round-off error

The error introduced because a computer stores only finitely many digits of a number.

Round-off error is the error introduced by representing a real number with a finite number of digits -- every arithmetic operation on stored floating-point numbers can introduce a new, tiny round-off error, even when the underlying formula is exact.

Examples

Storing $1/3$ in binary floating point never lands exactly on $0.333\ldots$ -- every stored copy already carries a small round-off error before any arithmetic even happens.