After we got new hardwood, I didn't want my office chair to scratch the floor. I've done it before and I have tried solving the problem with a plastic mat but I found that it didn't work too well. It was a bit small and so there was times where I would be off the mat.
I then learned that roller blade wheels can be swapped in for the wheels and this would solve my woes. I bought some roller blade wheels from amazon for 25$.
It has now been 4 years and they have worked perfectly. I don't have any scratches anywhere and I've bought an additional 2 sets for other chairs as well.
Would highly recommend getting some roller blade wheels for a chair.