Degree of dissociation of acetic acid at infinite dilution
As the dilution becomes infinite for the amount of acetic acid, then the acetic acid's contribution to the solution's acidity falls, and the pH of the water is controlled by the acid dissociation of water. So the pH falls to 7.00. Thus,

$$\begin{align}
\frac{(10^{-7})[\ce{CH3COO-}]}{[\ce{CH3COOH}]} &amp;= 1.85 \times 10^{-5} \\
[\ce{CH3COO-}] &amp;= 185 [\ce{CH3COOH}]
\end{align}$$

The fraction of unionised acid, $x$, is therefore given by

$$\begin{align}
x &amp;= \frac{[\ce{CH3COOH}]}{[\ce{CH3COOH}] + [\ce{CH3COO-}]} \\
&amp;= \frac{1}{1+185} \\
&amp;= 0.54\%.
\end{align}$$