Round-off error

Summary

Round-off error, or rounding error, is the difference between the exact result of a computation and the result computed with rounded numbers. In floating-point arithmetic each single rounding has relative error at most the unit roundoff, about $10^{-16}$ in double precision. Many roundings can add up, and a subtraction of nearly equal numbers can magnify them, as in catastrophic cancellation. It is distinct from truncation error, which comes from the method even in exact arithmetic.