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How can I modify the numbering of Figures in different sections so they will be labelled 1.1, 1.2 etc in Section 1 and 2.1, 2.2 etc in Section 2?

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There's a package for that. Add to your preamble:

\usepackage{chngcntr}
\counterwithin{figure}{section}

You also have the command counterwithin*{figure}{section}, which resets the figure counter at a new section, but does not prepend the section counter to \thefigure.

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