13/36=0.361111111 how would i reverse a decimal back to a fraction

Question

amoodarya · Answer

a=0.36111111111111...

100a =36.11111111111....
1000a =361.1111111111....

subtract 1000a-100a=361.1111111...-36.111111...=325
so a=325/900
then simplify that

anonymous · Answer

why is it over 900 though i dont understand

anonymous · Answer

because im trying to get 0.36111111111... back to 13/36

unklerhaukus · Answer

$$x=0.361111111$$
$$9x=0.361111111\times 9$$$$=0.3\times9+0.06\times9+0.00\dot1$$$$=2.7+0.54+0.00\dot9$$$$=2.7+0.54+0.01$$
$$9x=2.7+0.55$$$$\quad=3.25$$$$x=3.25/9$$$$x=\frac{3+1/4}9$$

unklerhaukus · Answer

$$x=\frac{13/4}9$$

amoodarya · Answer

if you simplify the 325/900=13/36

anonymous · Answer

where did u get the 900 from is what im stuck at

unklerhaukus · Answer

1000a-100a=900a

anonymous · Answer

what is the fastest way to simplyfly 325/900

unklerhaukus · Answer

cancel the common factor of 25