The actual cost of the fudge Anna purchases is \begin{align*} \frac{7}{9}\cdot 10 &= 0.\overline{7}\cdot 10\\ &= 7.\overline{7}\\ &= 7.777\ldots \end{align*}To round to the nearest hundredth, we must look at the thousandths place, which here is 7. Since 7 is greater than or equal to 5, we round the hundredths place, which in $ 7.\overline{7} $ is 7, up to 8. So, rounding $ 7.\overline{7} $ to the nearest hundredth yields $ \boxed{7.78} $ dollars.