Percentages
Per cent means out of one hundred
The word per cent means out of one hundred, and the symbol for it is %. A percentage describes a part of a whole by imagining the whole divided into 100 equal pieces and counting how many are taken. 25% means 25 out of 100, and 70% means 70 out of 100. Thinking of a hundred-square, shading the matching number of cells shows a percentage as a picture. Because every percentage is measured against the same hundred, percentages are an easy way to describe and compare parts.
One hundred per cent is the whole
One hundred per cent represents the complete whole, all of the amount with nothing left over. If every one of the hundred pieces is taken, that is 100 out of 100, or 100%. This makes percentages a natural scale: 0% is none of the whole, 50% is half, and 100% is all of it. A percentage larger than 100% would be more than the whole, which is why ordinary parts of a single whole run from 0% to 100%. Knowing that the whole is 100% anchors every other percentage.
Percentages, fractions and decimals
Percentages, fractions and decimals are three ways of writing the same part, and familiar percentages connect neatly to the other two. 50% is 50 out of 100, which is the fraction 1/2 and the decimal 0.5. 25% is 1/4, or 0.25, and 10% is 1/10, or 0.1. Because a percentage is already a number out of 100, writing it as a decimal just means dividing by 100, and writing it as a fraction means simplifying that hundredth. Knowing these equivalents lets a part be moved between the three forms whenever one is more convenient.
Comparing relative size with percentages
Percentages make relative size easy to compare, because every percentage is measured against the same whole of 100. 40% is a larger share than 25%, simply because 40 out of 100 is more than 25 out of 100. This is the real advantage of percentages: two parts of different wholes, like a score on a short test and a score on a long one, can be compared fairly once both are written as percentages. Describing a result as a percentage turns it into a share of 100 that can be lined up against any other.
Matching familiar percentages
A small set of familiar percentages is worth knowing by heart, because they appear again and again. 100% is the whole, 50% is 1/2, 25% is 1/4 and 75% is 3/4, 10% is 1/10, and 1% is 1/100. Matching each of these to its fraction and decimal makes everyday percentages quick to understand: a half-price sale is 50% off, and a tenth of a class is 10%. Recognising familiar percentages instantly is what makes the idea genuinely useful.
Using percentages with confidence
Percentages come down to one simple idea: a part written as a number out of 100, with 100% as the whole. Reading a percentage as so many out of a hundred, connecting familiar percentages to their fraction and decimal equivalents, and comparing percentages as shares of the same whole are the key skills. With these habits a child can describe a part as a percentage, switch between percentages, fractions and decimals, and compare relative sizes, ready for finding percentages of quantities in later years.