\[\left| \frac{17}{90} \right|\ :\left| - 1\frac{8}{9} \right| = \frac{17}{90}\ :\frac{17}{9} = \frac{17 \cdot 9}{90 \cdot 17} =\]
\[= \frac{9}{90} = \frac{1}{10} = 0,1.\]