According to Massie, Nicholas was 1/128th Russian, and his children 1/256 Russian. I tried calculating it myself on the basis that Peter the Great was 100% Russian and all his successors married foreigners, and it works.
Just for fun, I tried doing the same with George V and working out how much British blood he had. From a starting point that Edward IV was 100% English (he wasn't, but I needed a starting point), I got to fractions of 10,000ths and gave up.