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Question
Find a rational number and also an irrational number lying between the numbers 0.3030030003... and 0.3010010001...
Solution
Let
a = 0.3030030003...
b = 0.3010010001...
Here decimal representation of a and b are non-terminating and non-repeating. So a and b are irrational numbers. We observe that in first two decimal place of a and b have the same digit but digit in the third place of their decimal representation is distinct.
Therefore, a > b.
Hence one rational number is 0.3011 lying between 0.3030030003... and 0.3010010001...
And irrational number is 0.3020200200020000... lying between 0.3030030003... and 0.3010010001...
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