Good morning Dbg4thebest and Alan !
x = 2.01333... 10 x = 20.13333...
10x - x = 9 x 20.13333... - 2.01333 = 18.12
9x = 18.12 => 900x = 1812 => x = 1812 : 900 = 1812 / 900
x= $${\frac{{\mathtt{1\,812}}}{{\mathtt{900}}}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}} = {\mathtt{2.013\: \!333\: \!333\: \!333\: \!333\: \!3}}$$
$${\frac{{\mathtt{1\,812}}}{{\mathtt{900}}}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{151}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{75}}\right)}} = {\frac{{\mathtt{151}}}{{\mathtt{75}}}}$$
Gruß radix
!