Question

Express the following decimal in the form `p/q`: `0.4bar7`

Answer 1

Let `x=0.4bar7`

`rArr10x=4+0.bar7`

Let `y=0.bar7=0.777....`

⇒ 10y = 7.777...

⇒ 10y = 7 + 0.777...

⇒ 10y = 7 + y

⇒ 10y - y = 7

⇒ 9y = 7

⇒ y = 7/9

`therefore0.bar7=7/9`

Therefore,

`rArr10x=4+7/9`

`rArr10x=(36+7)/9`

`rArr10x=43/9`

`rArrx=43/90`

Hence, `0.4bar7=43/90`