Changing tabularx column alignment partway through table

Question

I have some very large and very small numbers being displayed in decimal notation (for a non-scientific audience). Normally—for small magnitude ranges—I would align on the decimal point with {r@{.}l}, but in this case I have to deal with about 20 orders of magnitude in the same table, so that becomes impractical. My real table has over twenty rows.

Currently all numbers can be right-aligned or left-aligned en-masse. I would like to right-align the positive powers (whole numbers), but left-align the negative powers (fractional numbers).

\begin{tabularx}{\textwidth}{>{\bfseries}clrX}
Name & Sci       & Decimal           & Notes \\
\hline
foo  & $10^{12}$ & 1 000 000 000 000 & Big number \\
bar  & $10^{5}$  &           100 000 & Fair size \\
\hline
baz  & $10^{-6}$ & 0.000 001         & Left-align these \\
qux  & $10^{-8}$ & 0.000 000 01      & numbers, please! \\
\end{tabularx}

I could do \multicolumn{1}{l}{0.000 0001} for each fractional number (or vice-versa for whole numbers)—and could perhaps even automate that I suppose—but as I haven't been at LaTeX very long[1], I'd like to learn the best practices before I start hacking.

The question, restated

1 000 000 Whole numbers align right
   10 000
      100
0.01
0.000 1
0.000 001 Fractional (decimal) numbers align left

As I admit this might be an X-Y problem, I'll accept any elegant answer that can produce the desired output. I'll also accept edits to the question to clear up anything confusing.

---

1. Only about 20 years. Funny this never came up.

Answer 1

You can exploit siunitx for easier input and define commands for left and right alignment:

\documentclass{article}
\usepackage{tabularx,siunitx}

\NewDocumentCommand\rnum{O{}m}{%
  \mbox{}\hspace{0pt plus 1filll}\num[#1]{#2}%
}
\NewDocumentCommand\lnum{O{}m}{%
  \num[#1]{#2}\hspace{0pt plus 1filll}\mbox{}%
}

\begin{document}

\noindent
\begin{tabularx}{\textwidth}{>{\bfseries}clcX}
Name & Sci       & Decimal           & Notes \\
\hline
foo  & $10^{12}$ & \rnum{1000000000000} & Big number \\
bar  & $10^{5}$  &        \rnum{100000} & Fair size \\
\hline
baz  & $10^{-6}$ & \lnum{0.000001}      & Left-align these \\
qux  & $10^{-8}$ & \lnum{0.00000001}    & numbers, please! \\
\end{tabularx}

\end{document}

Answer 2

You could use collcell to collect the content and test the value. (The "Decimal" is braced to avoid that it is tested too).

\documentclass{article}
\usepackage{tabularx}
\usepackage{siunitx}
\usepackage{collcell}


\ExplSyntaxOn
\newcolumntype{E}{>{\collectcell \my_is_braced_input:n }c<{\endcollectcell}}

\cs_new:Npn \my_align_numbers:n #1\scan_stop: 
 {
   \fp_compare:nTF { #1 < 1 }
    {\num{#1}\hfill\mbox{}}
    {\mbox{}\hfill\num{#1}}
 } 

\cs_new:Nn \my_is_braced_input:n 
 {
  \peek_catcode:NF \c_group_begin_token
  {\my_align_numbers:n}
  #1\scan_stop:
 }   
\ExplSyntaxOff

\sisetup{group-digits}
\begin{document}

\noindent
\begin{tabularx}{\textwidth}{>{\bfseries}clEX}
Name & Sci       & {Decimal} & Notes \\
\hline
foo  & $10^{12}$ & 1000000000000 & Big number \\
bar  & $10^{5}$  &        100000 & Fair size \\
\hline
baz  & $10^{-6}$ & 0.000001      & Left-align these \\
qux  & $10^{-8}$ & 0.00000001    & numbers, please! \\
\end{tabularx}

\end{document}