Question

find out thefraction which is equivalent to 0.033636363.....

Answer 1

x=0.03363636......................     -------------eq.1
since periodicity is 2 
multiply the both sides of eq.1 with 100
100x=3.363636....................     -------------eq.2

eq.2-eq.i
    100x=3.363636.................
          x=0.033636.................
(-)_____________________
      99x=3.330000.................
⇒x=3.33/99
⇒x=333/9900
⇒x=111/3300

Answer 2

Let x = 0.03363636363636.................. eq.1

Multiplying both sides by 100

100 x = 3.363636336363636................ eq.2

Multiplying both sides by 100

10000 x = 336.363636363636................ eq.3

Now subtracting eq.2 from eq. 3,
10000x - 100x = 336.3636..... - 3.3636.....
9900x =333
x = 333/9900
= 111/3300

Hope this helped you.....................