  In this paper, we introduce a rational $\tau$ invariant for rationally
null-homologous knots in contact 3-manifolds with nontrivial
Ozsv\'{a}th-Szab\'{o} contact invariants. Such an invariant is an upper bound
for the sum of rational Thurston-Bennequin invariant and the rational rotation
number of the Legendrian representatives of the knot. In the special case of
Floer simple knots in L-spaces, we can compute the rational $\tau$ invariants
by correction terms.
