1. If $\left[-\frac{1}{a}, a\right](a>0)$ contains exactly 10 integers, then the minimum value of $118 a-21+110 a-11$ is
$$
=1 . \frac{1}{9} \text {. }
$$

If $9 \leqslant a<10$, then
$$
|18 a-2|+|10 a-1|=28 a-3 \geqslant 249 ;
$$

If $\frac{1}{10}<a \leqslant \frac{1}{9}$, then
$$
|18 a-2|+|10 a-1|=1-8 a \geqslant \frac{1}{9} \text {. }
$$