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When we say a% of b, we mean 'a' parts out of the 100 parts of 'b'.
e.g. 1% of 200 means divide 200 in 100 equal parts and select 1 out of it, i.e. 2

what does it mean when we say any percentage of any percentage?
like, what is the significance of 100% of 100%?

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divide 100% in 100 equal parts and select 100 out of it, i.e. 100%. – wildildildlife Jul 18 '12 at 11:08
up vote 3 down vote accepted

100 percent. percent=per hundred. 100% is 100 per 100=100/100=1. So 100% of 100% is 100% of 1, which is 1. 50% of 50% is 50% of .5, or half of 50%, which is .25, or 25%. You convert them to their numeric representation and multiply.

For contrast, there is the (less common) per mil, which is 1/1000. 1000 per mil = 100 per cent = 1. You're really working with decimal numbers the whole time, just with units of 1/100 or 1/1000.

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