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.
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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