Question

How do you convert `0.bar5` (5 repeating) as a fraction?

Answer 1

`5/9`

Explanation:

Require to make 2 equations with the same repeating part and subtract them to eliminate the repeating part.

begin by letting x = 0.5555555................. (1)

To obtain the same repeating part after the decimal point need to multiply by 10

hence 10x = 5.555555........................(2)

It is important to obtain 2 equations in x, where the recurring part after the decimal points are exactly the same.

now subtract (1) from (2) to obtain fraction

(2) - (1) : `9x = 5 rArr x = 5/9`