Well if you display it as mV, at least you don't have to worry about whether to use a comma or a point as your decimal mark! (Since I would have read that as 3 thousand volts!)
However, apart from the internationalization aspect, the question arises - At what point do you determine that V becomes more appropriate than mV?
For example why is 3789 mV ok and 9873 mv less ok.
Most handheld voltmeters I have come across have ranges like 200mV to 2000mV; 2V to 20V; 20V-200V, (see DCV section of the dial on the digital voltmeter below) and actually I would usually align with that - ie, if it's equivalent to a 4 digit number starting with a 1 then it's ok to have 1234 mV or 1.234 V, but once you tip over 2000, it's better displayed as 2.345 V rather than 2345 mV.
A similar thing happens in speech - we might typically say 'eighteen hundred metres* but less likely to say 'twenty eight hundred metres'.
So if you can skirt the issues of decimal mark confusion, I would suggest 3.789 V by virtue of convention and picking 2.0 V as that unit-changing tipping point.