  A simple systematic rule, inspired by high-temperature series expansion
(HTSE) results, is proposed for optimizing the expression for thermodynamic
observables of ferromagnets exhibiting critical behavior at $\Tc$. This
``extended scaling'' scheme leads to a protocol for the choice of scaling
variables, $\tau=(T-\Tc)/T$ or $(T^2 - \Tc^2)/T^2$ depending on the observable
instead of $(T-\Tc)/\Tc$, and more importantly to temperature dependent
non-critical prefactors for each observable. The rule corresponds to scaling of
the leading of the reduced susceptibility above $\Tc$ as $\chi_{\rm
c}^{*}(T)\sim \tau^{-\gamma}$ in agreement with standard practice with scaling
variable $\tau$, and for the leading term of the second-moment correlation
length as $\xi_{\rm c}^{*}(T)\sim T^{-1/2}\tau^{-\nu}$. For the specific heat
in bipartite lattices the rule gives $C_{\rm c}^{*}(T) \sim T^{-2}[(T^2
-\Tc^2)/T^2]^{-\alpha}$. The latter two expressions are not standard. The
scheme can allow for confluent and non-critical correction terms. A stringent
test of the extended scaling is made through analyses of high precision
numerical and HTSE data, or {\it real} data, on the three-dimensional canonical
Ising, XY, and Heisenberg ferromagnets.
