Question

Express `0.bar(4)` as a rational number in simplest form.

Answer 1

Let x be `0.bar(4)`

`x = 0.bar(4)`   ...(1)

Multiplying both sides by 10, we get

`10x = 4.bar(4)`   ...(2)

Subtracting (1) from (2), we get

`10x - x = 4.bar(4) = 0.bar(4)`

⇒ 9x = 4

⇒ `x = 4/9`

Thus, simplest form of `0.bar(4)` as a rational number is `4/9`.