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Using a data set corresponding to an integrated luminosity of 6.32 fb−1 recorded by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV, an amplitude analysis of the decay D+s → π+π0π0 is performed, and the relative fractions and phases of different intermediate processes are determined. The absolute branching fraction of the decay D+s → π+π0π0 is measured to be (0.50 ± 0.04stat ± 0.02syst)%. Theabsolute branching fraction of the intermediate process D+s → f0(980)π+, f0(980) → π0π0 is determined to be (0.28 ± 0.04stat ± 0.04syst)%.