Jiggety Jig

I’m back home after a wonderful trip. I only fit in a little math during my week away, but I did make some progress on the questions posed in my post About Division. I have developed a good argument that the decimal representations of rational numbers must repeat (or terminate, which is simply ending in a repeating zero). An argument that a repeating decimal must represent a rational number is proving more elusive. I could use facts about the sums of geometric series, but I feel as if there should be another way. More on these things later in the week; today I have a lot of neglected chores to do.