▁Stock ▁Exchange ▁in ▁ 1 9 8 2 . ▁It ▁was ▁initially ▁set ▁at ▁ 1 0 0 0 . 0 0 0 ▁( three ▁decimal ▁places ▁of ▁accuracy ), ▁and ▁after ▁ 2 2 ▁months ▁had ▁fallen ▁to ▁about ▁ 5 2 0 ▁— ▁whereas ▁stock ▁prices ▁had ▁generally ▁increased ▁in ▁the ▁period . ▁The ▁problem ▁was ▁caused ▁by ▁the ▁index ▁being ▁re calcul ated ▁thousands ▁of ▁times ▁daily , ▁and ▁always ▁being ▁rounded ▁down ▁to ▁ 3 ▁decimal ▁places , ▁in ▁such ▁a ▁way ▁that ▁the ▁round ing ▁errors ▁accum ulated . ▁Rec al cul ating ▁with ▁better ▁round ing ▁gave ▁an ▁index ▁value ▁of ▁ 1 0 9 8 . 8 9 2 ▁at ▁the ▁end ▁of ▁the ▁same ▁period . ▁ ▁For ▁the ▁examples ▁below , ▁ ▁refers ▁to ▁the ▁sign ▁function ▁applied ▁to ▁the ▁original ▁number , ▁. ▁ ▁R ounding ▁down ▁round ▁down ▁( or ▁take ▁the ▁floor , ▁or ▁round ▁towards ▁minus ▁infinity ): ▁ ▁is ▁the ▁largest ▁integer ▁that ▁does ▁not ▁exceed ▁. ▁ ▁R ounding ▁up ▁round ▁up ▁( or ▁take ▁the ▁ce iling , ▁or ▁round ▁towards ▁plus ▁infinity ): ▁ ▁is ▁the ▁smallest ▁integer ▁that ▁is ▁not ▁less ▁than ▁. ▁ ▁R ounding ▁towards ▁zero ▁round ▁towards ▁zero ▁( or ▁trunc ate , ▁or ▁round ▁away ▁from ▁infinity ): ▁ ▁is ▁the ▁integer ▁that ▁is ▁closest ▁to ▁ ▁such ▁that ▁it ▁is ▁between ▁ 0 ▁and ▁ ▁( includ ed ); ▁i . e . ▁ ▁is ▁the ▁integer ▁part ▁of ▁,