Pi (π) rational or irrational?

Hello everyone..!!

Pi ( π ) : rational or Irrational

In this tutorial I will be focusing on pi ( π ).

so before starting this I want to ask you a question i.e.

• Why Pi (π) came in existence?

• Why pi (π) derived?

These are the question often asked by students,

the answer of the most asked questions​ is 

pi (π) is derived to calculate the different values of round ( spherical or circular) things.

From the ancient time it was considered that all the round things have one common constant value which differs them from straight or plane surfaces,

basically the need of that constant value arises to resolve the problems of space calculations.

later it was found that this constant value is approximately equal to 3.1428...or 22/7.

now a days when we are looking over classifications of numbers we have come across rational or irrational Numbers,

under this section it is often asked that 

• Whether pi(π) is rational or irrational?

  As we all knows that rational numbers are those which can be expressed as p/q formation​ where q ≠ 0 and also fractions are terminating.

but on other aspect of p/q formation those p/q formation whose decimal expansion never ends and non repeating i.e.

decimal expansion is non terminating and non repeating are irrational Numbers.

so this means π= 22/7 is rational because of p/q formation.

wait wait wait.....!!!

Only having p/q formation is not the decision making tool we'll have to look at decimal expansions of those fractions too,

so,

π = 22/7 

   = 3.142857.....

hence it is non terminating.

So, the conclusion is 

pi(π) is irrational Number.

Again I want to clear that the constant value ( which is discussed earlier in this post) 

is 3.1428571....was calculated first then it is approximated as 22/7, hence undoubtedly you can say 

pi(π) is irrational Number.