Is π Rational Number or Irrational Number?

A complete explanation whether π is a rational number or irrational number? 

 

If π is a Irrational Number-

π = 3.14159265358979323846433832750…..

This shows that value is non- terminating non- recurring decimal expansion. Because, remainder is not zero and numbers are not repeating in decimal expansion.

The numbers which have non- terminating non- recurring decimal expansion are known as irrational numbers.

Therefore, π is an irrational number.

But, If π is a rational Number-

π=22/7

Number can be written as p/q, where p and q are positive integers. The denominator q is not equal to zero but equal to 7.

These are properties of rational number. It shows π is a rational number.

But, It is not true. If we divide 22 by 7, we do not get 0 in remainder. Therefore, π is not rational number. Because rational number has terminating decimal expansion which is not true in case of π.

But, we use fraction value of π=22/7 for making calculation easy.

It is clear from above discussion that π is an irrational number.

A video below is explaining whether π is rational umber or irrational number:-

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