Round-off error

Round-off error occurs when digital calculations approximate numbers to fit within a limited number of digits or decimal places. Since computers and calculators can't represent every number precisely—especially irrational or very large numbers—they round values to the closest possible value within their capacity. This small difference, or error, can accumulate in complex calculations, affecting accuracy. Essentially, round-off error is the tiny discrepancy introduced whenever an exact number is approximated in digital form, influencing the precision of results in scientific, engineering, and financial computations.