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By trapping two different ions in the same Penning trap at the same time, we simultaneously measured the ratio of their cyclotron frequencies (from which we obtain their atomic mass ratio) with a precision of about 10-11 in only a few hours. In order to perform these comparisons, we must be able to measure and control all three normal modes of motion of each ion - cyclotron, axial, and magnetron. We have developed novel techniques to do, so and we are currently using these tools to carefully investigate the important question of systematic errors in those measurements. This new technique shows promise to expand the precision of mass spectrometry an order of magnitude beyond the current state-of-the-art.