for repeating decimal 0.333... let x = 0.333... (1)
multiply x with 10^n where n=number of unduplicated repeating digit. in this case only 1 digit which is 3 so we multiply with 10^1 or 10 so 10x = 3.333... (2)
now (2)-(1). 10x - x = 3.333... - 0.333... 9x = 3 x = 3/9 = 1/3 this is the fraction of 0.333...