Final answer:
9-fluorenone is more soluble in water than in methylene chloride.
Step-by-step explanation:
9-fluorenone is a polar molecule due to the presence of a carbonyl group which creates a dipole moment. Consequently, it will be more soluble in water, a polar solvent, than in methylene chloride, which is a non-polar solvent. This is because the polar nature of water allows it to form hydrogen bonds with the carbonyl group, increasing solubility.