▁one ▁of ▁the ▁closest ▁str add ling ▁integers ▁with ▁a ▁probability ▁dependent ▁on ▁the ▁proxim ity ▁is ▁called ▁st ochastic ▁round ing ▁and ▁will ▁give ▁an ▁un bi ased ▁result ▁on ▁average . ▁ ▁For ▁example , ▁ 1 . 6 ▁would ▁be ▁rounded ▁to ▁ 1 ▁with ▁probability ▁ 0 . 4 ▁and ▁to ▁ 2 ▁with ▁probability ▁ 0 . 6 . ▁ ▁Sto ch astic ▁round ing ▁is ▁accurate ▁in ▁a ▁way ▁that ▁a ▁round ing ▁function ▁can ▁never ▁be . ▁For ▁example , ▁say ▁you ▁started ▁with ▁ 0 ▁and ▁added ▁ 0 . 3 ▁to ▁that ▁one ▁hundred ▁times ▁while ▁round ing ▁the ▁running ▁total ▁between ▁every ▁addition . ▁The ▁result ▁would ▁be ▁ 0 ▁with ▁regular ▁round ing , ▁but ▁with ▁st ochastic ▁round ing , ▁the ▁expected ▁result ▁would ▁be ▁ 3 0 , ▁which ▁is ▁the ▁same ▁value ▁obtained ▁without ▁round ing . ▁This ▁can ▁be ▁useful ▁in ▁machine ▁learning ▁where ▁the ▁training ▁may ▁use ▁low ▁precision ▁arithmetic ▁iter atively . ▁Sto ch astic ▁round ing ▁is ▁a ▁way ▁to ▁achieve ▁ 1 - dimensional ▁d ither ing . ▁ ▁Com parison ▁of ▁approaches ▁for ▁round ing ▁to ▁an ▁integer ▁ ▁R ounding ▁to ▁other ▁values ▁ ▁R ounding ▁to ▁a ▁specified ▁multiple ▁The ▁most ▁common ▁type ▁of ▁round ing ▁is ▁to ▁round ▁to ▁an ▁integer ; ▁or , ▁more ▁generally , ▁to ▁an ▁integer ▁multiple ▁of ▁some ▁increment ▁— ▁such ▁as ▁round ing ▁to ▁whole ▁t enth s ▁of ▁seconds , ▁hundred th s