  Ghys established the relationship between the bounded Euler class in
$H_{b}^{2}(\mathrm{Homeo}_{+}(S^{1});\mathbb{Z})$ and the Poincar\'{e} rotation
number, that is, he proved that the pullback of the bounded Euler class under a
homomorphism $\varphi \colon \mathbb{Z} \to \mathrm{Homeo}_{+}(S^{1})$
coincides with the Poincar\'{e} rotation number of $\varphi(1)$. In this paper,
we extend the above result to the symplectic group in some sense, and clarify
the relationship between the bounded Euler class in
$H_{b}^{2}(Sp(2n;\mathbb{R});\mathbb{Z})$ and the symplectic rotation number
investigated by Barge and Ghys.
