A
round-off error, also called
rounding error, is the difference between the calculated
approximation of a number and its exact mathematical value due to
rounding. This is a form of
quantization error. One of the goals of
numerical analysis is to
estimate errors in calculations, including round-off error, when using approximation
equations and/or
algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits).