Find a rational number and also an irrational number lying betwee… - Vidyadip

Question

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

✓

Answer

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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