JediHDM> I think the current record is 100 million digits. However, irrational numbers are defined as those that CANNOT be expressed nicely, such as a fraction q/p.
Numbers such as the square-root of 2, e and pi have been proven. http://mathworld.wolfram.com/IrrationalNumber.html
It’s one of the things that separates our human intelligence from a machine. We can accept and work with the concept of an irrational number. A machine would short-circuit unless we somehow tell it to just terminate, say, pi after 10 digits.