By employing the Gaussian decomposition method, the analytical formulas of the Gaussian-beam Z-scan traces have been derived for an optically thin material exhibiting both refractive and absorptive parts of third-order nonlinearity, with Gaussian or hyperbolic secant squared laser pulses of femtosecond duration. The formulas have been verified experimentally with femtosecond-pulsed Z scans on a carbon disulfide and acetone solution of a chalcone derivative ( ${0.95\mathrm{C}}_{18}{\mathrm{H}}_{17}{\mathrm{ClO}}_4·{0.05\mathrm{C}}_{17}{\mathrm{H}}_{14}{\mathrm{Cl}}_2{\mathrm{O}}_3$ ). An efficient yet accurate analytical technique has been demonstrated for extracting both the nonlinear refraction coefficient and the nonlinear absorption coefficient from a single closed-aperture Z-scan trace.