documentclass[letterpaper,12pt]{article}

% things needed to include figures
usepackage{subfigure, graphicx}
% float must be included for the [H] to actually work
usepackage{float}
% formulas
usepackage{amsmath}
% Added to adjust captions
usepackage[singlelinecheck=false]{caption}
% added to adjust margins at the suggestion of Dr. Matt
usepackage[top=1in, bottom=1in, left=1in, right=1in]{geometry}
usepackage{fullpage}

begin{document}
% 2 column side by side table
begin{table}[H]
  subtable[Half-life for $^{108}$Ag] {%

    % -----------------------------------------------------%
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      142.92 & 158 $pm$ 7\
      hlinenoalign{smallskip}
    end{tabular}
    label{lefttable}
    % -----------------------------------------------------%

  }
  subtable[Half-life for $^{110}$Ag] {%

    % -----------------------------------------------------%
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      24.6 & 21 $pm$ 2\
      hlinenoalign{smallskip}
    end{tabular}
    label{righttable}
    % -----------------------------------------------------%

  }
  caption{2 Column tables side by side}
  label{sidebysidetable}
end{table}
end{document}

usepackage{caption}
      captionsetup[table]{justification=raggedright}
      captionsetup[subtable]{justification=raggedright}

usepackage{subcaption}

begin{table}[H]
  begin{subtable}[b]{0.48textwidth}
    % -----------------------------------------------------%
    caption{Half-life for $^{108}$Ag} label{lefttable}
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      142.92 & 158 $pm$ 7\
      hlinenoalign{smallskip}
    end{tabular}
    % -----------------------------------------------------%
  end{subtable}
  begin{subtable}[b]{0.48textwidth}
    % -----------------------------------------------------%
    caption{Half-life for $^{110}$Ag}     label{righttable}
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      24.6 & 21 $pm$ 2\
      hlinenoalign{smallskip}
    end{tabular}
    % -----------------------------------------------------%
  end{subtable}
  caption{2 Column tables side by side}
  label{sidebysidetable}
end{table}

caption{This table. hspace*{fill}}

documentclass[letterpaper,12pt]{article}
usepackage{caption, subcaption}
usepackage[top=1in, bottom=1in, left=1in, right=1in]{geometry}

begin{document}

begin{table}[H]
  begin{subtable}[b]{0.48textwidth}
    caption{Half-life for $^{108}$Ag hspace*{fill}} %NOTE
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      142.92 & 158 $pm$ 7\
      hlinenoalign{smallskip}
    end{tabular}
  end{subtable}
  begin{subtable}[b]{0.48textwidth}
    caption{Half-life for $^{110}$Ag hspace*{fill}} %NOTE
    begin{tabular}{c@{hskip 1cm} c}
      hlinenoalign{smallskip}
      Accepted $T_{1/2}$ & Experimental $T_{1/2}$\
      (s) & (s)\
      hlinenoalign{smallskip}
      24.6 & 21 $pm$ 2\
      hlinenoalign{smallskip}
    end{tabular}
  end{subtable}
  caption{2 Column tables side by side}
end{table}

end{document}