How do genetic testing kits like the ones with Ancestry.com work?

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I understand it matches DNA from their database, and helps you meet your blood relative, but for it to be completely accurate wouldn’t every person have to use the kit for the data to be up to date?
Also, how do people have varying percentages of nationalities? Shouldn’t DNA % be a fraction of 2 because it goes like 1/2 then 1/4th, 1/8th and so on (because we have 2 sets of biological parents)

In: Biology