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Are you seeing these objects move, or do you just see slight changes in the display in the Control panel or Transform panel? If the latter, then this is easy to explain. Illustrator stores all positions and sizes inside the file using points. If you enter a width of 4 mm, Illustrator stores that as 11.34 points (precision to 100th of a point, or smaller than 1/7000 inch). When you ask for the size to be displayed in a panel, the measurement is converted back into millimetres for display, but the size remains 11.38 points. Sometimes, due to rounding in the conversion or in the display, sizes or positions seem to change. A common example is 9 points = 1/8 inch = 0.125 inch. Illustrator will display that at 0.13 inch, due to rounding in the display, but the stored value of 9 points is exactly 1/8 inch, or 0.125 inch. It is annoying, confusing, and often confounding, even to veterans.
What Adobe should do is add a tag to Illustrator files defining the measurement within the file and storing positions and sizes using those units. But Adobe has a long list of shoulds for Illustrator, most of which they ignore.
Ahhhh, that makes sense, Scott. That seems to describe exactly what's happening.
So I'm trying to think of some kind of workaround. I definitely need to work in millimeters... is there any way to change the level of precision with which objects are positioned? I've never seen anything drift more than a few thousandths of a millimeter, and hundredths would do the job for me. If Illustrator only converted points out to hundredths of a millimeter, it seems that should solve the problem.
Is this something that can be adjusted?
There's nothing you can do. And nothing is drifting. You are just seeing the result of your millimetres converted to points and rounded, then the points converted to millimetres and rounded. The only workarounds are to either accept it or use a decent drawing program, which lllustrator is not, and never will be.