The inability to exactly express pi is largely due to lacking the skill, it's not necessarily pi's fault. As Karlos suggested, just use it as your number base. Now imagine a circle with radius pi.
base 10:
r = pi
area = pi^3 ~= 31,006276680299820175476315067101
base pi:
r=1
area = 1^3 =
1 - voilá
Having trouble counting your fingers in this number base? Well, it ain't
that easy.

In real life you're stuck with units anyway (cm, inch, whatever) which you can't break down, so just leave the pi as unit and you have an 'exact' figure.