If I ask for a percentage with 2 significant figures, I mean something like $62\%$ or $77\%$, with no decimals.
But what about percentages below 10? Do I have to write them like $5.6\%$ ajust because with no decimals they would be one digit? What about $100\%$?
These percentages come not from measurements but from dividing integers (numbers of elements in a set that satisfy a property over the cardinal of the set). Does it make sense to use significant numbers in this context?
On
Percentages do not differ from "ordinary" values. In every case, you are deemed to know how many digits are significant (i.e. exact) and how many are useful for the application at hand.
Assume for instance that you are considering an increase of 1.2° from 20°, i.e. a ratio of 0.064. If your thermometer is inaccurate, the true ratio might be between, say 0.060 and 0.068, so you can settle for 6%. In a different case, it might make sense to keep three decimals !
I think the answer is "it depends".
In general, you should choose the level of precision that roughly matches the precision of the input and the kind of information you want to convey. In your case the numerator and denominator are counts, which you presumably know exactly.
If your denominator is $1000$ then one decimal place in the percentage is the exact answer but reporting only the integer part will be easier to read. If your denominator is $1,000,000$ then four decimal places will be exact but zero or one or two may best convey what you are trying to say. If your denominator is $10$ just report the count.
For more advice you could edit the question to provide more context.