# Number system practice

Express a recurring infinite decimal as a fraction

#### Explanatory Answer

Let x = 1.363636...
Thus, 100x = 136.3636...

#### Why 100x?

The objective is to arrive at an integer after subtracting the decimal component. The decimal part in x is 0.3636.... If we multiply 100 to x, the decimal part of 100x is also 0.3636...
Your choice of what to multiply x with will always be determined by the decimal component.
100x – x = 136.3636... - 1.363636...
99x = 135
x = $\frac{135}{99}$ = $\frac{15}{11}$