# What is the exact value of pi?

Oct 18, 2015

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

Oct 18, 2015

$\pi$ 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:

$\pi = 4 \cdot {\tan}^{- 1} \left(1\right) = 4 \cdot \left(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \frac{1}{11} + \ldots\right)$

There are some useful rational approximations for $\pi$.

For example $\frac{22}{7} = 3. \dot{1} 4285 \dot{7}$ and the much more accurate $\frac{355}{113} \approx 3.1415929$

or of course, decimal approximations:

$\pi \approx 3.141592653589793238462643383279502884197$