Rational numbers are any number which can be expressed in p/q form where p and q are integers and q is not equal to zero. 
1, 4, 7, 5, 1/3, 2, 7/6 etc. These all are examples of Rational numbers.

What are irrational numbers?

A number which cannot be written in p/q form, where p and q are integers and q ≠ 0 is an irrational number.

History of irrational numbers.

Originally Greeks thought that all the numbers in the world were rational until one of Pythagoreans found a proof that the diagonal of a unit square, i.e. sqrt (2), is not the ratio of any two integers. It was until 17th century that specific numbers like pi, e etc. were proved to be irrational by Liouville and others. These numbers are called irrational numbers.

How to represent irrational numbers on a number line?

You can represent irrational numbers on number line in many ways. Two of them are here:

Method no. 1:

Take any irrational number, suppose we take √3.
1.    Construct BD of unit length ┴ OB.
2.    Using Pythagoras theorem, we see that OD = √(√2)2 + 12 = √3
3.    With a compass taking O as the centre and radius OD, draw an arc with intersects the number line at point Q. Then Q corresponds to √3.
4.    In the same way, you can locate √n for any positive integer n , after √n – 1 has been located.

Method no. 2:

Consider any irrational number, suppose we take √x.
Step 1: Mark the distance of the number of which the square root is to be mark. Here we take x units. (Units can be in cm, m etc.)
Step 2: Then extend it by 1unit.
Step 3: Now taking the mid – point of AC, construct an arc AC
Step 4: from B draw a perpendicular
This intersects arc AC at D. The length of  BD is √x.
To mark it on number line:
Step 5: extend the number line.
Step 6: take B as the centre and BD as the radius draw an arc to meet the number line at E. 

I have noticed these corrections and if anything left I shall inform you afterwards.