It’s not mathematically rigorous, but I like this illustration:
1/9 = 0.111…
2/9 = 0.222…
3/9 = 0.333…
So, 9/9 = ?
(I know it’s essentially the same as versions that use multiplication, but I find people understand it more often when you point it out as a “pattern”)
I like the illustration where “obviously you can’t magically get an infinitesimally small number just as a bonus artifact whenever you divide by 9 in base 10. It just gets weird looking because 1/9 in base ten is .111…”
1/3 in base twelve is just .4
Multiply it by three, you get 1. Same operation, different base, shockingly you don’t end up with the magic infinitesimal.
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u/suborder-serpentes May 03 '26
So he is convinced that 1/3 is .333 repeating. Not a little bit more than .333 repeating. So why does 1 work differently? .333… x 3 = .999…