▁ ▁Flo ating - point ▁round ing ▁In ▁floating - point ▁arithmetic , ▁round ing ▁a ims ▁to ▁turn ▁a ▁given ▁value ▁ ▁into ▁a ▁value ▁ ▁with ▁a ▁specified ▁number ▁of ▁ ▁digits . ▁In ▁other ▁words , ▁ ▁should ▁be ▁a ▁multiple ▁of ▁a ▁number ▁ ▁that ▁depends ▁on ▁the ▁magnitude ▁of ▁. ▁The ▁number ▁ ▁is ▁a ▁power ▁of ▁the ▁base ▁( us ually ▁ 2 ▁or ▁ 1 0 ) ▁of ▁the ▁floating - point ▁representation . ▁ ▁A part ▁from ▁this ▁detail , ▁all ▁the ▁variants ▁of ▁round ing ▁discussed ▁above ▁apply ▁to ▁the ▁round ing ▁of ▁floating - point ▁numbers ▁as ▁well . ▁The ▁algorithm ▁for ▁such ▁round ing ▁is ▁presented ▁in ▁the ▁Sc aled ▁round ing ▁section ▁above , ▁but ▁with ▁a ▁constant ▁scaling ▁factor ▁  =   1 , ▁and ▁an ▁integer ▁base ▁  >   1 . ▁ ▁Where ▁the ▁rounded ▁result ▁would ▁overflow ▁the ▁result ▁for ▁a ▁directed ▁round ing ▁is ▁either ▁the ▁appropriate ▁signed ▁infinity ▁when ▁" r ounding ▁away ▁from ▁zero ", ▁or ▁the ▁highest ▁represent able ▁positive ▁finite ▁number ▁( or ▁the ▁lowest ▁represent able ▁negative ▁finite ▁number ▁if ▁ ▁is ▁negative ), ▁when ▁" r ounding ▁towards ▁zero ". ▁The ▁result ▁of ▁an ▁overflow ▁for ▁the ▁usual ▁case ▁of ▁round ▁to ▁nearest ▁is ▁always ▁the ▁appropriate ▁infinity . ▁ ▁R ounding ▁to ▁a ▁simple ▁fraction ▁In ▁some ▁context s ▁it ▁is ▁des irable ▁to ▁round ▁a ▁given ▁number ▁ ▁to ▁a ▁" ne at " ▁fraction ▁— ▁that ▁is