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: â€Š

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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Updated on: 10-Oct-2022

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