Question

Express the following as a fraction.

`1.bar(42)`

Answer 1

To express `1.bar(42)` as a fraction:

Step-by-step:

Let `x = 1.bar(42)`

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

`100x = 142.bar(42)`

Now subtract the original equation:

`100x - x = 142.bar(42) - 1.bar(42)`

`99x = 141`

`x = 141/99`

Now simplify:

`141/99 = 47/33`