If you want to see the question for this answer, go back to the post on 6/5/10. (Of course, you could treat it like "Jeopardy" and come up with our own question that fits this answer.
I was using the 1900 US Federal Census. The reason I could get that specific about my ancestor’s birth date is that during that census, the month and year of birth was asked for each person recorded on the census. This was the only census year that age can be determined with that preciseness...at least for adults. Children born within a year of the effective date of the census have their ages typically reported in twelfths. That, of course, gives us their year and month of birth also.