You could come at it in a similar way to how the real second was developed. Initially the second was defined as 1/86,400th of a day, later narrowed to a mean solar day, but that still wasn't specific enough so they switched it to the current caesium atom definition.
If we wanted to subdivide the day into 100,000 new units instead of 86,400 seconds, we could simply take the current caesium atom definition * 864,000 / 100,000 and you would get a precise, scientifically acceptable unit that would be about 1/100,000 of a day, but still have the need for the occasional leap units.