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Find two irrational numbers lying between 0.1 and 0.12.

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Let, a = 0.1 = 0.10

 And, b = 0.12

 We observe that in the second decimal place a has digit 0 and b has digit 2, Therefore

 a < b .So, if we consider irrational numbers

x = 0.11011001100011... 

y = 0.111011110111110... 

We find that,

 a < x < y < b

Hence, x and y are required irrational numbers. 

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