A ketone is a functional group with the general formula R-CO-R', where R and R' are alkyl or aryl groups. The simplest ketone would have the smallest possible alkyl groups, which are methyl groups \((CH_3).\)
Thus, the simplest ketone is acetone (propanone), with the structural formula \(CH_3-CO-CH_3\).
(1) \(CH_3-O-CH_3 \)is dimethyl ether (an ether)
(2) \(CH_3-NH_2 \)is methylamine (an amine)
(3) \(CH_3-CO-CH_3 \)is propanone (acetone), the simplest ketone
(4) \(CH_3-COOH\) (corrected to CH3-CO-OH here) would be acetic acid, but \(CH_3-C-OH \)in the way its written doesn't work
Thus, the correct option is (3). Final Answer: The final answer is $\boxed{CH3—C—CH3}$