Question

Express `0.bar(23)` as a rational number in simplest form.

Answer 1

Let x be `0.bar(23)`

`x = 0.bar(23)`   ...(1)

Multiplying both sides by 100, we get

`100x = 23.bar(23)`   ...(2)

Subtracting (1) from (2), we get

`100x - x = 23.bar(23) - 0.bar(23)` 

⇒ 99x = 23

⇒ `x = 23/99`

Thus, simplest form of `0.bar(23)` as a rational number is `23/99`.