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We study the relation between the metallicities of ionized and atomic gas in star-forming galaxies at z = 0-3 using the Evolution and Assembly of GaLaxies and their Environments (EAGLE) cosmological, hydrodynamical simulations. This is done by constructing a dense grid of sight lines through the simulated galaxies and obtaining the star formation rate- and H i column density-weighted metallicities, Z SFR and Z H I, for each sightline as proxies for the metallicities of ionized and atomic gas, respectively. We find Z SFR ≳ Z H I for almost all sight lines, with their difference generally increasing with decreasing metallicity. The stellar masses of galaxies do not have a significant effect on this trend, but the positions of the sight lines with respect to the galaxy centers play an important role: the difference between the two metallicities decreases when moving toward the galaxy centers, and saturates to a minimum value in the central regions of galaxies, irrespective of redshift and stellar mass. This implies that the mixing of the two gas phases is most efficient in the central regions of galaxies where sight lines generally have high column densities of H i. However, a high H i column density alone does not guarantee a small difference between the two metallicities. In galaxy outskirts, the inefficiency of the mixing of star-forming gas with H i seems to dominate over the dilution of heavy elements in H i through mixing with the pristine gas. We find good agreement between the available observational data and the Z SFR-Z H I relation predicted by the EAGLE simulations. Though, observed regions with a nuclear starburst mode of star formation appear not to follow the same relation.