Rounding is a mathematical technique used to simplify a number by reducing the number of digits while maintaining a value that is approximately equivalent to the original number. This process is commonly applied to make calculations easier or to present numbers in a more digestible form. The rules of rounding generally involve looking at the digit immediately to the right of the place value you want to round to: 1. **If that digit is less than 5**, you round down (leave the target place value as is).
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Rounding replaces a number by a permitted representable value according to a specified rule. Rounding to nearest minimizes absolute error; directed rounding instead selects the next permitted value toward positive infinity, negative infinity or zero. A tie between equally near values needs an explicit convention.
On the decimal grid with spacing , rounds to nearest as , with error . Rounding to nearest has error at most half the grid spacing. In normal floating-point arithmetic, that spacing depends on magnitude, leading to a relative-error bound described by unit roundoff. The IEEE round-to-nearest-even rule resolves ties by an even final significand digit.[ref]
IEEE arithmetic in Oracle's Numerical Computation Guide. Chapter 2, IEEE Arithmetic Model, four rounding directions