floating-point number

A computer's usual way to store a real number: a sign, a fixed number of significant digits (the mantissa), and a power-of-two exponent that slides the decimal point.

A floating-point number is stored as sign $\times$ mantissa $\times$ (base) $^{\text{exponent}}$ , with the mantissa held to a fixed number of bits -- so it represents an exact value only when that value lands exactly on the format's own grid, and rounds to the nearest grid point otherwise.

Examples

$6.5 = 1.101_2\times2^2$ stores exactly; $0.1$ (a repeating binary fraction) does not, and rounds to the nearest representable neighbor instead.