = 75\%.

To go the other way, undo each step: a percentage is "over 100" as a fraction, and dividing by 100 turns it back into a decimal.

See it explained

Sal Khan walks through turning a percentage into a decimal and a fraction, step by step.