$$\frac{2}{{2 + \frac{2}{{3 + \frac{2}{{3 + \frac{2}{3}}}}} \times 0.39}}$$     is simplified to = ?

$$\eqalign{ & {\text{According to question,}} \cr & \,\,\,\,\,\frac{2}{{2 + \frac{2}{{3 + \frac{2}{{3 + \frac{2}{3}}}}} \times 0.39}} \cr & = \frac{2}{{2 + \frac{2}{{3 + \frac{6}{{11}}}} \times 0.39}} \cr & = \frac{2}{{2 + \frac{{22}}{{39}} \times 0.39}} \cr & = \frac{2}{{2 + \frac{{22}}{{100}}}} \cr & = \frac{{200}}{{222}} \cr & = \frac{{100}}{{111}} \cr} $$