Question

Express the following as a fraction.

`0.bar(39)`

Answer 1

To express the repeating decimal `0.bar(39)` as a fraction:

Step-by-step:

Let `x = 0.bar(39)`

Multiply both sides by 100 (since two digits repeat):

`100x = 39.bar(39)`

Now subtract the original equation:

`100x - x = 39.bar(39) - 0.bar(39)`

`99x = 39`

`x = 39/99`

Now simplify:

`39/99 = 13/33`