Significance Arithmetic

Significance arithmetic is the arithmetic of approximate numerical quantities that not only keeps track of numerical results, but also uses error propagation to track their accuracy. In this way, numerical computations can carry accuracy and precision information with them, returning in the end a numerical quantity together with its estimated (or worst-case) uncertainty. Significance arithmetic is an extremely powerful technique that offers many advantages over fixed precision (most commonly, floating-point or integer arithmetic), and is implemented in high-end mathematical software and languages such as the Wolfram Language.