I think the day needs time units which are factors of 10x or 1000x to match SI prefixes. I give translations assuming current solar day length and current normal units:

- deciday (2.4 hrs)

- centiday (~0.24 hrs, ~14.4 minutes)

- milliday (~1.44 minutes, ~86.4 seconds)

- microday (~86.4 milliseconds)

But, to really get into the decimal clock, we want to also extend this into culturally useful multi-day units.

- decaday is somewhat akin to weeks

- hectoday is somewhat akin to months or quarters

- kiloday is somewhat akin to years

So we need to do some hard thinking and invent some insane tech to adjust planetary mechanics so that we can have decimal relationships between diurnal, lunar, and annual cycles. ;-)