accuracy to the last digit.
It's still more accurate than a trillion decimal points. Although if you don't need it, that's fine...

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saloon

So, it wouldn't really help us practically to find a new equation, although it might be quite interesting mathematically.

Also, we also know π so accurately that the error come entirely from circles in the real world not being perfect, as well as somewhat imprecise measurements. π is know to millions of decimal places. That kind of accuracy is unheard of in anything else.