Rewrite as a simplified fraction.

Question

\[\large{0.8\overline{3} = ?}\]

Answer 1

To rewrite the decimal as a simplified fraction, we can let $x=0.8333\ldots$. Multiplying both sides of this equation by 10, we get $10x=8.3333\ldots$. Subtracting the original equation from this equation, we get \[10x-x=8.3333\ldots-0.8333\ldots \Rightarrow 9x = 7.5.\]Dividing both sides by 9, we have $x=\boxed{\dfrac{5}{6}}$.