finite precision

Finite precision refers to the limitation of representing numbers with a specific, fixed number of digits, often encountered in mathematics and computer science. This contrasts with exact or infinite precision.

In mathematics, significant figures are used to express the precision of a measured or calculated value. They include all digits from the leftmost non-zero digit to the rightmost digit that is either non-zero or a zero considered exact. The precision of a measurement is limited by the equipment used.1

Floating-point notation is a way to represent numbers where the decimal point can "float." This allows for a wide range of values to be expressed, but it inherently involves finite precision. Calculations with floating-point numbers can lead to rounding errors because not all real numbers can be perfectly represented.2

The calculus of finite differences deals with variations represented by small, but finite, increments, rather than infinitesimally small ones. Precision in measurements refers to how close repeated measurements are to each other, distinct from accuracy, which is how close a measurement is to the true value.34