Round

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Round, by default, corresponds to rounding towards nearest integer; if equidistant (this happens with even bases) to two nearest integers, then rounding towards nearest even integer [balanced rounding]. With balanced rounding, if we have a random half-integer, then the probabilities of rounding up or rounding down are equal (both 50%).

Round to multiple of $k$ corresponds to rounding towards nearest multiple of $k$; if equidistant to two nearest multiples of $k$, then rounding towards nearest even multiple of $k$ [balanced rounding]. With balanced rounding, if we have a random half-multiple of $k$, 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 $b$, it is customary to round to a multiple of a given power of $b$, the default being $b^0=1.$

See also

• Help:Calculation#Round operator (rounds towards a multiple of a given power of 10)