[cnvogel]

The ratio of the observable universe's circumference to a proton diameter may be 10^-35, but that doesn't really say anything for the precision of Pi you'd need in practice for any calculation involving these scales.

Because for everything involving real-world data, you'll have to measure quantities, and this is hardly ever done to more than just a few decimal digits. Whenever I want to state the circumfence of anything I know the diameter of down to single numbers of proton diameters, I first have to measure the diameter of to a precision of 1/3 proton diameter. Only when I reach such an absurdly nonsensical precision, I'd introduce errors by using an inadequately runded value for Pi.

More practically: I might know that I could line up 2.611*10^25 protons (disregarding the fact that due to their charge they would repel each other) around the earth, but to calculate that I only need 5 decimal digits of the earth's diameter, and only 5 decimal places of Pi.