# Detecting/Recognizing Irrational Number by Computers

I would like to know if there is a way to determine/recognize a irrational number by computers. Let me explain it a little more. I know that, in computer science, a computable number "a" is a number that can be approximated by two rational number, i.e. (k-1)/n<=a<=(k+1)/n where k&n are in N. Also, due to the limitation of floating point, all numbers in computers have limited number of significant figures. So, I was wondering if there is a way (more like an algorithm) to define irrational number for computers and consequently detect irrational number? Off course, I'm talking about an approximation with some adjustable level of accuracy. Thanks

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"...floating point, all numbers in computers..." Floating point is not the only way to represent numbers. Integers are naturally there (up to some limiting size), rationals can be handled with infinite precision as a pair of integers, quadratic irrationals can be handled by their continued fraction, algebraic numbers can be handled by manipulating their minimal polynomials, etc. Programs like Sage and Mathematica can handle e, pi, and many other common transcendentals formally, thereby maintaining infinite precision. –  Kevin O'Bryant Mar 22 '12 at 17:15