An irrational number is one that does not have a last digit. It's not a matter of finding the last digit; rather, mathemeticians have proven that the number of digits continues to infinity without ever ending or turning into a repeating pattern. Another popular irrational number is √2 (if I recall correctly, any square root of a whole number that does not resolve to a whole number is irrational—so √5 and √7 are irrational, while √4 and √9 are not).

Thus, we can approximate the value of pi. "3" is one such approximation and 22/7 is another. But we can never define π exactly—which is why we use a symbol (Π) instead of a numeric value.

On that same note, no physical circle is ever perfectly round in a mathematical sense. There is always some (possibly very small) error that turns the ratio between the circumference and the diameter into a non-irrational number. Even if you made the circle very, very precise, you would not be able to refine it past a certain point because of quantum limits. There is a specific size/energy limit beyond which we cannot go any smaller. Quantum theory tells us that the real world is digital, not analog, but that the sampling rate is so extremely high that it appears to be analog. Mathematics, on the other hand, is not limited by the physical universe and can easily handle an analog world with irrational, infinite numbers.

-----------------------
Check out Chad's News
-----------------------