Rounding Errors

Abstract Rounding errors present an inherent problem to all computer programs that involve floating‐point numbers. They appear nearly in all elementary operations. By accumulation, these errors can affect the accuracy of a computed result possibly leading to some or total inaccuracy. First in this article, computer arithmetic that uses binary system and the IEEE standard for floating‐point numbers is described together with some problems introduced by rounding errors. The effects of these rounding errors can be analyzed and studied by some methods like forward/backward analysis and interval or stochastic arithmetic. Finally, it is shown how the accuracy of the results can be improved by using compensated methods and multiprecision arithmetic.