+118609 $$\begin{array}{rlll}
100*0.3636363636... =&36.363636...\\
1*0.363636..... =&\;\;0.36363636 \qquad \mbox{now subtract on both sides}\\
99*0.36363636=&36 \qquad \mbox{so}\\\\
0.36363636=&\frac{36}{99} \qquad \mbox{which can be simpified to}\\\\
0.36363636=&\frac{12}{33} \qquad \mbox{}\\
\end{array}$$
You can also do this as the sum of a GP
+118609 $$\begin{array}{rlll}
100*0.3636363636... =&36.363636...\\
1*0.363636..... =&\;\;0.36363636 \qquad \mbox{now subtract on both sides}\\
99*0.36363636=&36 \qquad \mbox{so}\\\\
0.36363636=&\frac{36}{99} \qquad \mbox{which can be simpified to}\\\\
0.36363636=&\frac{12}{33} \qquad \mbox{}\\
\end{array}$$
You can also do this as the sum of a GP
It can simplify dont to 4/11 because its repeating. Now ive seen an answer of 12/33 and it said it was in simplest form. I thought they could both be divivded by 3. so i got 4/11. Anyway If you check 4/11 on a calculator it should say, 0.3636363636... going on forever. I hoped this answer helped.
