Answer
\[-\frac{5}{6}=-0.8\overline{3}\,\,\text{and}\,\,-\frac{8}{9}=-0.\overline{8}\]
This shows that \[-\frac{5}{6}>-\frac{8}{9}\].
Work Step by Step
The rational number \[-\frac{5}{6}\] can be written in decimal form as follows:
\[-6\overset{-0.8333}{\overline{\left){\begin{align}
& 5.000 \\
& \underline{4\,\,8} \\
& \,\,\,\,20 \\
& \underline{\,\,\,\,18} \\
& \,\,\,\,\,\,20 \\
& \,\,\,\,\,\,\,\,\,\,. \\
& \,\,\,\,\,\,\,\,\,\,. \\
\end{align}}\right.}}\]
The rational number \[-\frac{8}{9}\] can be written in decimal form as follows:
\[-9\overset{-0.888}{\overline{\left){\begin{align}
& 8.000 \\
& \underline{7\,\,2} \\
& \,\,\,\,\,80 \\
& \,\,\,\,\,\,\,\,. \\
& \,\,\,\,\,\,\,\,. \\
\end{align}}\right.}}\]
Thus, the rational numbers in decimal form can be written as \[-\frac{5}{6}=-0.8\overline{3}\,\,\text{and}\,\,-\frac{8}{9}=-0.\overline{8}\]
This shows that \[-\frac{5}{6}>-\frac{8}{9}\].
