arrondi

Arrondi is the operation of replacing a real number by a nearby value with a lower level of precision. It is used to simplify numbers for representation, reporting or subsequent computations and can be applied to a specified number of decimal places or to a fixed unit.

Rounding methods vary. The most common is rounding to the nearest value. Under this rule, numbers are replaced by the closest value with the desired precision; rules for ties differ. The traditional round-half-up rule turns 2.5 into 3 and 3.5 into 4. An alternative, round-half-to-even (banker's rounding), replaces 2.5 by 2 and 3.5 by 4. Other approaches include rounding toward zero (truncation), which discards excess digits, and rounding toward plus or minus infinity (ceil or floor), known as rounding up or down.

Examples: rounding 3.14159 to two decimals gives 3.14 under most "nearest neighbor" rules, while 2.5 to the nearest integer is 3 under half-up rules but 2 under round-to-even.

In computing and statistics, different languages implement rounds differently, and floating-point representation can introduce small errors that affect the result. Rounding is central in finance, measurement, and data presentation, where a balance between precision and simplicity must be maintained.

The term arrondi comes from French, literally “made round,” and is used in mathematics, accounting and engineering to describe this simplification process.