Formal notation for representing decimal numbers

Question

What is the formal mathematical notation for representing a decimal number using variables as it's digits?

I am honestly surprised that this has not been asked yet on MSE. Let me clarify a little using an example. Consider the $3$ digit decimal number $123$. Say I have $3$ variables for each of the decimal places $a,b,c$ such that $$a=1$$ $$b=2$$ $$c=3$$ I know that I can represent the number using $$a\times 100+b\times 10 + c$$ But this is too tedious. All I want to know is if there is any shorthand notation developed specifically for this purpose.
I have faint memory of using some notation for this exactly ONCE in my life but I think my memory is playing tricks on me. Does anybody actually remember some notation?
Thanks

---

Note

Not to be misunderstood as asking for notations of summations, et cetera. I am asking for specific purpose notation only.

Answer 1

I have seen $\overline {abc}$ used by some people on this site. Others will just write $abc$ and state that it means concatenating the digits instead of multiplication. Usually it is clear what problems want it that way.

Answer 2

For integers, it is $$n = \sum_{m=0}^k a_m10^m $$

where $n$ is the whole number, $k$ is the number of digits and $a_m$ gives the value of the digit at position $m$ (as it varies from $0$ to $k-1$).

For real numbers, there are subtleties having to do with duplicate representations of numbers like $0.5 = 0.4999999\ldots$ but the idea is the same.

Answer 3

Alternatively, I have found another less convenient but formally correct symbol
$$100a+10b+c=a\|b\|c$$ This of course is also usable on numbers $$123=1\|2\|3$$ The "$\|$" (represented by \| in $L^AT_EX$) operation is called concatenation (as mentioned by @GitGud and @RossMillikan).
More can be read about this operation here