Question

How do you convert `0.bar(45)` (meaning the `45` is being repeated) to a fraction?

Answer 1

`0.45454545.............=5/11`

Explanation:

Let `x=0.45454545.............` ............................(1)

then `100x=45.45454545............` ............................(2)

subtracting (1) from (2) we get

`99x=45`

or `x=45/99=5/11`

Hence `0.45454545.............=5/11`

Answer 2

`5/11`

Explanation:

When two numbers in a decimal sequence repeat forever, the denominator will be `11`.

To think about the numerator, let's just take the number `45`.

This number would round to `50` or `5` tens. Whatever number of tens the numerator rounds to, this will be our numerator.

Thus, we have

`5/11`

Hope this helps!