Abstract: In scientific computing,irrational operation is considerably intractable．Transform irrational into integer will greatly convenient in scientific computing．To achieve integer representation to irrational,the first step is to achieve rational representation to irrational．We first transform irrational into continued fraction by utilizing continued fractions technique．Secondly,it is possible and reasonable to choose the most concise expression of the fraction according to the accuracy demand,so that we can achieve the rational approximation of irrational number．A list of the simplest form and the approximation error of some commonly used computing constants under various accuracy requirements is given,which has guiding significance for scientific computing.

Key words: Continued fraction,Rationalization,Progressive score,Rational approximation,Accuracy