I love how the example is super confusing. You sleep 3.33… metric hours. You fall asleep 9:50 metric time. You'd think we can just interchange the . and : so you should wake up 12:83…, or 2:83… the next day. But no, it's apparently 2:75 metric time. Why? Also nice how they IMMEDIATELY ran into a continuing fraction 1/3, which is exactly the point of the 60-minute hour, 24-hour day, or 360-degree circle: lots of facto…
I didn't check the details of that metric time system but there would be no problem living a 10 hours day with 100 minutes hours and 100 seconds minutes. The second would be defined with a different number of "cycles of the radiation produced by the transition between two levels of the cesium-133 atom" and that's all. Instead of rounding our lives at "our" quarters of hours or ten minutes, five minutes marks we would…
Presently, we use 24-hour time (AM/PM or otherwise), so the loss in precision is enormous going from 24 to 10.
Think about it.
A tenth of a standard hour is 6 standard minutes.
A tenth of a metric hour is 144 standard minutes, more than two standard hours.
A hundredth of a standard hour is 36 standard seconds, or half a minute. It is in the context of hours a negligible amount of time.
A hundredth of a metric hour is 14.4 standard minutes! Imagine being 0.01 metric hours late for a meeting.
So everywhere you now have to specify time to two decimal places /at least/, three to have sub-standard-minute precision.
Layer on top of this the fact that the new system has significantly fewer distinct prime factors, so you quickly run into continuing fractions. Disaster.