▁in ▁the ▁reported ▁result . ▁R ounding ▁is ▁almost ▁un av oid able ▁when ▁reporting ▁many ▁comput ations ▁– ▁especially ▁when ▁div iding ▁two ▁numbers ▁in ▁integer ▁or ▁fixed - point ▁arithmetic ; ▁when ▁computing ▁mathematical ▁functions ▁such ▁as ▁square ▁roots , ▁log arith ms , ▁and ▁s ines ; ▁or ▁when ▁using ▁a ▁floating - point ▁representation ▁with ▁a ▁fixed ▁number ▁of ▁significant ▁digits . ▁In ▁a ▁sequence ▁of ▁calculations , ▁these ▁round ing ▁errors ▁generally ▁accum ulate , ▁and ▁in ▁certain ▁ill - condition ed ▁cases ▁they ▁may ▁make ▁the ▁result ▁meaning less . ▁ ▁Acc ur ate ▁round ing ▁of ▁trans c endent al ▁mathematical ▁functions ▁is ▁difficult ▁because ▁the ▁number ▁of ▁extra ▁digits ▁that ▁need ▁to ▁be ▁calculated ▁to ▁resolve ▁whether ▁to ▁round ▁up ▁or ▁down ▁cannot ▁be ▁known ▁in ▁advance . ▁This ▁problem ▁is ▁known ▁as ▁" the ▁table - maker ' s ▁d ile m ma ". ▁ ▁R ounding ▁has ▁many ▁similar ities ▁to ▁the ▁quant ization ▁that ▁occurs ▁when ▁physical ▁quantities ▁must ▁be ▁encoded ▁by ▁numbers ▁or ▁digital ▁signals . ▁ ▁A ▁w avy ▁equals ▁sign ▁( ≈ : ▁approximately ▁equal ▁to ) ▁is ▁sometimes ▁used ▁to ▁indicate ▁round ing ▁of ▁exact ▁numbers , ▁e . g ., ▁ 9 . 9 8 ▁ ≈ ▁ 1 0 . ▁This ▁sign ▁was ▁introduced ▁by ▁Alfred ▁George ▁Green hill ▁in ▁ 1 8 9 2 . ▁ ▁Ide al ▁characteristics ▁of ▁round ing ▁methods ▁include : ▁▁ ▁R ounding ▁should ▁be ▁done ▁by ▁a ▁function .