▁be ▁used ▁for ▁Monte ▁Carlo ▁arithmetic , ▁but ▁in ▁general , ▁just ▁round ing ▁up ▁or ▁down ▁with ▁equal ▁probability ▁is ▁more ▁often ▁used . ▁Re pe ated ▁runs ▁will ▁give ▁a ▁random ▁distribution ▁of ▁results ▁which ▁can ▁indicate ▁the ▁stability ▁of ▁the ▁computation . ▁ ▁Ex act ▁computation ▁with ▁rounded ▁arithmetic ▁It ▁is ▁possible ▁to ▁use ▁rounded ▁arithmetic ▁to ▁evaluate ▁the ▁exact ▁value ▁of ▁a ▁function ▁with ▁integer ▁domain ▁and ▁range . ▁For ▁example , ▁if ▁we ▁know ▁that ▁an ▁integer ▁ ▁is ▁a ▁perfect ▁square , ▁we ▁can ▁compute ▁its ▁square ▁root ▁by ▁converting ▁ ▁to ▁a ▁floating - point ▁value ▁, ▁computing ▁the ▁approximate ▁square ▁root ▁ ▁of ▁ ▁with ▁floating ▁point , ▁and ▁then ▁round ing ▁ ▁to ▁the ▁nearest ▁integer ▁. ▁If ▁ ▁is ▁not ▁too ▁big , ▁the ▁floating - point ▁round - off ▁error ▁in ▁ ▁will ▁be ▁less ▁than ▁ 0 . 5 , ▁so ▁the ▁rounded ▁value ▁ ▁will ▁be ▁the ▁exact ▁square ▁root ▁of ▁. ▁This ▁is ▁essentially ▁why ▁slide ▁rules ▁could ▁be ▁used ▁for ▁exact ▁arithmetic . ▁ ▁Double ▁round ing ▁ ▁R ounding ▁a ▁number ▁twice ▁in ▁succession ▁to ▁different ▁levels ▁of ▁precision , ▁with ▁the ▁latter ▁precision ▁being ▁co ar ser , ▁is ▁not ▁guaranteed ▁to ▁give ▁the ▁same ▁result ▁as ▁round ing ▁once ▁to ▁the ▁final ▁precision ▁except ▁in ▁the ▁case ▁of ▁directed ▁round ing . ▁For ▁instance ▁round ing ▁ 9 . 4 6 ▁to ▁one ▁decimal ▁gives ▁ 9 . 5 , ▁and ▁then ▁ 1 0