In the previous post, I showed a quick way of obtaining a full decimal representation using a calculator that only displays ten digits at a time. To review: here’s what a TI-83 Plus returns as the (approximate) value of :

Using this result and the Euler totient function, we concluded that the repeating block had length . So we multiply twice by (since ) to deduce the decimal representation, concluding that

Though this is essentially multi-digit long division, most students are still a little suspicious of this result on first exposure. So here’s a second way of confirming that we did indeed get the right answer. The calculators show that

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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One thought on “Thoughts on 1/7 and other rational numbers (Part 10)”

## One thought on “Thoughts on 1/7 and other rational numbers (Part 10)”