  For cluster algebras from surfaces, there is a known formula for cluster
variables and F-polynomials in terms of the perfect matchings of snake graphs.
If the cluster algebra has trivial coefficients, there is also a known formula
for cluster variables in terms of continued fractions. In this paper, we extend
this result to cluster algebras with principal coefficients by producing a
formula for the F-polynomials in terms of continued fractions.
