Is it possible to have multiple decimal points in a number?

Mathematical notation, like other aspects of human language, is a human creation - we decide what things mean. The system that is most commonly used at the moment is decimal notation:

• A "digit" is one of the following integers: $0,1,2,3,4,5,6,7,8,9$.

• If $a_n,\ldots,a_0$ and $b_1,\ldots,b_m$ are digits, and $a_n\neq 0$, then the expression $$\Large\color{red}{a_na_{n-1}\,\underset{\substack{\small\strut\,\uparrow\\\small\mathsf{ellipsis}}\,}{{\scriptsize\ldots}}\; a_1a_0\;\underset{\substack{\small\uparrow\,\strut\\\small\mathsf{decimal}\,\\ \small\mathsf{point}\,}}{.}\;b_1b_2\,\underset{\substack{\small\strut\,\uparrow\\\small\mathsf{ellipsis}}\,}{{\scriptsize\ldots}}\; b_m}$$ denotes the number $$a_n10^n+a_{n-1}10^{n-1}+\cdots+a_110+a_0+b_110^{-1}+\cdots+b_m10^{-m}$$

The purpose of the single decimal point in this notation (ignore the ellipses) is to clarify which parts of the expression correspond to the powers of $10$ where the exponent is $\geq 0$, and those where the exponent is $<0$.

In this system of notation, there is no meaning of adding a second decimal point. That is not to say that it is impossible to come up with a meaning - perhaps there is some usage in mathematics where a second decimal point would be a convenient and clear way of indicating something, and if there were, perhaps it would then be adopted as a part of our system of notation. But currently, it does not mean anything to write $1.1.2$.

I'm surprised no one has mentioned this yet.

The answer is Yes. Case in point: IP addresses. Example: 192.168.1.1

:)

Think about time in hours, minutes and seconds - 8:12:56 - that is a form which uses a double separator.

The point is not whether it can be done, but when it is useful and coherent to do it.