Question

Express the following as a fraction.

`0.bar(285)`

Answer 1

To express `0.bar(285)` as a fraction:

Step-by-step:

Let `x = 0.bar(285)`

Since 3 digits repeat, multiply both sides by 1000:

`1000x = 285.bar(285)`

Subtract the original:

`1000x - x = 285.bar(285) - 0.bar(285)`

`999x = 285`

`x = 285/999`

Now simplify:

Divide numerator and denominator by 3:

`285/999 = 95/333`