Question

how do we know that frozen water (ice) is less compact than liquid water? because ice floats in liquid water because ice sinks in liquid water

Explanation:

According to the principle of buoyancy, an object will float in a fluid if its density is less than that of the fluid. Since ice floats in liquid water, it implies that the density of ice (frozen water) is less than that of liquid water. Density is related to compactness (more density means more compact particles). So, ice being less dense (from floating) shows it is less compact.

Answer:

because ice floats in liquid water