Below about a thou, various tricky factors start causing trouble, and they get progressively worse:
- Temperature – a rod warmed to 40°C is measurably bigger than the same rod at 20°C. If temperature isn't accounted for, you ain't measuring tenths!
- Calibration becomes vital. Second-hand gauge blocks and ancient micrometers aren't good enough.
- Technique is difficult and tiny flaws destroy accuracy.
- Although a large diameter dial helps, don't expect much from dials, and especially not small ones. Dial marks are usually indicative rather than accurate: the operator is expected to use a micrometer, calipers, or DTI
- The brand-new lead-screw of an ordinary lathe is unlikely to be tenths accurate and older lead-screws will be more-or-less worn too. The accuracy of fine-cuts is fundamentally limited.
- Tiny saddle, headstock and other alignment errors show up
- Work and tools both bend under cutting pressure, making it likely that cuts are not all of equal depth end-to-end. (Ever noticed that tools often remove more metal when reversed out of a cut?)
- Scale causes the relative surface finish to go to pot! As the size of cut is small compared with the lathe's automatic feed-rate, fine cuts leave spiral grooves rather than a smooth surface. Looked at with a microscope after a few passes, the surface resembles knurling. Is a tenths micrometer measuring between peaks, or has the anvil crushed them towards the valley bottoms? Dunno: unless the surface is good, the tenths are uncertain
What this boils down to is that lathes (and milling machines) struggle to take cuts that are both fine and accurate. Tool-room lathes and jig-borers do better, but they're elaborately engineered and maintained to hold accuracy. They have obvious limits too.
The answer to high accuracy isn't a lathe. Industry are fond of grinding machines but these are expensive. Fortunately small workshops can get good accuracy and surface finish with manual abrasives, notably emery papers,and lapping. Making pistons, the lathe is used to get close to size, but turning stops a little above target. After that a succession of ever finer abrasives are used remove unwanted metal, not cutters. Unlike cutters, correctly used abrasives improve the surface as well as removing metal. The main problem with abrasives are removing metal evenly, and the amount of time it takes.
Larger pistons don't go for a very tight fit: instead the seal is provided by piston rings which can expand slightly to fit. Although cylinders are bored very accurately in big engines, I've got the impression surface finish is even more important. There is no 'Running In, Please Pass'. Au contraire, I've built 5 model engines and they all needed a lot of running in! I spoiled several pistons by rushing the finishing stage. Patience in the workshop is not one of my virtues.
I rarely work to better than ±0.05mm and avoid high-accuracy if I can. I stay with innocent measuring because high-accuracy is dangerously additive. 'Chasing Tenths' could easily take over my life. As Chasing Microns is even more difficult, only real men dare go metric!
Dave