\(A=1,\left(35\right)-\frac{0,1\left(35\right)}{2,2}\)
\(\Rightarrow10A=13,\left(53\right)-\frac{1,\left(35\right)}{2,2}\)
\(\Rightarrow10A=13+0,\left(53\right)-\frac{1+0,\left(35\right)}{2,2}\)
\(\Rightarrow10A=13+\frac{53}{99}-\frac{1+\frac{53}{99}}{2,2}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{\frac{152}{99}}{2,2}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.2,2}{99}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.22:10}{99}\)
\(\Rightarrow10A=\frac{1340}{99}-\frac{152.2:10}{9}\)
\(\Rightarrow10A=\frac{1340-304}{9.10}\)
\(\Rightarrow10A=\frac{1036}{90}\)\(\Rightarrow A=\frac{1036}{900}=\frac{259}{225}\)
