  In this article, we investigate F-pure thresholds of polynomials that are
homogeneous under some N-grading, and have an isolated singularity at the
origin. We characterize these invariants in terms of the base p expansion of
the corresponding log canonical threshold. As an application, we are able to
make precise some bounds on the difference between F-pure and log canonical
thresholds established by Musta\c{t}\u{a} and the fourth author. We also
examine the set of primes for which the F-pure and log canonical threshold of a
polynomial must differ. Moreover, we obtain results in special cases on the ACC
conjecture for F-pure thresholds, and on the upper semi-continuity property for
the F-pure threshold function.
