Rewrite as a simplified fraction.

\[\large{2.\overline{8} = {?}}\]

Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

To write the repeating decimal $2.\overline{8}$ as a fraction, we can call it $x$ and subtract it from $10x$. This way, the repeating part of $x$ will cancel out and we will be left with a whole number: \begin{align*}

10x-x &= 28.\overline{8} - 2.\overline{8} \\
&= 26 \\
\end{align*}Since $10x-x=9x$ and $26=\frac{26}{1}$, we have $9x=\frac{26}{1}$. Dividing both sides by 9 gives $x=\boxed{\frac{26}{9}}$.

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