Which of the following is a rational number ____.

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Detailed Solution

We are asked to check whether the given numbers are rational or not.
Let's check each option one by one.
(1) √5
Here we see that the number 5 is not a perfect square.
We know that the square root of an imperfect square is always an irrational number.
We also know that the square root of a prime number is an irrational number.
So we can conclude that the number √5 is not a rational number.
(2) π
We know that the value of π is a universal irrational number.
So we can conclude that the number π is not a rational number.
(3) 0.101001000100001....
We know that the condition that a rational number can have either finite digits after the decimal point or there will be repeating digits after the decimal point.
Here we see that the given number does not repeat at all and is also not a finite number
So we can conclude that the number 0.101001000100001.... is not a rational number.
(4) 0.853853853...
We know that the condition that a rational number can have either finite digits after the decimal point or there will be repeating digits after the decimal point.
Here we see that there are repeating digits in the given number which are 853
Therefore, we can conclude that the number 0.853853853... is a rational number.
So we can conclude that the rational number of all the given numbers is 0.853853853...
So option (4) is the correct answer.

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