When you travel in one direction the error accumulates as you calculated. When you travel back to the start point the error is 0 because Mach travels all the same way back.
Normally not a big problem as long as the diameter is not too big or the amount of rotaton is huge and you are in G90 mode. If you are in G91 ( incremental ) mode and
working with lots of sub recalls and do a short rot on 360 then the fraction of the last step will be lost ( not really lost - only within your operatin ) whitch can cause a greater
error at the end. The error is alway 0 in G90 mode at the home ( G53 ) position regardless what you did before. That all is what I found by testing no guarantee that is 100% correct
You can type in 222.2222222 ( 10 places ) When your diameter is 100mm then the circumference is 314 mm you said you miss 0.00376 steps after 470 rounds that is
314 / 360 = 0.87222 mm per degree / 222.2222222 steps = 0.00392 mm per step * 0.00376 steps = 0.000145 mm error on the circumference after 470 rounds at 50mm radius.
Not too bad I think. Anyway, the best thing of course is to have the mechanical setup so that gives you a even number. If you doent want to change the mechanics there is one way
left to get it 100% precise, you can coose your circle eg. 400 degree or what ever gives you even numbers, but short rot on G0 or 360 rollover will not work with this setup.
Alex