I am a non-native speaker.
It doesn't make sense to me that around-the-clock means 24hours.
Would you tell me the origin of it?
I'm not a Native speaker myself but I think it is because looking at the clock, 24 hours would only pass if the short hand(hour hand) goes around the clock, even twice, to complete the day(24 hours).
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just an English-lover
The phrase is more usually "round the clock" = uninterrupted. So round the clock care means that at no time does care cease.
Anglika, what do you think of my explanation?