1
general::
To the utmost, as in They'd decked out the house to the nth degree. This expression comes from mathematics, where to the nth means "to any required power" (n standing for any number). It was first recorded in 1852.
American Heritage Idioms
2
general::
Phrase(s): to the nth degree
to the maximum amount. • Jane is a perfectionist and tries to be careful to the nth degree. • This scientific instrument is accurate to the nth degree.
McGrawhill's American Idioms And Phrasal Verbs