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I found the answer, simply using QQ and getting back to RR does the trick:

A = matrix([[27.6, 30.2], [3100, 6400], [250, 360]]);
B = vector([162 , 23610, 1623]);
C = A.augment(B, subdivide = True);
C.change_ring(QQ).rref().change_ring(RR);