The 1935 race laws defined 3 categorie of 'jews', 'full', 'half', and 'quarter'. Generally speaking they did not go further back than the grandparents, and their 'jewishness'.

Definitions:

Full Jew -- both parents jews.
Half Jew -- one parent jew, or 2 grandparents jews (not clear on wether these two had to be
married to each or not.)
Quarter Jew -- One grand parent jew.

The laws eliminated state approval for 'full' jews and non-jews. There were various permissions for half/quarter jews to marry non-jews, but after 1942 these were eliminated.

In the case of 'black', during the period of slavery, 1/16, 1/32, 1/64 'black' ancestry were used at various times to determine who was 'black', and therefore potentially subject to enslavement, property rights, or other legal states. There were of course free blacks in the Southern States, and some of these blacks are listed in census records of the era as being slave owners.

Back to Germany. One of the most interesting and of course almost unknown to most in the US is that in 1943 a group of 'halfjews' were arrested, mostly if not exculsively men. Their non-jewish wives, began a series of protests, usually standing outside of the building where the men were incarcerated, Rosen Strasse, and as the protest grew, Goebbels eventually relented and the men were freed. The theory is that the war was beginning to turn to the german disadvantage, and the thinking on the part of the german leadership was that this unrest could spread, as it involved 'non-jews', and further 'women', who had been propagandized into the minds of the german public as 'The Rock Bed of Civilization', and so the men, many of them survived the war.

The points to poinder here is had many people during the NSDAP period done similar, perhaps history would be different. The people in general did not, and so we have the example of a rise of a totalitarian state, which utlimately did evil even for the group it proclaimed to protect, but it was too late when the realization came to the general population.