When I was a young man, a common arrangement for loose bound technical manuals is to number pages by chapter. (It’s quite a good scheme, in those situations: even if your corrections add a whole page to the chapter, the most you have to redistribute is that chapter.)
The problem, at first sight, seems pretty much the same as that in another answer on running numbers within a chapter, and the basic technique is indeed pretty similar.
However, tidying-up loose ends, making sure the page number gets reset to the correct value at the start of each chapter, and so on, is slightly more challenging. This is why the chappg package was written: it does the obvious things, and more.
Users have been known to ask for running page numbers within a section, but this really doesn’t make sense: you need to run page numbers within document objects that always start on a fresh page.