The degrees of unsaturation for a hydrocarbon of formula $\mathrm{C_xH_y}$ is equal to $\dfrac{(2x+2-y)}{2}$. The addition of an oxygen atom does not change the number of degrees of unsaturation, so acetone has 1 degree of unsaturation. This is confirmed by looking at acetone's structure, which contains a double bond between the carbon and the oxygen. Reacting acetone with $\ce{H2}$ will result in 2-propanol according to the reduction reaction found here, and thus, 1 mole of hydrogen should be required to convert acetone into a saturated compound.
While acetone is not a saturated compound according to the aforementioned criteria found from this source, the degree of unsaturation comes from the carbon-oxygen bond, meaning that within some contexts, it is considered a saturated compound. According to the wikipedia article on saturated vs. unsaturated compounds, unsaturation only counts when it is the result of double or triple carbon-carbon bonds. All of the carbon-carbon bonds on the compound in acetone are saturatedsingle, andimplying that is probably what the teachers who said that this compound wasis saturated meantaccording to these criteria. Here
Either way, this is a link to learn more about degrees of unsaturationpoorly written question, and either answer should be considered acceptable.