> How often do we use fifths?
I can't say I use thirds much more often than fifths.
I can't say I use thirds much more often than fifths.
If you bake or cook using imperial units, 1/3 comes up much more often than 1/5, in my experience.
We often talk about half an hour and a quarter of an hour.
But almost never about a third of an hour or a fifth of an hour.
How often do you talk about 20 minutes because you can neatly stuff 3 of those time periods in one hour?
I'd say the fact that 15, 20 and 30 fit nicely into an hour plays a role in their popularity, even if you don't realize you use them for that reason.
Not really. Quarter hours and half hours are natural units. This is true no matter how many minutes we divide an hour into. There's nothing special about "25" when you're building up from 1. 25 is only special when you're splitting up 100, and nothing uses 100-minute blocks so that doesn't happen.
> I'd say the fact that 15, 20 and 30 fit nicely into an hour plays a role in their popularity
I'm skeptical for 20. I think 20 being a nice round number plays a much bigger factor here. If hours were 65 minutes I think you'd see just as much use of "20 minutes".
As for non-time-related units, I hear 25 deko more often than 20 deko when buying food. I don't think there's really a distinction between building up and down. When you're talking about 250 meters do you build up from meters or down from kilometers? I think both.
Dunno. I personally 'visualize' 20 minutes as a third of an hour. I don't know how common it is to actually stuff an hour full of 20 minute periods, but it happens - you see a schedule with X:00, X:20, X:40. Multiples of 15 or 10 minutes do seem to be more common in that case.
But it definitely matters to some extent that it's a divisor. Consider how rare 25 minutes is compared to 20 or 30. If you look at it only as a number of minutes, 25 seems a bit less 'round', but not too much; we often say "25 cents", after all. (And it's 5 squared and a quarter of 100.) But 25 minute periods are less convenient to calculate with, because adding them tends to result in odd/less consistent minute values, because it's not a divisor of 60.
I’m not sure what your point is. If you have a family of 7 or 11, you’re probably going to have a bad time using positional arithmetic regardless.
The point here is that decimal is noticeably less efficient and less regular than some alternatives.