Question

What is the exact value of `pi`?

Answer 1

no one can give you the complete value of pi because as technology in searching for pi increases number of decimal places increases.

Answer 2

`pi` is an irrational number.

It is not expressible as a fraction, terminating or repeating decimal.

Explanation:

`pi` is expressible as the sum of an infinite series.

For example:

`pi = 4 * tan^(-1)(1) = 4 * (1-1/3+1/5-1/7+1/9-1/11+...)`

There are some useful rational approximations for `pi`.

For example `22/7 = 3.dot(1)4285dot(7)` and the much more accurate `355/113 ~~ 3.1415929`

or of course, decimal approximations:

`pi ~~ 3.141592653589793238462643383279502884197`