Question

How do you convert 0.0005 (5 repeating) to a fraction?

Answer 1

`0.000bar(5) = 1/1800`

Explanation:

Using the notation of a bar over a digit or set of digits to denote them repeating indefinitely:

Let `x = 0.000bar(5)`

`=> 10x = 0.005bar(5)`

`=> 10x - x = 0.005bar(5)-0.000bar(5)`

`=> 9x = 0.005 = 5/1000 = 1/200`

`:. x = 1/200*1/9 = 1/1800`