decimal

A decimal is a way of writing numbers that aren’t whole by extending the place-value system past the ones place. Just as the digits to the left of a marker count ones, tens, and hundreds, the digits to the right count tenths, hundredths, and thousandths. The little dot — the decimal point — marks the boundary between the whole part and the fractional part.

So 3.25 means 3 ones, plus 2 tenths, plus 5 hundredths: 3 + 2/10 + 5/100. Each step to the right divides the place value by 10. This makes decimals just another notation for the same numbers fractions describe — 0.5 and 1/2 are the very same value, written two ways.

Decimals come in three flavors by how their digits behave after the point. They may stop (terminating, like 0.25), repeat a block forever (repeating, like 0.3333…), or run on with no pattern at all (the infinite non-repeating expansions of irrational numbers like pi). The first two kinds are always rational; only the third escapes the rationals.