We report an experimental measurement of a light wavelength at which the ac electric polarizability equals zero for 87Rb atoms in the F=2 ground hyperfine state. The experiment uses a condensate interferometer both to find this tune-out wavelength and to accurately determine the light polarization for it. The wavelength lies between the D1 and D2 spectral lines at 790.03235(3) nm. The measurement is sensitive to the tensor contribution to the polarizability, which has been removed so that the reported value is the zero of the scalar polarizability. The precision is fifty times better than previous tune-out wavelength measurements. Our result can be used to determine the ratio of matrix elements |<5P3/2||d||5S1/2>/<5P1/2||d||5S1/2>|^2 = 1.99219(3), a 100-fold improvement over previous experimental values. Both the tune-out wavelength and matrix element ratio are consistent with theoretical calculations, with uncertainty estimates for the theory about an order of magnitude larger than the experimental precision.
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