Tariq does not literally mean 1/16th. He means that people with very little Native American ancestry are considered Native American which means they are eligible for affirmative action. Native Americans have to be officially enrolled with their tribes. Some tribes, like the Seminoles, require members to have 1/4 or more Native American blood. Cherokees only require that you be a direct descendent of someone who was on the tribal roll during 1899-1906.
There was an adoption case that went before the Supreme Court. The bio-father, Dusten Brown, is Cherokee. He is 2% Native American and 98% white.