Answer
$d\approx0.601
\text{ units}
$
Work Step by Step
Using $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ or the Distance Formula, the distance, $d$, between the given points, $\left(
\dfrac{1}{2}, \dfrac{1}{3}
\right) \text{ and } \left(
\dfrac{5}{6}, -\dfrac{1}{6}
\right),$ is
\begin{array}{l}\require{cancel}
d=\sqrt{ \left(\dfrac{1}{2}-\dfrac{5}{6} \right)^2+\left(\dfrac{1}{3}-\left(-\dfrac{1}{6}\right) \right)^2}
\\\\
d=\sqrt{ \left( -\dfrac{1}{3} \right)^2+\left(\dfrac{1}{2}\right)^2}
\\\\
d=\sqrt{ \dfrac{1}{9}+\dfrac{1}{4}}
\\\\
d=\sqrt{ \dfrac{13}{36}}
\\\\
d= \dfrac{\sqrt{13}}{6}
\\\\
d\approx0.601
\text{ units}
.\end{array}