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

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Let, a = 0.3010010001

 And, b = 0.3030030003...

We observe that in the third decimal place a has digit 1 and b has digit 3, therefore a < b . in the third decimal place a has digit 1. so, if we consider rational and irrational numbers

x = 0.302

y = 0.302002000200002.....

We find that

a < x < b

 And, a < y < b

 Hence, x and y are required rational and irrational numbers respectively.

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