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what is more dense, liquid water or water ice?

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Simple answer: Ice is less dense than liquid water. This is why ice floats on top of water. 
Density=mass/volume, or in less scientific terms, density describes how many molecules of something can fit in a particular space. 
Most liquids are more dense than their frozen versions, but water is a rare and important exception. Water molecules like to arrange themselves in a very specific position as they cool down, and because of this, the molecules are highly ordered and spread out. This means that all of the molecules that fit in a water bottle will expand and take up more space as they freeze. 
Because of this, lakes and oceans do not freeze solid in the winter, allowing fish and sea creatures to survive. Instead, low density blocks of ice float to the surface as they form, leaving the "heavy" liquid water at the bottom. Without this, life on Earth would not be possible. 
Opposite of water are certain forms of alcohol. Frozen cubes of alcohol are more dense than liquid alcohol, and will sink to the bottom. This is a common demonstration in college chemistry classrooms. 
Feel free to comment if you would like more specific information about how the geometry and bond angles of water molecules can cause this phenomenon.