Round[x] gives the integer closest to x.
Mathematical function (see Section A.3.10).
Examples: Round[2.4] ; Round[2.6] ; Round[-2.4] ; Round[-2.6] .
Round rounds numbers of the form x.5 toward the nearest even integer.
Round[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.
Example: Round[Pi^2] .
For exact numeric quantities, Round internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
See The Mathematica Book: Section 1.1.3 and Section 3.2.2.
See also: IntegerPart, Floor, Ceiling, Chop.