The mathematical system will be either base-12 or base-16, depending on which provides more benefits.
Monetary units are suggested in each section, however, the number of types that seem most logical is more than most cultures deal with. Some may have to be removed. Of course, the likelyhood of a physical currency is slim, and so the issues presented by the bills will be moot.
Units of measure shall be similar to the metric system in consistency and naming, however they will obviously not be decimal, since that would go against the new numbering system. Also, the actual prefixes that mimic kilo, mega, etc, will be from the new language system.
length metre (metric decimeter) area hetre (metre^2) volume litre (metre^3 -- same as metric liter) mass gram weight temperature degrees (0 is frozen water, 100 (144) is boiling water --
conversion of celcius*1.44)
Although many things are beyond our control (the number of days in a year, etc), the calendar may be slightly different from the gregorian system. If duodecimal is decided on, the current 12 month system would be maintained, however the weekly structure may be modified in either case -- resulting in either 6 or 8 day weeks. Also, the start of each year may be changed to (for example) the summer solstice, in order to for it to appear less arbitrary.
Most likely, the calendar will consist of 12 months, each with 5 six-day weeks (on leap years). Even months will have 30 days, odd ones will have 31 (months are 0 based. On non-leap years, the final month (11) will only have 30 days.
Or, there will be 11 months with 5 weeks, and a twelfth with six (with a short final week on non-leap years).
DUODECIMAL number system
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B
bills: 1, 2, (3), (4), 6, 10, 20, (30), (40), 60, 100 change: 1, 2, (3), (4), 6, 10, 20, (30), (40), 60
HEXIDECIMAL number system
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F (these symbols will be replaced by something more unique and consistent)
bills: 1, (2), 4, (8), 10, (20), 40, (80), 100 change: 1, 4, 10, 40