Significant numbers of $2900 \pm 100$ is 2. How to generalize derivation of significant figures?

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Significant figures with a plus-minus
$2900 \pm 100$

I would calculate:
100 -> #1 minimum sigfig
and then increase that with 1, because otherwise 29 will not fit
-> #1 + #1 = #2.

But is the answer given as
$\log_{10}(\frac{2900}{2\cdot 100}) \approx 1.16$

also correct and meaningfull? And why?