[hm8]

Yes 0.5 inches would be exactly 12.7 mm but that comes from the way the inch is now defined (which is 1 in equal to 25.4 mm) as opposed to the earlier definition (i.e. 1/12th of a foot (this definition being the older imperial definition). machined to 12.7 mm simply means that the original imperial definition is abandoned for imperial units and although the chuck/collet/etc is still sold as 0.5 inch chuck/collet/etc; when constructing it, it was measured in the SI units of mm for precision purposes.