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The following should fix the problem for all new documents.
If you change the Document settings of a template file, then all new files made from that template will have those settings. You just need to close all new parts and go open up the actual template from it's location, not by creating a new file. One way to find the location of your Templates is to click 'New', select 'Projects...' and hover your mouse over 'Templates = [Default]', it wll have a popup text showing where the location of your templates are. Now just go open up each template you want to change and apply any document settings you would like. Tools/Document Settings/Units Tab, and change linear and angular precision up to 5 digits.
I needed to do this because when creating a constraint the 'predict offset' feature is only based off this precision setting, while Inventor itself goes much higher. So if I tried to predict an offset that was exactly .0625 and the part was grounded, then the predict offset would think it was .063, which was wrong, and so the constraint would fail.