$\text{a)}$

  $x=0,363636\dots$   

$100x=36,363636\dots$

$100x-x=36$

$99x=36$

$x=\frac{36}{99}$

$x=\frac{12}{33}$  

$x=\frac{4}{11}$  

---

$\text{b)}$

$x=3,727272\dots$

$100x=372,727272\dots$

$100x-x=369$

$99x=369$

$x=\frac{369}{99}$

$x=\frac{123}{33}$

$x=\frac{41}{11}$  

$x=3\frac{8}{11}$   

---

$\text{c)}$

$x=-6,242424\dots$

$100x=-624,242424\dots$

$100x-x=-624,242424\dots -\left(-6,242424\dots \right)$

$99x=-624,242424\dots +6,242424\dots$

$99x=-618$

$x=-\frac{618}{99}$

$x=-\frac{206}{33}$  

$x=-6\frac{8}{33}$  

---

$\text{d)}$

$x=0,99999\dots$

$10x=9,99999\dots$

$10x-x=9$

$9x=9$

$x=1$

---

$\text{e)}$

$x=41,79999\dots$

$10x=417,99999\dots$

$10x-x=417,9999\dots -41,7999$

$9x=376,2$

$x=\frac{376,2}{9}$

$x=\frac{3762}{90}$  

$x=\frac{1254}{30}$  

$x=\frac{209}{5}$  

$x=41\frac{4}{5}$