Why doesn't the water level change when ice floating on it melts?

The floating ice exactly displaces the amount of water equal in weight to that of the ice. As the ice melts, its water replaces the exact same volume as the part that is underwater when it's floating. An example: You add a 100cc cube of ice to a jug of water which originally contained 900cc of water. Because ice is about 0.9 times the density of water, only 90cc of it will sink, and the water level in the jug goes to 990cc. The 100cc ice cube will melt to form 90cc of water, so the level in the jug stays the same, at 990cc.