[bjz_]

Relevant wikipedia article: https://en.wikipedia.org/wiki/Dimensionless_quantity

Radians and degrees are both ratios where the units cancel out - ie. m/m. The point that is made is that adding degrees to radians without any conversions is technically fine from a dimensional analysis perspective, but it's often a bug in programming that we might want to prevent.

[ajuc]

You can define 1 meter as ratio between the measured length and a known length. Both of these have the same units so they cancel out, just like with degrees/radians.

The only difference is that full circle is a little less arbitrary than Earth circumference.