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Rational and irrational: two kinds of decimal

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The problem

Counting sheep needs only 1, 2, 3, ... But what if two sheep never came back? You needed 0, and the herd of numbers grew.

Every time a question had no answer, someone invented a bigger set of numbers for it. Negatives answered “owe more than you have”, fractions answered “split 3 rotis between 2 people”. Each new problem forced a new kind of number.

Then came a question fractions couldn't answer: what number, multiplied by itself, gives 2? No fraction does it exactly — so a whole new family, the irrationals, had to be invented.

A rational number can be written as p/q, with p, q integers and q ≠ 0. An irrational number cannot. Together they make up the real numbers.

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