This is solvable using arbitrary-precision decimal libraries, but relying on one of those for just dealing with general time stuff is a Bad Idea.
But yes, any humane 'decimal' time system is just optionally giving names to different places in the fractions of a day decimal (I say 'humane' because days have varying lengths, and so should not be used as the basis for a unit used for scientific measures).
I still think naming the fractions might be useful (like 'satoshi').
Check this out: http://www.youtube.com/watch?v=-nC8J6YXqdo
10 divides by 1 5 and 10 so you can easily figure out halves and tenths thats about it.
12 divides by 1 2 3 4 6 and 12 so you can easily figure out halves, thirds, quarters, sixths, and twelths without much of an issue, less non terminating decimal nastyness.
60 is even better, as it divides by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 you get a whole wealth of easy fractions, and easy mental division.
This is probably the reason why a lot of ancient societies had a preference for base 60 and base 12.
you can count to 12 on your fingers aswell, using your individual finger bones on one hand + your thumb as an index.
You can extend this system to count to 60 by using the 5 fingers of your other hand seqentially to represent each set of 12.
I would say binary is the best base, and perhaps the least arbitrary of all bases since it is the simplest.
EDIT: whoops, bad formatting.