If 0<a<b are integers, p a prime not dividing b, then in base p, a/b is a pure repeating pattern. In p-adics -a/b is also a pure repeating pattern to the left. I've been a bit slow to see that it is the same pattern. Eg
1/19 = .024024024... base 7, and
-1/19= ...024024024. in 7-adics.
