Find One Rational And One Irrational Number Between 0.101001000100001000001... And 0.1001000100001000001

Given The two ration numbers 0.101001000100001000001... And 0.1001000100001000001...
To Do: Find One Rational And One Irrational Number Between the above two numbers 

Solution:

Let a = 0.101001000100001000001... 

b = 0.1001000100001000001...

Comparing three places of decimal of a and b, 

a = 0.101...; b = 0.100...; a > b

Let c = 0.101 be a terminating decimal

c  < a but c > b. So b < c < a

That is c lies between a and b. So c = 0.101 is a rational number lying between a and b  Let d = 0.10020000100000.....be a non-repeating non-terminating decimal or an irrational number. We see that

d > b and d < a or b< d < a or d lies between a and b.

So d = d = 0.10020000100000.....is an irrational number lying between a and b.

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Updated on: 10-Oct-2022

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