I have a numeric field in my Oracle database that represents the number of days since Dec 28, 1800. However I am trying to select it (for another application) as the current
Firstly, get this out of the way, your life would be easier if you stored dates in a date data-type.
However, to answer your question to add days to a date in Oracle you can use the +
operator.
Firstly though you have to have a date so I'll convert the 28th December 1800 into a date using to inbuilt to_date function then add the number. In your case you would want:
select to_date('1800/12/28','yyyy/mm/dd') + 77650 from dual
I've set up a little SQL Fiddle to demonstrate for you.