Dual Dimensioning

By far the easiest thing to do is measure the part in the unit it's made/designed in. Consider asking the QA guy to push the little inch/mm button on his measuring device. If he doesn't have such a button, seriously consider buying him some new tools--it'll be cheaper than doing the engineering to dual dimension everything.
Unit conversion is fraught with issues, but at least in general terms, you're correct--the "converted unit" (inches in your case) needs extra decimal places to deal with round off error. I've been down the road you're starting out on, and it's not a pretty process--good luck.

Yeah, I agree that would be the easiest thing to do, but getting QA to agree to that may be a challenge.
If I can't do that, I'd still like to hear other people's input on the issue. Is there a "correct" number of decimal places to use?

The way we handle this is to make all the drawings and parts in mm. You can set the tolerance of the dual dimension to 3 or 4 places in the precision option (RMB on dimension, PROPERTIES, PRECISION and change the dual dimension to the tol you want. The thing to remember is that a 0.1 place tolerance in mm is only about .004 in inches so tolerance them similar.
+0.000/-.004.

Jason, pardon me if I'm not understanding correctly -- but why get hung up on number of decimal places? The number of decimal places in BOTH English/Imperial and Metric units are only relevant relative to default tolerances (in your title block or in the original print's title block). It's generally true that if you use more decimal places than three or four (in English/Imperial units) it MAY cause QA to have some difficulty in verifying out to the extremes of the tolerances . . . but only if the parts to be measured vary toward close to the extremes. But if your company's QA department is so pig-headed that they refuse to take their English measurements and convert ("hey guys, can you multiply by 25.4 or do I have to do it for you?") then they rather deserve what they get in difficulties. Even considering my intolerance for their stupidities, if I were in your place I would round off tolerances to three decimal places most times . . . or four if I felt that that the tolerance was critical AND was already so tight that giving a slight bit more via more decimal places would help prevent rejecting GOOD parts. In your example (.039 +.000/-.004) I would just your conversion to be appropriate.
Don't confuse the forest for the trees. Keep in mind the purpose of tolerances and the purpose of QA (not so much to reject parts, but to accept parts which are acceptable) and you'll keep your priorities straight.
'Spork'
Jas>

Great, thanks for your comments.
dimensioning, +0.000/-.004.