Rounding Error

A rounding error is an error in a numerical computation that results from rounding the numbers involved in the computation. For example, 6.42*5 can be approximated as 6*5=30, when the real value is 32.1. The resulting rounding error is 2.1. Rounding errors are usually small, which is why scientists, engineers and businessmen usually ignore them. However, they can become very large if one is not careful, through error propagation. Scientists account for rounding errors using significant digits.

Rounding in fundamental values such as π and e can also result in two people getting different answers for the same computation. This leads to practical problems such as flaws in design and machinery components that don't fit. The National Institute of Standards & Technology (NIST) was established in 1901 to address national concerns of rounding error, by providing exact values of numerous fundamental quantities and measures.