Very nice use of math. The actual method was developed by Enrico Fermi, he made estimates on the size of things like the universe, and was famous for not giving an exact number, but saying "on the order of." He didn't put much value in exact numbers, but whether or not he was 10times too small or 10times too large, if not, then it was close enough.
Just a little tidbit from HighSchool Physics....