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First, I think you mean “iron is 7.8 g/cm^3”. You’re missing the ^3 (cubic) part.
Density is a measure of how much stuff exists in a space. An area like a city is considered dense if there are a lot of people living in a small area.
In science, . Matter is measured with mass, and space is measured with volume. So, when you state that iron has a density of 7.8g/cm^3, you provide an amount of mass (7.8 grams), and you specify that it occupies one cubic centimeter.
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