As a matter of practice, it is only possible to consistantly read a compass (or any needle like meter) to one-half of the smallest marking. Five degrees means two and a half precision is possible. MostlyHarmless is correct, the biggest question is the user. Without a good sighting system, as HikinJim indicated, even that ability is moot because of the ability to transfer that to a place in the world. My Brunton Pocket transit reads to one degree. Sighting it to that level is difficult even as large as the sighting system is. Best on a tripod. Not something that is necessary for hiking. If you are talking about the intrensic capability of a magnetic compass, it is so high that even the one-tenth degree markings on my transit are not up to the capability of a magnetic compass (but that requires exact time and good corrections for deviation, etc.).

Izzy, the body will make no difference to at least one-tenth. What you are wearing (or carrying) can make a huge difference. Knives, watches and belt buckles are the most common offenders.

Respectfully,

Jerry