Q:

Notation for apply operation to digits of a number

what is the standard notation to represent that a operation has been applied to each digits of a number 
for example
let x = 81
it can be said the sum of each digit is equal to the square root of x

a representation of this would be
$$\sum  digits = x^\frac{1}{2} $$ 
however would the nth digits of the number x be represented

A:

You can say something like:
Let $\displaystyle x=\sum_{i\mathop=0}^n a_i \times 10^i$.
Then the sum of digits is $\displaystyle \sum_{i\mathop=0}^n a_i$

You can also define a "sum of digits" function recursively (for positive integer only):
$\text{sum_of_digits}(x)=\begin{cases}x \text{ , if } x<10\\ \text{sum_of_digits}(\left\lfloor\dfrac x{10}\right\rfloor)+10\left\{\dfrac{x}{10}\right\}\end{cases}\text{ , otherwise}$
where $\lfloor\cdot\rfloor$ is the floor function and $\{\cdot\}$ is the fractional part.

