How many digits does $x\in \mathbb{Z}$ have if it satisfies $|x|<10$ in base ten?

Question

So I recently got into an argument with someone about this. If $x\in\mathbb{Z}$ satisfies $|x|<10$ in base ten, how many digits does it have? My position is that we can't say for sure, it can have one or more, because for example $x=one=1=1.0=1.00=0.999...$ is an integer and it satisfies $|x|<10$. The other person says that in mathematics, insignificant digits are ignored. So $x$ is just 1, which is a single digit. Is he/she correct?