10. Given the function
$$
f(x)=\left\{\begin{array}{ll}
x, & x \text { is irrational; } \\
\frac{q+1}{p}, & x=\frac{q}{p}\left(p, q \in \mathbf{Z}_{+},(p, q)=1, p>q\right) .
\end{array}\right.
$$

Then the maximum value of the function $f(x)$ in the interval $\left(\frac{7}{8}, \frac{8}{9}\right)$ is . $\qquad$