Every rational number has a unique position on the number line.
But does every point on the number line represent a rational number?
To verify let us draw a number line.
With O as center, OB as radius, draw an arc cutting the number line at P.
OB=OP=√2
Hence point P represents √2 on the number (√2 is irrational).
=> There are many points on the number line which are irrational.
Thus, we have learnt that every irrational number can be represented on the number line.
This method is recalled here through the diagram.
Accuracy of this representation depends on the accuracy of construction.
