Bases are funny things. The clock isn't base 12 or 60. We still use base 10 to count the hours, minutes and seconds. It's an odd mixture of base 10 and base 12 and base 60. Base 10 is used for normal, low numbers but as soon as they get too big they get put into buckets of 60 which in turn are put into buckets of 12, and then buckets of 2.
I think the same was true with the Babylonians. They used base 10 for everyday things (whole numbers below 60), but they used 60ths and 3600ths and so on to denote fractional parts of numbers. This continued all the way into the Italian renaissance and some of the early accurate calculations of mathematical constants were expressed this way. Maybe pi or square root of 2, not sure. The Babylonians may also abandoned base 10 for numbers over 60 and started putting things into buckets of 60 and 3600 for very big numbers. (This may be wrong in some details I'd have to look in a book to check, and as this is the internet I can't be arsed).
It's the same with the imperial system of measurements. They deal in base 10 for low-ish whole numbers, but then the next measurement up is a bucket of a random number depending on what you are dealing with: 3, 8, 10, 12, 14, 16, 20, 22 are all used.
Quite why users of the imperial system prefer rational fractions like 21/32nds rather than decimal fractions, I don't know. It could be due to an affinity with the Pythagoreans