Calculating a 20% discount by multiplying by 0.8333?

A $20\%$ discount means that the price is $80\%$ of what it was originally, so you multiply by $1-0.2=0.8$.

$0.8\dot{3}$ is $1/1.2$, which is used to find out the original price when you have been given $120\%$ of it (if there's $20\%$ tax included in it, for example)

Note that multiplying by $0.83\bar3$ is really dividing by $1.2$. In order to know which one is right, you need to keep in mind which number represents $100\%$, or the origin. Calculating percentages from the origin is done by multiplying, while recovering the origin from some given percentage is done by dividing.

So finding $80\%$ of a price is done by multiplying with $0.8$. If you have the $80\%$ price and want to find the original price, you divide by $0.8$ (which becomes multiplying by $1.25$).

So multiplying with $0.83\bar3$, when we're talking about $20\%$ and not $16.6\bar6\%$, is, as mentioned above, really dividing by $1.2$. That means that what we find is the original price when we're given the new price after a $20\%$ price increase. That's not the same as finding $80\%$.

An $x \%$ discount normally means you subtract $x \%$ of the original price.