A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value. Numerical analysis specifically tries to estimate this error when using approximation equations, algorithms, or both, especially when using finitely many digits to represent real numbers. When a sequence of calculations subject to rounding errors is made, errors may accumulate, sometimes dominating the calculation.

Example

Try to round-off Error?

\( \sqrt{4.582+3.282}=? \)
\( =\sqrt{4.582+3.282} \)
\( =\sqrt{21.0+10.0} \)
\( =5.64 \)

Rounding these numbers off to one decimal place or the nearest whole number would change the answer to 5.7 and 6, respectively. The more rounding off that is done, the more errors are introduced