Actually, for any practical use case or possible observation, there is an approximation of Pi that is good enough. The ancient Egyptians apparently did quite well in their architecture approximating Pi as 22/7 (3.(1428571)).
You only need the exact number Pi if you want to measure something like the ratio between the length of a perfect circle and its radius with infinite precision. But you can't be sure your measurement has infinite precision with a finite number of measurements, and so you can't observe the difference between a perfect circle and a many, many sided X-agon, even if perfect circles do exist in the geometry of the universe.
Just as a fun aside, even if perfectly circular shapes do exist, it's unlikely that perfect circles would exist in physical objects - at best, you would have ellipses, and there is no (known?) way to compute the ratio between the length of an ellipse and the properties of its foci.
