▁without ▁its ▁fraction ▁digits . ▁ ▁R ounding ▁away ▁from ▁zero ▁round ▁away ▁from ▁zero ▁( or ▁round ▁towards ▁infinity ): ▁ ▁is ▁the ▁integer ▁that ▁is ▁closest ▁to ▁ 0 ▁( or ▁equival ently , ▁to ▁) ▁such ▁that ▁ ▁is ▁between ▁ 0 ▁and ▁ ▁( includ ed ). ▁ ▁R ounding ▁to ▁the ▁nearest ▁integer ▁R ounding ▁a ▁number ▁ ▁to ▁the ▁nearest ▁integer ▁requires ▁some ▁tie - bre aking ▁rule ▁for ▁those ▁cases ▁when ▁ ▁is ▁exactly ▁half - way ▁between ▁two ▁integers ▁— ▁that ▁is , ▁when ▁the ▁fraction ▁part ▁of ▁ ▁is ▁exactly ▁ 0 . 5 . ▁ ▁If ▁it ▁were ▁not ▁for ▁the ▁ 0 . 5 ▁fraction al ▁parts , ▁the ▁round - off ▁errors ▁introduced ▁by ▁the ▁round ▁to ▁nearest ▁method ▁would ▁be ▁symmetric : ▁for ▁every ▁fraction ▁that ▁gets ▁rounded ▁down ▁( such ▁as ▁ 0 . 2 6 8 ), ▁there ▁is ▁a ▁complement ary ▁fraction ▁( nam ely , ▁ 0 . 7 3 2 ) ▁that ▁gets ▁rounded ▁up ▁by ▁the ▁same ▁amount . ▁ ▁When ▁round ing ▁a ▁large ▁set ▁of ▁fixed - point ▁numbers ▁with ▁uniformly ▁distributed ▁fraction al ▁parts , ▁the ▁round ing ▁errors ▁by ▁all ▁values , ▁with ▁the ▁om ission ▁of ▁those ▁having ▁ 0 . 5 ▁fraction al ▁part , ▁would ▁statist ically ▁compens ate ▁each ▁other . ▁This ▁means ▁that ▁the ▁expected ▁( aver age ) ▁value ▁of ▁the ▁rounded ▁numbers ▁is ▁equal ▁to ▁the ▁expected ▁value ▁of ▁the ▁original ▁numbers ▁when