Question

Express the following in the form p/q, where p and q are integers and q ≠ 0.

`0.4bar7`

Answer 1

`0.4bar7`

`"Let "x = 0.4bar7 = 4.7777` ....................(1)

Multiplying both sides by 10 (since one digit is repeating),

we get 10x = 4.7777 ..........................(2)

(2) - (1)

⇒ 10x - x = 4.3

⇒ 9x = 4.3

`⇒ x = (4.3/9) = 43/90`

`"Thus, " 0.4bar7=43/90`

Here p = 43, q = 90(≠0)