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Updated on : 2022-09-05

Solution

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The decimal expansions of $32 $ and $43 $ are as follows:

Here, the one decimal expansions are non-terminating recurring, while the other is terminating.

Hence, $32 $ and $43 $ are two rational numbers.

We know, between any two rational numbers, there are infinitely many irrational numbers.

An irrational number has non-terminating non-recurring decimal expansions.

Then $3$ different irrational number between $32 $ and $43 $ can be:

$a=0.6707007000$

$b=0.6808008000$

$c=0.6909009000$

Here we observe that $32 <a<b<c<43 $.

NOTE:

This is $3$ of the various possible answers. It might have different solution.

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