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A millimetre of water weighs nothing, because a millimetre is a measurement in one dimension - a measurement of length. 3 dimensions are needed to describe a real quantity, with mass. A millilitre of water, on the other hand, equivalent to 1cm3, has a mass of exactly a gram. This is because the properties of water are among the principle constants upon which the metric system is based. A cubic millimetre of water has a mass of 0.001g.

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Q: How much does one millimeter of water weigh?
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