Ten sixteenths:

1. Andrew Johnson (sixteenth Vice President of the United States)
2. Π (sixteenth letter of the greek alphabet)
3. Samuel Chatto (sixteenth in line of succession to the British Throne)
4. Tennessee (sixteenth U.S. state admitted to the Union)
5. Agostino Depretis (sixteenth Prime Minister of Italy)
6. Cardinal Health, Inc. (sixteenth largest publicly traded U.S. company, measured by gross revenue)
7. Timothy I (sixteenth Patriarch of the Orthodox Church of Constantinople)
8. Gemini 10 (sixteenth U.S. spaceflight)
9. Michael Tovy (sixteenth Lord Mayor of London)
10. Grace (sixteenth most common girl's name for babies born in 2001)