Question

The value of 1.999... in the form `p/q`, where p and q are integers and q ≠ 0, is ______.

Options

• `19/10`

• `1999/1000`

• 2

• `1/9`

Answer 1

The value of 1.999... in the form `p/q`, where p and q are integers and q ≠ 0, is 2.

Explanation:

Let x = 1.999...

Now, 10x = 19.999...

On subtracting equation (i) from equation (ii), we get

`10x - x = (19.999...) - (1.9999...)`

⇒ `9x = 18`

∴ `x = 18/9` = 2