Thank you. After thinking about it overnight, I realized I asked a wrong question. Your answer still helps greatly and get me more than half way to satiate my curiosity.
Tolerance grade and example objects that require different grade/minimum pi accuracy is what I was looking for.

TIL there is a closer approximation than 22/7

Thank you, I already skimmed through that article before posting. Maybe I failed to put my question into words properly.

I want examples similar to pool/fence circumference in the article. Along the line of “We’re building x, and this is the worst rounding we can go, one fewer digit and it will be off by y”