What is 0.121212 expressed as the quotient of two integers in simplest form?

4/33

the way i do it, is i want 12 to be recurring, so i do 12/100, then i take away one from the denominator, so i get 12/99 = 0.121212

similarly, if i wanted 0.123123123, 

i could do 123/1000 then take away one from the denominator to get 123/999 and that should give us 0.123123123123