[oofabz]

How about continued fractions? Unlike floating point, they can represent any rational number in finite memory. Using generators, you can even represent many irrational numbers, like square roots and pi, in finite memory.

Richard Schroeppel and Bill Gosper explored continued fractions in the '70s:

http://www.inwap.com/pdp10/hbaker/hakmem/cf.html

[darkmighty]

What's special about representing rationals in finite memory? By definition they can be represented by two finite integers. There are many ways of describing irrational numbers in finite memory if you allow this kind of generalization, e.g. make a datatype to represent equations and numbers as solution to the equations.