▁we ▁remove ▁numbers ▁with ▁fraction al ▁part ▁ 0 . 5 ▁from ▁the ▁set . ▁ ▁In ▁practice , ▁floating - point ▁numbers ▁are ▁typically ▁used , ▁which ▁have ▁even ▁more ▁computational ▁nu ances ▁because ▁they ▁are ▁not ▁equally ▁spac ed . ▁ ▁Round ▁half ▁up ▁The ▁following ▁tie - bre aking ▁rule , ▁called ▁round ▁half ▁up ▁( or ▁round ▁half ▁towards ▁positive ▁infinity ), ▁is ▁widely ▁used ▁in ▁many ▁discipl ines . ▁That ▁is , ▁half - way ▁values ▁of ▁ ▁are ▁always ▁rounded ▁up . ▁If ▁the ▁fraction ▁of ▁ ▁is ▁exactly ▁ 0 . 5 , ▁then ▁  =    +   0 . 5 ▁ ▁For ▁example , ▁by ▁this ▁rule ▁the ▁value ▁ 2 3 . 5 ▁gets ▁rounded ▁to ▁ 2 4 , ▁but ▁− 2 3 . 5 ▁gets ▁rounded ▁to ▁− 2 3 . ▁ ▁However , ▁some ▁programming ▁languages ▁( such ▁as ▁Java , ▁Python ) ▁define ▁their ▁half ▁up ▁as ▁round ▁half ▁away ▁from ▁zero ▁here . ▁ ▁This ▁method ▁only ▁requires ▁checking ▁one ▁digit ▁to ▁determine ▁round ing ▁direction ▁in ▁two ' s ▁complement ▁and ▁similar ▁representations . ▁ ▁Round ▁half ▁down ▁One ▁may ▁also ▁use ▁round ▁half ▁down ▁( or ▁round ▁half ▁towards ▁negative ▁infinity ) ▁as ▁opposed ▁to ▁the ▁more ▁common ▁round ▁half ▁up . ▁If ▁the ▁fraction ▁of ▁ ▁is ▁exactly ▁ 0 . 5 , ▁then ▁  =    −   0 . 5 ▁ ▁For ▁example , ▁ 2 3 . 5 ▁gets ▁rounded ▁to ▁