Question

How do you convert -5.7 (7 repeating) as a fraction?

Answer 1

`a=5 7/9`

Explanation:

Let the required number be `a =- 5.dot7` .....(1)
Multiply both sides with `10`, as there is one repeating digit therefore multiply with `10^1`
`10a = -57.dot 7` .....(2)

Subtracting (1) from (2)

`10a - a = -57.dot 7 - (-5. dot7)`
`=>9a = -57.dot 7 +5. dot7`

or `9a = -52`

Solving for the required fraction
`a = 52/9=5 7/9`