A lead-in to ten-adic numbers

Most people are willing to say that 0.9999… (infinitely many nines to the right of the decimal point) is worth contemplating even though we might debate over whether or not the value of this infinitely long decimal is 1. But we do seem to be comfortable playing with infinitely long decimals: 1/3 = 0.333… and 4/7 = .571428571428571428…. in general, with no real qualms or concerns.

But what about infinitely many digits to the left of the decimal point. Is the quantity …99999 worth considering?

Welcome to ten-adic numbers!

This PDF essay is a bit rough, but it is my quick attempt to give a story that leads to and explains ten-adic number arithmetic. We focus it on the work of 1 <--10 machine from the story of Exploding Dots.

Ten-adic Thinking with Exploding Dots


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)

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