How irrational numbers are different from rational numbers?

Answer 1

A rational number can be expressed exactly by a fraction, with whole numbers in the numerator and denominator; an irrational number is one that can't be written that way. For example, it is easy to prove that you can't write the square root of 2 (or, for that matter, the square root of any natural number that isn't a perfect square), so those numbers are irrational. In the decimal representation, a rational number can have no decimals (e.g., 4), a finite number of decimals (e.g., 3.15), or decimals that eventually repeat over and over again (e.g., 3.12727272727...). An irrational number has an infinite number of decimals, without such a repetition.

Answer 2

Another clue is that the decimal goes on forever without repeating. So you can tell if it is Rational or Irrational by trying to write the number as a simple fraction.