Ümardamise

Ümardamise (rounding) is the process of replacing a numeric value with a nearby value that has fewer digits or a different precision. It is used to simplify numbers for readability, to fit data into fixed-precision representations, or to reflect limits of measurement and calculation.

Common methods include round to nearest, floor, ceiling, and truncation. Round to nearest replaces the number with the closest value at the target precision; ties can be resolved by different rules, such as round half up (the 0.5 is rounded away from zero) or round half to even (banker's rounding). Truncation discards digits beyond the chosen precision without increasing the magnitude, effectively rounding toward zero. Floor rounds down to the greatest value not exceeding the original, while ceiling rounds up to the smallest value not less than the original.

In computing, rounding modes are standardized in IEEE 754. Typical modes include round to nearest (with ties to even), toward zero, toward positive infinity, and toward negative infinity. Banker's rounding (ties to even) minimizes cumulative bias in repetitive calculations.

Applications of ümardamise span mathematics, computer science, finance, engineering, and digital media. It affects numerical analysis, statistical reporting, monetary computations, and graphics where fixed precision is necessary. Proper rounding helps ensure consistent results, but rounding errors can accumulate across multiple operations, highlighting the importance of choosing appropriate rules and documenting them in software and analyses.

Example: rounding 3.145 to two decimals yields 3.15 under round half up, but 3.14 under round half to even. Rounding 7.9 to the nearest integer gives 8. Negative values behave similarly under the chosen rule set.