▁This ▁way , ▁when ▁the ▁same ▁input ▁is ▁rounded ▁in ▁different ▁instances , ▁the ▁output ▁is ▁un changed . ▁ ▁Calcul ations ▁done ▁with ▁round ing ▁should ▁be ▁close ▁to ▁those ▁done ▁without ▁round ing . ▁ ▁As ▁a ▁result ▁of ▁( 1 ) ▁and ▁( 2 ), ▁the ▁output ▁from ▁round ing ▁should ▁be ▁close ▁to ▁its ▁input , ▁often ▁as ▁close ▁as ▁possible ▁by ▁some ▁metric . ▁ ▁To ▁be ▁considered ▁round ing , ▁the ▁range ▁will ▁be ▁a ▁subset ▁of ▁the ▁domain . ▁A ▁classical ▁range ▁is ▁the ▁integers , ▁Z . ▁ ▁R ounding ▁should ▁preserve ▁symmet ries ▁that ▁already ▁exist ▁between ▁the ▁domain ▁and ▁range . ▁With ▁finite ▁precision ▁( or ▁a ▁discrete ▁domain ), ▁this ▁transl ates ▁to ▁removing ▁bias . ▁ ▁A ▁round ing ▁method ▁should ▁have ▁utility ▁in ▁computer ▁science ▁or ▁human ▁arithmetic ▁where ▁finite ▁precision ▁is ▁used , ▁and ▁speed ▁is ▁a ▁consideration . ▁ ▁But , ▁because ▁it ▁is ▁not ▁usually ▁possible ▁for ▁a ▁method ▁to ▁satisfy ▁all ▁ideal ▁characteristics , ▁many ▁methods ▁exist . ▁ ▁As ▁a ▁general ▁rule , ▁round ing ▁is ▁ide mp ot ent ; ▁i . e ., ▁once ▁a ▁number ▁has ▁been ▁rounded , ▁round ing ▁it ▁again ▁will ▁not ▁change ▁its ▁value . ▁R ounding ▁functions ▁are ▁also ▁monot onic ; ▁i . e ., ▁round ing ▁a ▁larger ▁number ▁results ▁in ▁the ▁same ▁or ▁larger ▁result ▁than ▁round ing ▁the ▁smaller ▁number . ▁ ▁Types ▁of ▁round ing ▁Typ ical ▁round ing ▁problems ▁include :