Answer: Option C
$$\eqalign{
& = \frac{{1 + \sqrt {0.01} }}{{1 - \sqrt {0.1} }} \cr
& = \frac{{1 + 0.1}}{{1 - 0.316}} \cr
& = \frac{{1.1}}{{0.684}} \cr
& = \frac{{1100}}{{684}} \cr
& = 1.6 \cr
& \,\,\,\,\,\,\,3|\overline 0 \,.\,\overline {10} \,\,\overline {00} \,\,\overline {00} \,(0.316 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,9 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& \,\,\,61|\,\,\,\,\,\,\,\,\,\,100 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,61 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - - \cr
& 626\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,3900 \cr
& \,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,3756 \cr
& \,\,\,\,\,\,\,\,\,\,| - - - - - - - \cr} $$