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Find two irrational numbers between 0.5 and 0.55. 

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Let a = 0.5 = 0.50

And, b = 0.55

We observe that in the second decimal place a has digit 0 and b has digit 5, therefore a < b  

so, if we consider irrational numbers 

x = 0.51051005100051...

 y = 0.530535305353530... 

We find that a < x < y < b 

Hence, x and y are required irrational numbers.

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