Floating-point arithmetic

Summary

Floating-point arithmetic is the way computers represent real numbers and compute with them. A floating-point number is a fixed number of significant digits times a power of a base, such as $1.0110 \times 2^{-3}$. The result of each operation is rounded to a nearby floating-point number, so most computations carry a small round-off error. Its relative precision is measured by the machine epsilon, and the IEEE 754 standard fixes the formats used in practice.