If you want to know "why", you need to know how to solve it.
Write:
(Equation 1) x = 0.151515...
Multiply that by 100 (the factor 100, a one followed by two zeros, is chosen because the repetition occurs every two digits):
(Equation 2) 100 x = 15.151515...
Subtract equation 1 from equation 2, and solve the resulting equation for "x". That will give you the number as a fraction.
.015 as a fraction is 15/1000. In simplified form it is 3/200.
0.78 repeating as a fraction = 78/99
If you mean: 0.151515.....repeating then as a fraction it is 5/33
What is 1.49 repeating (9 is repeating)
0.54 repeating as a fraction = 54/99 or 6/11
0.13333333 repeating in fraction = 12/90 or 2/15
The fraction for .4 repeating is 2/5.
As a fraction it is 193/990 = .1'94' repeating '94'
If you mean: 0.181818.....18 repeating then as a fraction it is 2/11
It is: 53/99It is: 0.5333 ... repeating = 8/15 as a fraction
The fraction of the repeating decimal 0.7... is 7/9
If all 3 digits are repeating then as a fraction it is 215/999