Divided by Seven

A couple weeks ago, I was having a cup of coffee before school and working out a problem that I was going to give to my students. I found myself doing some long division - dividing by 7, to be exact - when all of a sudden it hit me: that sweet, sweet sensation of uncovering a universal truth.

Since the number I was dividing by 7 wasn't a multiple of 7, my answer wasn't going to be a whole number. So as I added a decimal point and kept dividing, I realized (to the Patty Mayonnaise sound of angels singing) that I could sit in that chair and keep writing all day because the numbers after the decimal were never going to end. Not only that, but it would be true any time I divided by 7 and my answer wasn't a whole number**.

It might seem trivial (or, at the very least, dorky), but in that moment, it was euphoric. I'm sure hundreds of thousands have made the same useless realization before me and have since taken it for granted, much like I take 7th grade knowledge for granted every day. But I've forgotten how exciting and eye-opening those light-bulb moments can be. Though they happen less and less frequently to me, they are happening all around me every day. I need to do a better job of celebrating them.

**Free EiBiT (Everything is Blogger in Texas) Mug*** to the first commenter who provides the proof... c'mon T-CAMS, this is your time to shine

*** these do not exist

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EDIT: What I originally posted isn't entirely clear. For example, when you divide 0.07 by 7 you get an answer (0.01) that isn't whole, repeating, or irrational, which disproves what I was saying. I'm talking about any situation when you need to start adding zeros after the decimal to complete the long division. (Extra Credit: does it work for any other number?)