Question

Rewrite as a simplified fraction.
\[\large{0.8\overline{7} = {?}}\]

Answer 1

Let $x=0.8\overline{7}$. Multiplying both sides of this equation by 10, we have $10x=8.\overline{7}$. Subtracting the left side of this equation from the right side, we have $10x-x=8.\overline{7}-0.8\overline{7}$. Simplifying, we have $9x=8$. Dividing both sides of this equation by 9, we have $x=\dfrac{8}{9}$. Therefore, $\dfrac{0.8\overline{7}}{1}=\boxed{\dfrac{8}{9}}$.