# Calculators are bad at Arithmetic

Consider the following fraction:

17/30

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

0.566666666666666666666666666667

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?

Hint:

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

## 1 Answer

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 $$b$$.

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