Effects of the centrality determination method for the equation of state and nucleonic observables from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Au</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Au</mml:mi> </mml:mrow> </mml:

Centrality determination remains one of the major sources of systematic uncertainty in intermediate-energy heavy-ion collision analyses, especially for probing the nuclear equation of state (EoS) at supra-saturation densities. To quantitatively assess the uncertainties associated with different centrality determination methods and to investigate their effects on final-state EoS-sensitive observables. Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, Au+Au collisions at $\sqrt{s_{NN}}$=2.4 GeV are performed within a soft and a hard EoS. Event centrality is determined using the multiplicity of all charged particles ($M_\mathrm{ch}$) and two impact parameter-based centrality filters, one based on a geometrical interpretation and the other based on the Glauber Monte Carlo (MC) model, denoted as $b_{f}$ and $b_{r}$, respectively. It is shown that there exist significant differences between the real impact parameter distributions of event samples selected by $M_\mathrm{ch}$, $b_{f}$, and $b_{r}$, particularly between $M_\mathrm{ch}$ and $b_{r}$. When the $b_{f}$ is employed, uncertainties associated with centrality selection have a weaker influence on observables than the effects induced by the EoS. In contrast, when the $b_{r}$ is used, the influence of centrality-related uncertainties becomes more pronounced than that of the EoS. These results demonstrate that a rigorous and consistent mapping between $M_\mathrm{ch}$ and impact parameter is essential to impose quantitative constraints on the high-density nuclear EoS. Furthermore, our study indicates that the geometrical interpretation of centrality remains valid and consistent with dynamical multiplicity selection, whereas the Glauber MC-based centrality determination becomes unreliable at the investigated energy.