rounding error

In mathematics, rounding error occurs when a number is approximated to a simpler form, leading to a difference between the true value and the approximation. This is common in numerical analysis when dealing with irrational numbers, like π, or when truncating infinite series. For example, using 3.14 for π introduces a rounding error because it's a rational approximation of an irrational number.1

The precision of a measurement dictates the number of significant figures used to represent it. Significant figures include all digits from the first non-zero digit to the last non-zero digit, or a trailing zero that is considered exact. When performing calculations with measured values, the number of significant figures in the result is limited by the measurement with the fewest significant figures. Rounding rules are applied to maintain appropriate precision, ensuring that the reported value reflects the accuracy of the original measurement.2