I think the basic idea is that highly composite numbers [1] make good bases. It's a trade off between the number of divisors of the base and the number of digits we want to learn.
Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.
psh, it's 2017. Clearly we should switch to hex, ditch scientific notation and decimal points and all that difficult junk, and just use IEEE 754 double precision notation for all our calculations. Granted the sign bit in front makes hex notation a bit awkward but I believe it will give us a nice kickstart for when we will inevitably be subsumed by our AI overlords.
> IIRC, it's not possible to represent .1 (or is it .2) accurately in IEEE 754.
> Better to use duodecimal.
Assuming you mean the decimals 0.1 and 0.2, they can't be represented as terminating duodecimals (which is different from not being represented accurately!), either. Whatever base you choose, someone's favourite fraction won't have a terminating expansion.
IEEE754 includes two decimal floating point basic formats: decimal64 and decimal128. 0.1 can be accurately represented.
Of course in any base there will be some non-terminating representations of rational numbers, so changing the base of the floating point system changes which numbers these are but does not eliminate them.
Note that both 12 and 60 are such numbers.
[1] https://en.wikipedia.org/wiki/Highly_composite_number
Also it looks like the Babylonian is a composite system, where the 'digits' are represented in base 10 (the 10s use a different digit, but it doesn't matter). They could alternatively use base 12 for this digit.