[tex]\stackrel{\textit{converting to a rational}}{37.\underline{46}\implies \cfrac{3746}{1\underline{00}}}\implies \cfrac{1873}{50} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{37.46}{18}\implies \cfrac{~~ \frac{1873}{50}~~}{18}\implies \cfrac{~~ \frac{1873}{50}~~}{\frac{18}{1}}\implies \cfrac{1873}{50}\cdot \cfrac{1}{18} \\\\\\ \cfrac{1873}{900}\implies 2\frac{73}{900}\implies \stackrel{a~rep eating~decimal}{2.08\overline{1}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{converting to a rational}}{-37.\underline{46}\implies -\cfrac{3746}{1\underline{00}}}\implies -\cfrac{1873}{50} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{37.46}{18}\implies -\cfrac{~~ \frac{1873}{50}~~}{18}\implies -\cfrac{~~ \frac{1873}{50}~~}{\frac{18}{1}}\implies -\cfrac{1873}{50}\cdot \cfrac{1}{18} \\\\\\ -\cfrac{1873}{900}\implies -2\frac{73}{900}\implies \stackrel{a~rep eating~decimal}{-2.08\overline{1}}[/tex]
