When using poppof’s rule, remember that the ketone group stays with that alkyl group which has les number of carbon atoms.
In the compound you’ve mentioned in the question, i.e CH3COCH(CH3)2 the ketone group (C=O) is surrounded on the two sides with two alkyl groups out of which one is Methyl and the other is Propyl (superficially). When oxidised with HNO3 the ketone group stays with methyl group and the propyl group separates out forming Ethanoic acid and Propanoic acid respectively. Also remember the fact that HNO3 oxidises ketones only at high temperaures.