One of the things that regularly gets discussed is the accuracy that we should expect from our machines and that we should work to.
In practice, if you look at the specifications of various fits, it is extremely unusual to come across a requirement to work to better than 0.01mm or about half a thousandth of an inch (from here forward I will just use metric).
Even when testing tools, Schelsinger's limits don't rely on better measurement than 0.01mm, with precision being achieved my measuring deviations over an extended length of a bar, for example.
But lots of folk still chase 'tenths of a thou' so let's put the dimensions we work to into a context:
1mm = Typical size of a grain of sand, half a pinhead. About as small an object as you can handle without tweezers.
0.1mm = The thickness of a piece of paper.
0.75mm = roughly the smallest size difference you can see with the naked eye at a distance of about 300mm, normal reading distance. Diameter of a coarse hair.
0.02mm = diameter of a very fine hair.
0.01mm = diameter of a fungal hypha, length of a human chromosome.
0.005mm = diameter of spider silk.
0.005mm = about the size of a red blood cell.
0.001mm = the diameter of an E. coli bacteria, smallest eukaryote cells
0.0006mm = 600nm = wavelength of red light
200nm = smallest free living bacteria.
100nm = resolution of top-end Mitutoyo micrometer (accuracy 500nm)
180nm = deviation from round of the roundest man-made object
50nm = deviation of a top quality telescope mirror from perfect*.
13nm = the finest pattern you can feel with your fingertips.
1nm = how much your fingernail grows in a second.
0.1nm = size of a phosphorus atom.
Neil
*presumably this is better than the roundest object because it's relatively easy to measure and correct a mirror's accuracy by optical means.