\documentclass[a4paper]{article}

\usepackage{pgfplots}


\begin{document}

\parindent=0pt

\def\pretty[#1]#2{%
	\[ #2 \mapsto \pgfmathprintnumber[#1]{#2} \texttt{ [#1]}\]
}

\pretty[fixed relative]{0}
\pretty[fixed relative]{nan}
\pretty[fixed relative]{1.2345}
\pretty[fixed relative]{1000.2345}
\pretty[fixed relative]{0.000012345}
\pretty[fixed relative,precision=1]{0.000012345}
\pretty[fixed relative,precision=5]{1234.56}
\pretty[fixed relative,precision=5]{1000.50001234}
\pretty[fixed relative,precision=5]{0.000100050001234}
\end{document}

