Find a rational number and also an irrational number lying between the numbers, $0.3030030003…$ and $0.3010010001…$

Given:

Given numbers are $0.3030030003…$ and $0.3010010001…$

To do:

We have to find a rational number and also an irrational number lying between the numbers, $0.3030030003…$ and $0.3010010001…$

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,

$0.3030030003…$ and $0.3010010001…$ are irrational numbers.

We can insert infinite rational and infinite irrational numbers between two irrational numbers.

Therefore,

$0.3000000001$ is greater than $0.3010010001…$ and less than $0.3030030003…$.

$0.3020020002…$ is greater than $0.3010010001…$ and less than $0.3030030003…$.

Therefore, a rational number between $0.3010010001…$ and $0.3030030003…$ is $0.3000000001$ and an irrational number between $0.3010010001…$ and $0.3030030003…$ is $0.3020020002…$.

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Updated on: 10-Oct-2022

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