How to align values in table according to the \pm and point?

Question

{
\renewcommand{\arraystretch}{1.3}
\begin{table}
\begin{tabular}{lc}
\hline\hline\noalign{\smallskip}
F&                      R         \\
\noalign{\smallskip}\hline\noalign{\smallskip}

42.34 \pd 0.16 & 42.34 \pd 0.16          \\
424.34 \pd 0.16          &   5542.34 \pd 50.16  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
21.9            &   20.8            \\
9.1             &   8.7             \\

\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table}
}

The code after your help:

{
\renewcommand{\arraystretch}{1.3}
\begin{table*}
\caption[]{Solution in \phoebe for different input photometry files, based on photometric data sets and Gaussian RVs for
the primary}\label{PHOEB}
\begin{flushleft}
\sisetup{separate-uncertainty}
\begin{tabular}{l*{6}S[table-format = 3.3(3)]}
\hline\hline\noalign{\smallskip}
Data&                       B.R         &   B.B         &   A            &  B            &  K + K    &  K + L +\\&&&&&&+ S \\
\noalign{\smallskip}\hline\noalign{\smallskip}

Co $ \chi^2$   &    3.758           &   1.721           &   76.945          &   1.008           &   11.389          &   4.067               \\
$b$                  &   42.34 \pd 0.16  &  41.63 \pd 0.37  &   41.56 \pd 0.47  &   40.71 \pd 0.21  &   41.91 \pd 0.18  &   41.81 \pd 0.43      \\
\noalign{\smallskip}\hline\noalign{\smallskip}
A           &   21.9            &   20.8            &   20.7            &   19.4            &   21.1            &   21.1                \\
B           &   9.1             &   8.7             &   8.6             &   8.1             &   8.8             &   8.8                 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
The rms errors of the last two quoted digits are given in brackets after the respective value. 
\end{flushleft}
\end{table*}
}

Answer 1

Using siunitx:

\documentclass{article}
\usepackage{siunitx}
\begin{document}
{
\renewcommand{\arraystretch}{1.3}
\begin{table}
\sisetup{separate-uncertainty}
\begin{tabular}{S[table-format = 3.2(3)]S[table-format = 4.2(4)]}
\hline\hline\noalign{\smallskip}
F&                      R         \\
\noalign{\smallskip}\hline\noalign{\smallskip}

42.34 \pm 0.16 & 42.34 \pm 0.16          \\
424.34 \pm 0.16          &   5542.34 \pm 50.16  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
21.9            &   20.8            \\
9.1             &   8.7             \\

\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table}
}
\end{document}

I took a liberty and add image of table produced with above code:

Answer 2

I would also use siunitx and exploit its option separate-uncertainty:

\documentclass{article}
\usepackage{siunitx}

\begin{document}
    \begin{table}
\renewcommand{\arraystretch}{1.3}
\sisetup{separate-uncertainty,
         group-four-digits}
\begin{tabular}{S[table-format = 3.2(3)]
                S[table-format = 4.2(4)]}
\hline\hline
F           & R                     \\
\hline
 42.34(16)  &   42.34(16)           \\
424.34(16)  & 5542.34(5016)         \\
\hline
21.9        &   20.8                \\
 9.1        &    8.7                \\
\hline
\end{tabular}
    \end{table}
\end{document}

which gives:

Addendum

It seems that you looking for something like this:

Above table is composed with two successive tables and manual tweaks for position of the column header. From comment of Barbara Beeton follows that this is somewhere already settled, but I didn't find this.

\documentclass{article}
\usepackage{siunitx}

\begin{document}
    \begin{table}
\renewcommand{\arraystretch}{1.3}
\sisetup{separate-uncertainty,
         table-column-width=6em}
\begin{tabular}{S[table-format = 3.2(3)]
                S[table-format = 4.2(4)]}
    \hline\hline
\hphantom{XX}F
            & \hphantom{XXx}R        \\
\hline
 42.34(16)  &   42.34(16)           \\
424.34(16)  & 5542.34(5016)         \\
    \hline
\end{tabular}\\
\begin{tabular}{S[table-format = 4.2]
                S[table-format = 5.2]}
21.9        &   20.8                \\
 9.1        &    8.7                \\
    \hline
\end{tabular}
    \end{table}
\end{document}

Answer 3

This may alternatively be done fairly simply using the dcolumn package, and then some spacing adjustments. The new column type defined here centers on the + but prints \pm:

\documentclass[11pt]{article}

\usepackage{dcolumn}

\begin{document}

\renewcommand{\arraystretch}{1.3}
\begin{table}
\newcolumntype{e}[1]{D{+}{\,\pm\,}{#1}} % see dcolumn documentation, page 2

\begin{tabular}{e{6.4}e{7.5}}
\hline\hline\noalign{\smallskip}
\multicolumn{1}{c}{F} &   \multicolumn{1}{c}{R} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
42.34+0.16  &   42.34+0.16   \\
424.34+0.16 & 5542.34+50.16  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
21.9            &   20.8      \\
9.1             &   8.7       \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table}

\end{document}

Some of the prior comments requested further centering of the heading and the decimal in the next rows. To cover the headings, one way is to make numbers in the newcolumn type symmetric, so that the \pm is in the center of the column. To deal with the decimal numbers below, we can add a phantom character to bring the decimal to the center of the column.

\renewcommand{\arraystretch}{1.3}
\begin{table}
\newcolumntype{e}[1]{D{+}{\,\pm\,}{#1}} % see dcolumn documentation, page 2

\begin{tabular}{e{6.6}e{7.7}} % These only need to be 6.4 and 7.5, but making the 6.6 and 7.7 (symmetric) centers F and R on pm.
\hline\hline\noalign{\smallskip}
\multicolumn{1}{c}{F} &   \multicolumn{1}{c}{R} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
42.34+0.16  &   42.34+0.16   \\
424.34+0.16 & 5542.34+50.16  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\multicolumn{1}{c}{21.9\phantom{9}}  &   \multicolumn{1}{c}{20.8\phantom{9}} \\ % <== add phantom character to make the decimal centered
\multicolumn{1}{c}{9.1}              &  \multicolumn{1}{c}{8.7}              \\% <== add phantom character to make the decimal centered
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\end{table}