I was learning Santa Lucia when I came across a Fermata (bird's eye) over a whole rest. I wasn't sure how to play it. Is it that we have to rest for a little more time, like an eighth/sixteenth more?
It looks something like this:
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There's no specified extra length for a fermata, so it will depend on the mood of the piece (and that of the performer!), and that can vary from performance to performance.10-20% longer would be about right. I've seen it exactly as you show, at the end of a piece, on a rest, and thought that in this case it could be a very long fermata! It's probably not actually like that, though?
I'd read that as the composer wanted you to really make that pause important. So take your time with it, especially if it's in between two very different feeling parts of the piece. (Fast to Slow section, major to minor, etc) Since there really isn't an official length to hold a rest with a fermata do what feels right.