It might have to do with the fact that plural units are a numeric consensus where the singular is the exception. That's largely related to the fact that the idea of one-or-many existed before the (widespread) concept of Math (and mathematical subdivisions of an item) and the concept of zero in many cultures and languages. Relative subdivisions of a whole were largely considered independent units, especially in (but, again, not limited to) English. Consider and compare 0.5 days to half day, or 0.25 days to a quarter day.
I personally find it odd to use the singular noun on something that is not a singular unit, even if it is part of a singular unit. However, such examples do exist, and people would be prone to verbally append of a between the numeric and the unit, such as 0.5 (of a) day whenever encountered with a written 0.5 day.