Irrational numbers are any number ,where the decimals go to infinity and the order of the decimal digits is random . 

Pi is the classic example of an irrational number ; pi = 3.141592654....

The square roots of prime numbers are irrational ; sqrt(2) = 1.414213562....

Such a number as 3.33333.... is NOT irrational because it can be converted to a fraction

Your correspondent 'hayharbr' is correct. 

Irrational numbers cannot be written as a fraction using integers.

π can't be written as an exact fraction so anything with π in it is irrational.

You also can't have 0 on bottom of a fraction, or do the square root of a negative number with just integer fractions.  And square roots of any number that is not a perfect square are irrational.