To find the greatest decimal, compare place values from left to right: ones, tenths, hundredths.

Numbers	=	0.990, 9.099, 9.900, 9.090
Compare ones: 0, 9, 9, 9. 9 is greater. Among 9.099, 9.900, and 9.090, compare tenths: 0, 9, 0. 9 is greatest. So 9.9 is the greatest.
Greatest	=	9.9