2

I would like to be able to say X percent of something, but I haven't been able to find the particle that would correspond to of. Could you use の? 

For example:

人口の10パーセント (10 percent of population)?

4

Yes, I think you can say の here:

人口の10%
10% of the population

I think it would be more common to write % than パーセント, but either way.

As an aside, for even tenths I think you can use 割 instead:

人口の一割
a tenth of the population

Each 割 is one tenth.

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