▁ ▁R ounding ▁to ▁integer ▁The ▁most ▁basic ▁form ▁of ▁round ing ▁is ▁to ▁replace ▁an ▁arbitrary ▁number ▁by ▁an ▁integer . ▁All ▁the ▁following ▁round ing ▁modes ▁are ▁concrete ▁implementations ▁of ▁an ▁abstract ▁single - argument ▁" round ()" ▁procedure . ▁These ▁are ▁true ▁functions ▁( with ▁the ▁exception ▁of ▁those ▁that ▁use ▁random ness ). ▁ ▁Direct ed ▁round ing ▁to ▁an ▁integer ▁These ▁four ▁methods ▁are ▁called ▁directed ▁round ing , ▁as ▁the ▁disp lac ements ▁from ▁the ▁original ▁number ▁ ▁to ▁the ▁rounded ▁value ▁ ▁are ▁all ▁directed ▁towards ▁or ▁away ▁from ▁the ▁same ▁limit ing ▁value ▁( 0 , ▁+ ∞ , ▁or ▁− ∞ ). ▁Direct ed ▁round ing ▁is ▁used ▁in ▁interval ▁arithmetic ▁and ▁is ▁often ▁required ▁in ▁financial ▁calculations . ▁ ▁If ▁ ▁is ▁positive , ▁round - down ▁is ▁the ▁same ▁as ▁round - t ow ards - zero , ▁and ▁round - up ▁is ▁the ▁same ▁as ▁round - away - from - zero . ▁If ▁ ▁is ▁negative , ▁round - down ▁is ▁the ▁same ▁as ▁round - away - from - zero , ▁and ▁round - up ▁is ▁the ▁same ▁as ▁round - t ow ards - zero . ▁In ▁any ▁case , ▁if ▁ ▁is ▁an ▁integer , ▁ ▁is ▁just ▁. ▁ ▁Where ▁many ▁calculations ▁are ▁done ▁in ▁sequence , ▁the ▁choice ▁of ▁round ing ▁method ▁can ▁have ▁a ▁very ▁significant ▁effect ▁on ▁the ▁result . ▁A ▁famous ▁instance ▁involved ▁a ▁new ▁index ▁set ▁up ▁by ▁the ▁V ancouver