Question
Find one irrational number between $0.2101$ and $0.2222\ ...=0.\bar{2}$
✓
Answer
Let, $a = 0.2101$ and, $b = 0.2222...$
We observe that in the second decimal place a has digit $1$ and $b$ has digit $2$,
therefore $a < b$ in the third decimal place a has digit $0$. So, if
we consider irrational numbers $x = 0.211011001100011...$
We find that $a < x < b$ Hence $x$ is required irrational number.
We observe that in the second decimal place a has digit $1$ and $b$ has digit $2$,
therefore $a < b$ in the third decimal place a has digit $0$. So, if
we consider irrational numbers $x = 0.211011001100011...$
We find that $a < x < b$ Hence $x$ is required irrational number.
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