Computer algebra
Exact arithmetic
Computation that preserves an exact mathematical value instead of rounding it.
Definition
Exact arithmetic
Exact arithmetic represents values such as integers and rational numbers without floating-point approximation.
Exact representation allows equality checks that rounding can obscure. Symbolic algorithms often depend on exact coefficients and exact zero tests.
01
Example
One third plus one sixth is exactly one half. A finite decimal approximation may only approach those values.
02
Important distinction
Exact arithmetic can require more memory and time than fixed-width floating-point arithmetic.
After reading this article, you should be able to
- Define Exact arithmetic in the sense used on this site.
- Choose between exact and approximate arithmetic for a stated computation.