As a practicing physicist, I found it illuminating and non-trivially useful to know this when it was first introduced to me years ago. This is true even though

As a practicing physicist, I found it illuminating and non-trivially useful to know this when it was first introduced to me years ago. This is true even though I will never use in a paper, and even if I only rarely write it in my notes. In my head, 2\pi is a single character, to the point that I often write \frac{1}{2} 2\pi.