rational , irrational is the classification of real numbers. Before we talk about them , first let's talk about p / q size. p / q is a fraction where p and q will meet two conditions-- ( i) Both p and q can be any positive or negative integer , but q will never be zero. ( ii) p and q will not be coexistent with each other , i.e. G.S.G. of p and q . There will be only 1. rational numbers: Numbers that can be expressed in terms are called rational numbers. Such as: 1,2,3,7,0, 2/3, 4 / 5,3 / 4,7 / 8, 1.23, 1.45 etc. They are limited to the part after the decimal (right). Irrational numbers: Numbers that cannot be expressed in any way are called irrational numbers. E.g. 256.2368 ...........; 17392.192837 ............, √2, √3, √5, √7, √11, √19 ( especially of prime numbers Square root) etc. In their case the whole part after the decimal is immeasurable. Note: Needless to say , one of our most familiar irrational numbers is pi ( 7) . π = 3.14159265359 ............................................... .................................................. ....