Consider the following fraction:


Punch this into a calculator and you'll get the following answer:


However, I disagree. I say the answer is most certainly "0.6"

I could be rounding (0.56 can round to 0.6), but I'm not.

I could be saying that "0.6" is a limit of some kind, like in 0.999999999... = 1, but, for the purposes of this puzzle at least, I'm not. I'm am asserting that this is true equivalence in the mathematical sense of the word, in the same way that 2 + 2 = 4.

How could this be?


All these numbers appear to be in base 10. But why be so closed minded?


1 Answer 1


You're computing in base eleven.

In case anyone's wondering, here's how I found the base: The given equation, $17/30=0.6$, if it's written in base $b$, says that $(b+7)/3b=6/b$. And then we solve that for $b$.

  • $\begingroup$ Excellent. Did you need the hint? $\endgroup$
    – Chipster
    Jan 23, 2020 at 23:49
  • 1
    $\begingroup$ I guessed it might be a different base before seeing the hint, but looked at the hint before figuring out which base. $\endgroup$
    – msh210
    Jan 23, 2020 at 23:50
  • $\begingroup$ Beat me too it, good eye! $\endgroup$
    – Jchang43
    Jan 23, 2020 at 23:53
  • $\begingroup$ I like the equation. Didn't think of that. $\endgroup$
    – Chipster
    Jan 24, 2020 at 17:20

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