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The meaning of the original statement is that if you have a cubic meter of water (an amount of water that is one meter in height, one meter in width, and one meter in depth), that amount of water would weigh 1000 kilograms.
The way to convert kilograms per cubic meter to grams per cubic centimeter is by using the following formula:
1 kilogram per cubic meter = .001 grams per cubic centimeter
So to find the actual answer, you could set up the equation
1000 = x/.001
So then you multiply both sides by .001
This gets you x = 1
So water has the density of 1g/cm^3
By density 1000kg/ m^3 you mean the mass of the substance (here water) for a volume of water occupying a cube whose length breadth and depth is 1 meter each.
Density water in g/cm^3 is the mass of the water occupying in a volume of 1 cubic centimeter.
To derive the density of water from Kg/m^3 dimensional unit to gram/cm^3 unit:
1000kg/m^3 = 1000Kg/ (1M)^3
= 1000*(1000gram)/ (100cm)^3
Density of a substance is defined as the mass of the substance per unit volume of the substance. There can be different units of density depending the units used for measuring mass and volume. For example, in British units usually mass is measured in pounds and volume is measured in cubic foot. Therefore in British system of measurement the density may be measured in terms of pounds per cubic foot.
In metric system, the density is usually measure in terms of either mass in kg per cubic meter of volume (kg/m^3), or mass in grams per cubic centimeter of volume(g/cm^3). Thus when we say that water has a density of 1000 kg/m^3, it implies that 1 cubic meter of water has mass of 1000 kg. We can convert density in kg/m^3 to density in g/cm^3 by converting kg to g and m^3 to cm^3 using appropriate factors.
As 1 kg = 1000 g, and 1 m^2 = 1,000,000 cm^3, we will need to multiply the density in kg/m^3 with 1000, and divide it by 1,000,000 to arrive at density in g/cm^3. Thus:
Density of water in g/cm^3 = (Density of water in kg/m^3)*1000/1000000
= 1000*1000/1000000 = 1 g/cm^3
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