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I was figuring the angle of a 3d-designed part in my head the other night. It's a cylindrical polyhedron with 32 faces (because 32 seemed like a good number). I didn't expect to end in the exact value of 11.25. That is a derived value, but it is still exact (effectively to infinite decimal places, like inches in a foot).

It made me wonder how these numbers are handled in more formal, complex calculations with significant digits.

If the above values were used in a calculation that involved others values that have, say, 10 or more sigdigs in them, I assume these values don't count against precision i.e. I wouldn't drop all but the last 4 sigdigs from my 10 sigdig values, yes?

Which makes sense, but how does one track that if the steps of the calculation are, like 50 lines long? Especially if the 11.25 is then operated upon by some other number that

*does*have a number of sigdigs. Now the 11.25 goes away.

So does one simply track these non-sigdig values all the way through the calculations? Is this often a problem that warrants proofreading?