Question

why does pi never end?

Answer 1

If the decimal expansion of pi would end, then it would have to be a rational number (found on yahoo)

Answer 2

From the normal definition of pi (Circumference / Diameter), you probably wouldn't be able to figure it out.

However, in Calculus with sequences and series, we learned that there's another way to define pi:
\[\pi = 4*(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} -... )\]
(... means that it continues on infinitely)

Even though this series continues on infinitely, the amount we're changing it by each time gets smaller and smaller. But no matter how many terms we add, there are always more to add, so no matter how far out we get in pi, there will always be more digits we don't know yet.