Day 28: Mr. Elephante and Repeating Decimals

The photo above needs no verbal embellishment from me. Hooray for seventh graders!

Instead, I’ll share with you the story and idea that I shared with my class. Two years ago, I was teaching seventh grade for the first time, and consequently really teaching things about repeating decimals for the first time. I had an epiphany in the shower one morning: once you accept that .9 is equal to 1, you can figure out how to write other repeating decimals as fractions by comparing them to it.  For example, these two infinite decimals

.373737…

.999999…

compare as 37 compares to 99, since for every chunk of 37 above, there’s a corresponding chunk worth 99 below. That means .37 is equal to 37/99. Neat! Other ones, like .273 can be found through a little adjustment via fraction addition or subtraction (37/99 – 1/10). I find these methods more charming and intuitive that the classic algebraic explication of turning repeating decimals into fractions, although this method also has its place. Perhaps one is often partial to the insights one hews out for oneself.

But really, folks—hurray for Mr. Elephante and Mr. Elephante Jr.!

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