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# Round

Round to multiple of ${\displaystyle \scriptstyle k\,}$ corresponds to rounding towards nearest multiple of ${\displaystyle \scriptstyle k\,}$; if equidistant to two nearest multiples of ${\displaystyle \scriptstyle k\,}$, then rounding towards nearest even multiple of ${\displaystyle \scriptstyle k\,}$ [balanced rounding]. With balanced rounding, if we have a random half-multiple of ${\displaystyle \scriptstyle k\,}$, then the probabilities of rounding up or rounding down are equal (both 50%). The default meaning of round thus means round to multiple of 1. We may also round to multiple of a noninteger, e.g. round to multiple of 0.01. In base ${\displaystyle \scriptstyle b\,}$, it is customary to round to a multiple of a given power of ${\displaystyle \scriptstyle b\,}$, the default being ${\displaystyle \scriptstyle b^{0}\,=\,1.\,}$