Set ticks precision with pgfplotsset [closed]

Question

First, this forum has been a great resource for me for some time now. I recently started using pgfplots and tikz, so some things I still need to figure out. I hope my question will be clear and the MWE is ok...

I export my plots from Matlab using matlab2tikz. Some of my data happens to be in a range as shown, where standard precision on the ticklabels is not sufficient to distinguish them (everything is labeled as "1" on the y-axis). I can do the format change manually in each plot, but I really would rather do it using \pgfplotsset before my actual tikzpictures begin. What should I add to the \pgfplotsset command to achieve this?

\documentclass{article}
\usepackage{tikz,pgfplots}

\begin{document}
    \pgfplotsset{%
    every axis plot post/.append style={line width = 2pt}}


\begin{tikzpicture}
\begin{axis}
[title=Trying to set precision with pgfplotsset]
\addplot +[domain=0:1] {(x+rnd)/4000+1};
\end{axis}
\end{tikzpicture}%

\begin{tikzpicture}
\begin{axis}[
title=Precision set manually inside tikzpicture,
    /pgf/number format/.cd,
    fixed,precision=4]
\addplot +[domain=0:1] {(x+rnd)/4000+1};
\end{axis}
\end{tikzpicture}

\end{document}