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How to insert rational and irrational numbers between

a) two rationals

b) two irrtaionals

1
by harshitsri99

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a) two rationals

b) two irrtaionals

by harshitsri99

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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:-

(x+d),(x+2d),(x+3d),.....,(x+nd).

(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.

Thankyou.