I have a pair of very nice dial calipers that display marks every 0.001" and can be used to round to the nearest .0002" accurately. How should I go about centering these so that they are as accurate as possible? When just using my eyes there is a fairly apparent amount of error because of parallax.
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There should be a locking screw securing the bezel of the dial. If all you're trying to do is calibrate for zero, you should be able to close the jaws (don't force it), loosen the locking screw and rotate the bezel until the zero and the needle line up.
To get a more useful calibration, you're going to need to check other non-zero measurements. That will give you some other fixed points from which you can derive a linear model of error over the full measurement range.