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Find one irrational numbers between $0.2101$ and $0.2222… = 0.\overline{2}$.
Given:
Given numbers are $0.2101$ and $0.2222… = 0.\overline{2}$.
To do:
We have to find one irrational number between $0.2101$ and $0.2222… = 0.\overline{2}$.
Solution:  
A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.
This implies,
$0.2101$ is a rational number and $0.2222… = 0.\overline{2}$ is an irrational number.
We can insert infinite irrational numbers between a rational number and an irrational number.
Therefore,
$0.22010010001......$ is greater than $0.2101$ and less than $0.2222…$
Therefore, one irrational number between $0.2101$ and $0.2222… = 0.\overline{2}$ is $0.22010010001......$.
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