How can I modify the \dfrac command to automatically display thousands separators?

In small math classes, students are asked to respect the thousand separators, like this:

This forces me to use the \num{} command from the siunitx package in each argument of the \dfrac command.

How can I define a new \dfrac command so that I don't have to do this and write \newfrac{1}{10000000} instead of \dfrac{1}{\num{10000000}}?

\documentclass{article}
\usepackage{mathtools}
\usepackage{siunitx}
\sisetup{locale=FR}

\begin{document}

\begin{multline*}
\num{0.27609390226}=\dfrac{2}{10}+\dfrac{7}{100}+\dfrac{6}{1000}+\dfrac{9}{100000}+\dfrac{3}{1000000}+\dfrac{9}{10000000}\\
+\dfrac{2}{1000000000}+\dfrac{2}{10000000000}+\dfrac{6}{100000000000}
\end{multline*}


\begin{multline*}
\num{0.27609390226}=\dfrac{2}{10}+\dfrac{7}{100}+\dfrac{6}{\num{1000}}+\dfrac{9}{\num{100000}}+\dfrac{3}{\num{1000000}}+\dfrac{9}{\num{10000000}}\\
+\dfrac{2}{\num{1000000000}}+\dfrac{2}{\num{10000000000}}+\dfrac{6}{\num{100000000000}}
\end{multline*}

\end{document}