TITLE: Which base of numerical system have $\frac 15 = 0.33333\ldots$?
QUESTION [14 upvotes]: Which base of numerical system have $\frac{1}{5} = 0.33333\ldots$?
I need assistance in solving this one.

REPLY [12 votes]: A reworking of Arturo's answer: let $x=0.333\dots$, let the base be $b$, then $$bx=3.333\dots$$ so $bx-x=(3.333\dots)-(0.333\dots)$ and you can take it from there.