how do you interpret divided units?

[Klaynos]

I'd say it's more complicated than that as there is a clear difference between degrees and radians. You need more information than just "an angle of 8"

[John Cuthber]

But the conversion from radians to degrees is just multiplication by a pure number. They are both dimensionless.

[Klaynos]

Dimentionless yes. but you still have "meaning" with the units.