An irrational number is a real number that can't be expressed as a ratio of integers, i.e. as a fraction.

Put another way, it can never be specified with absolute accuracy.

Well known examples are π and √2

For many irrational numbers, relatively simple mathematical proofs exist which show that it's impossible to ever arrive at a finite solution. For example, √2 was proved to be an irrational number by Greek mathematicians more than 2,000 years ago.

Further details at Wikipedia