The whole argument started when somebody above claimed that we probably do not sleep exactly 8 hours, but some weird irrational number. That problem persists even if you measure in radians...
Do the physicist thing and just define all your constants to be one.
"How long is a day? 1 day."
"I slept for .37 days."
This nicely unifies things with the tao manifesto[1] people since 1 day = 1 turn = 1 tau = 2 * pi radians and reinforces the periodic nature of these things.
