Fractional/rational form of $0.999...$

Question

Is it possible to express $0.999...$, a repeating number, as a fraction? Or as a ratio of two numbers?

Basically all (my) attempts at the problem cancels all the terms and returns $1$. Is it even possible? Or has it been proven to be an exercise of futility?

Answer 1

Yes, it can: $0.999999999999\ldots=\dfrac11$.

Answer 2

$$0.9999\dots= 3*0.3333\dots= 3 * \frac 1 3=1$$

Answer 3

Let $$x=0.99999\ldots ,$$ now $$10x=9.99999\ldots ,$$ then $$10x-x=9x=9\Rightarrow x=1.$$

Answer 4

0.9 lacks 1 by 0.1

0.99 lacks 1 by 0.01

0.999 lacks 1 by 0.001

0.9999 lacks 1 by 0.0001

0.9999.... lacks 1 by 0.0000...

Hence it is equal to 1