Adding to Kay's and Julie's comment, we also have to keep in mind that when it comes to the "dilution" of our autosomal DNA, we aren't testing the ancestor. At least, not usually.
So it's the number of intervening births that count, the number of chances for the DNA of two parents to recombine and comingle when they produce an offspring. That 0.39% number comes from a simple calculation called the Coefficient of Relationship. Theoretically, all your 6g-grandparents will contribute about that amount of DNA to yours. But research by population geneticist Graham Coop at the University of California Davis has shown that by your 6g-grandparents you have about a 17% chance of inheriting no DNA from any given one of them. By your 8g-grandparents, only about half of them will have contributed to your own DNA.
And it's 8 birth events from you to that 6g-grandparent. But since we test living or recently deceased individuals, that same 8 birth-event count takes you only as far as your 3rd cousins (who would be expected to share about 0.78% DNA with you, by the way...which is what you'd expect from a 5g-grandparent; but never mind; forget that part; WikiTree just counts generations for the cutoff number, not DNA dispersion). 
Two recent, really handy articles that can give you an idea of the probabilities of you sharing measurable DNA with cousins are by Amy Williams at Cornell University: "How often do two relatives share DNA?" and "How often do two half relatives share DNA?"
