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Objects float in a liquid or gas if they have a lower density, or a lower mass per unit of volume, than the liquid or gas itself.
The easiest example of an object floating is a piece of light wood in water. Water has a density of 1 gram per cubic centimeter. Balsa wood, in comparison, has a density of 0.1 to 0.2 gram per cubic centimeter, and thus it floats.
Another commonly seen example is that of a helium balloon. At sea level, air has a density of about 0.00129 grams per cubic centimeter - far less than that of water or balsa wood. But helium has a density of only about .0001785 grams per cubic centimeter, so a balloon filled with it will, even factoring in the weight of the balloon itself, float upward in the air. Air becomes thinner as altitude increases, though, so if the balloon doesn't pop first, it will stop rising at an altitude where the density of the air outside matches the density of the balloon.
Objects aren't the only things that can float, of course. A light oil will float in a layer on top of water.
If an object is hollow and contains air, it can float in water, as long as it weighs less than one gram per cubic centimeter overall. This realization enabled humanity to progress from rafts made of wood to ships made of metal and other non-floating materials. University engineering departments even hold races in canoes made of concrete! However, if a hollow ship springs a leak and fills with water, its overall density will be greater than that of water, and it will sink.
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