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The microwave spectrum of the weakly-bound complex argon acetone was measured by Fourier transform microwave spectroscopy. A preliminary version of this work was reported at this conference in $1997a$. The torsional state splittings caused by the two internal methyl rotors varies from several kHz to tens of MHz. The spectra was analyzed using a modified iam $methodb$. More than 200 transitions were recorded between 6 GHz and 20 GHz. Additional fine splittings beyond those caused by the internal rotations have been observed. An approximate ``sum rule'' for the various torsional splittings was very helpful for the initial $assignmentsc$. The rotational constants for the complex are $A=4991.808(1),B=1442.432(1)$, and $C=1401.040(1)MHz$. The argon atom is above the C=O bond, perpendicular to the plane of the acetone, at a distance of $\sim 3.48$ {\AA}. The barrier to internal rotation $V3\sim 260cm-1$, is similar to that of acetone itself ($V3=266cm-1)d$.