Combine two \tikzmark solutions

Question

I would like to combine the following two solutions provided in the question: How to draw arrows between parts of an equation to show the Math Distributive Property (Multiplication)?

1. https://tex.stackexchange.com/a/35721/10898 and
2. https://tex.stackexchange.com/a/61990/10898

The first is not reusable (at least I don't find a way to reuse several instances in one document since only one source can be defined.) The second is. What I am looking is to combine the \target command (this provides a north or south of the node in question, therefore directly targeting the character, like \target{x^2} as opposed to x\tikzmark{a}^2 or the sort.) and the second I can reuse in my example shown below:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node ({#1}) {};}
\tikzset{square arrow/.style={to path={-- ++(0,-.125) -| (\tikztotarget)}}}

\newcommand{\sn}[2]{\ensuremath{{#1}\times 10^{#2}}}
\begin{document}

    \begin{align*}
    \sn{23,900,00\tikzmark{b}0.\tikzmark{a}}{0} &= \sn{2,390,00\tikzmark{d}0.\tikzmark{c}0}{1}\\
                                                &= \sn{239,000}{2}\\
                        &= \sn{23,900}{3}\\
                        &= \sn{2,390}{4}\\
                        &= \sn{239}{5}\\
                        &= \sn{23.9}{6}\\
                        &= \sn{2.39}{7}
\tikz[overlay,remember picture] {\draw[->,square arrow] (a.south) to (b.south);}
\tikz[overlay,remember picture] {\draw[->,square arrow] (c.south) to (d.south);}
    \end{align*}
\end{document}

This yields:

Of course it is not a systematic (I welcome a systematic response.) way of doing it, but gets the job done. If the arrows could be set either as curves or as squares as they are, it is fine. If the arrows could be closer to the the targeted character that would be fine as well. What I want to achieve is something like the following:

Answer 1

It seems that you just need to tweak the points slightly to get the desired results which can be done using the tikz calc library. I have also defined a macro, \DrawArrow that has an optional first parameter to control the line style. Now you can produce both the square arrow, or curved arrows, with just changing the options to \DrawArrow:

Also shown is a version that uses \, to insert a small space for the thousands separator instead of a comma.

Notes:

• I have defined two tweaks \PeriodAdjust and \DigitAdjust which are used to slightly move the two points, which is the simplest way to do this. An alternative is to let tikz compute the appropriate widths but not sure it would be worth the effort.
• As per egreg's suggestion I used {,} for the commas so that additional space is not inserted.

Code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}
\newcommand{\PeriodAdjust}{0,0.60ex}%
\newcommand{\DigitAdjust}{-0.15em,0.60ex}%
\newcommand{\DrawArrow}[3][]{%
    \tikz[overlay,remember picture] {\draw[->,square arrow, thick, #1] 
        ($(#2.south)+(\DigitAdjust)$) to ($(#3.south)+(\PeriodAdjust)$);}
}
\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node ({#1}) {};}
\tikzset{square arrow/.style={to path={-- ++(0,-.125) -| (\tikztotarget)}}}
\newcommand{\sn}[2]{\ensuremath{{#1}\times 10^{#2}}}
\begin{document}
    \begin{align}
    \sn{23{,}900{,}00\tikzmark{b}0.\tikzmark{a}}{0} &= \sn{2{,}390{,}00\tikzmark{d}0.\tikzmark{c}0}{1}\
    \sn{23,900,00\tikzmark{f}0.\tikzmark{e}}{0} &= \sn{2,390,00\tikzmark{h}0.\tikzmark{g}0}{1}
    \end{align}
    \DrawArrow[blue]{a}{b}
    \DrawArrow[red, out=-110, in=-70, distance=0.19cm, shorten >= -0.1ex]{c}{d}
    \DrawArrow[orange]{e}{f}
    \DrawArrow[cyan, out=-110, in=-70, distance=0.19cm, shorten >= -0.1ex]{g}{h}
\end{document}