tenths and hundredths of an inch "don't mean anything" because we don't divide inches that way in common use, but in subtractive manufacturing and the like they do use "thou" - and 0.001" is a thou.

Personally, i use microns instead of 0.001mm, too, when measuring that small. I forget the accuracy of my good calipers, but i could detect errors of around 2 microns if memory serves. It's been a long time since i cared about anything that accurate so i have two pairs of cheap plastic ones - scale and digital.