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Give two rational numbers lying between 0.515115111511115 ... and 0.5353353335 ...

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Let, a = 0.515115111511115...

 And, b = 0.5353353335... 

We observe that in the second decimal place a has digit 1 and b has digit 3, therefore, 

a < b  . So if we consider rational numbers

 x = 0.52 

y = 0.52052052... 

We find that, 

a < x < y < b 

Hence x, and y are required rational numbers

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