Since the discovery of the metallic antiferromagnetic (AF) ground state near superconductivity in iron-pnictide superconductors, a central question has been whether magnetism in these materials arises from weakly correlated electrons, as in the case of spin-density-wave in pure chromium, requires strong electron correlations, or can even be described in terms of localized electrons such as the AF insulating state of copper oxides. Here we use inelastic neutron scattering to determine the absolute intensity of the magnetic excitations throughout the Brillouin zone in electron-doped superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K), which allows us to obtain the size of the fluctuating magnetic moment $<m^2>$, and its energy distribution. We find that superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ and AF BaFe$_2$As$_2$ both have fluctuating magnetic moments $<m^2>approx3.2 mu_B^2$ per Fe(Ni), which are similar to those found in the AF insulating copper oxides. The common theme in both classes of high temperature superconductors is that magnetic excitations have partly localized character, thus showing the importance of strong correlations for high temperature superconductivity.
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