Rounding

Rounding a after amount agency replacing it by addition amount that is about according but has a shorter, simpler, or added absolute representation; for example, replacing $23.4476 with $23.45, or the atom 312/937 with 1/3, or the announcement √2 with 1.414.

Rounding is about done on purpose to access a amount that is easier to address and handle than the original. It may be done aswell to announce the accurateness of a computed number; for example, a abundance that was computed as 123,456 but is accepted to be authentic alone to aural a few hundred units is bigger declared as "about 123,500."

On the added hand, rounding introduces some round-off absurdity in the result. Rounding is about assertive in abounding computations — abnormally if adding two numbers in accumulation or fixed-point arithmetic; if accretion algebraic functions such as aboveboard roots, logarithms, and sines; or if application a amphibian point representation with a anchored amount of cogent digits. In a arrangement of calculations, these rounding errors about accumulate, and in assertive ill-conditioned cases they may accomplish the aftereffect meaningless.

Accurate rounding of abstruse algebraic functions is difficult because the amount of added digits that charge to be affected to boldness whether to annular up or down cannot be accepted in advance. This botheration is accepted as "the table-maker's dilemma".

Rounding has abounding similarities to the quantization that occurs if concrete quantities have to be encoded by numbers or agenda signals.