\[\left| \frac{1}{6} - 0,16 \right| = \left| \frac{1}{6} - \frac{4}{25} \right| = \left| \frac{25}{150} - \frac{24}{150} \right| = \frac{1}{150}.\]
\[Ответ:\ \frac{1}{150}.\]