(a) To insert rational numbers between two rational numbers follow the steps:-
Step1- Let x and y be two ratonal numbers such that x<y.
Step2- Then,1/2(x+y)is a rational number lying between x and y.
Step3- Suppose we want to find n rational numbers between x and y.
Step4- Let d=(y-x)/(n+1).
Step5- Then n rational numbers lying between x and y are:-
(b) To insert rational numbers between two irrational numbers follow the steps:-
Step1- Let X'OX be a horizontal line,taken as the x-axis and let O be the origin.Let O represent 0.
Step2- Take OA=1 unit and draw AB perpendicular to OA such that again AB=1 unit.Join OB Then,
OB = √OA²+AB² = √1²+1² = √2 units.
Step3- With O as centre and OB as radius,draw an arc,meeting OX at P.
Then OP=OB=√2 units.
Like this you can continue and find more.