Question

Find a rational number and also irrational number lying between the numbers 0.3030030003…..and 0.3010010001….

Answer 1

Given :  Numbers 0.3030030003….. and 0.3010010001….

 Let a = 0.3030030003….. and b = 0.3010010001….

 We observe that the second place of their decimal representations are same but the third place of their decimal representations are distinct . Number a has digit 1 and b has digit 3. So, a < b.  

So , if we Consider the rational and irrational number c = 0.3011 and d = 0.30202002000200002…..

 clearly, c = 0.3011 and d 0.30202002000200002…..  are rational number and an irrational numbers such that a < c < b and a < d < b

Hence, c (0.3011) and d (0.30202002000200002….. ) are required rational and an irrational numbers.  

HOPE THIS ANSWER WILL HELP YOU…..

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Answer 2

Numbers = 0.3030030003... And 0.3010010001...

The first digit distinct and non-consecutive for these numbers is 3 and 1. Thus, we can insert a digit 2 there, for a different number.

For rational number:-

0.302

For irrational number:-

0.30200200020002...