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I am a bit confused with using the appropriate units. I have two values for density and volume which contain units of:

Density $\rho$ = kg m^-3

Volume v = m^3

One thing i am confused here is why density is per meters negative cubed and volume is per meters positive cubed?

What is the difference between the two ? I am trying to visualize this in my mind in a physical aspect to understand why this is the case but don't fully understand it.

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  • $\begingroup$ Units for volume are not kg m$^3$, just m$^3$. The reason for the negative sign is that density is inversely related to volume. $\endgroup$ – HDE 226868 Jan 8 '16 at 1:14
  • $\begingroup$ Oops sorry that was a typo for volume. $\endgroup$ – WDUK Jan 8 '16 at 1:15
  • $\begingroup$ @HDE226868 wikipedia states: Density is kg/m3 which is a postive cubed.. $\endgroup$ – WDUK Jan 8 '16 at 1:21
  • $\begingroup$ I expanded that into an answer, addressing your comment. $\endgroup$ – HDE 226868 Jan 8 '16 at 1:24
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It doesn't necessarily make conceptual sense to use units of m-3. After all, can you picture one meter-1? Not easily.

The units of density you give there are kg$\cdot$m-3. This is equivalent to a different formulation: kg/m3. We now have a positive exponent, because we're treating the total units as a fraction: kilograms over cubic meters.

This leads to a better conceptual interpretation. If our density is $x$ kg/m3, then in every m3 - a cubic meter - there are $x$ kilograms of matter.

The way to read negative exponents in units is "something" per "something", which makes more sense conceptually (I hope!).

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  • $\begingroup$ So how would a positive exponent be read if negatives mean per something ? $\endgroup$ – WDUK Jan 8 '16 at 1:26
  • $\begingroup$ @WDUK Just read it normally - say "kilograms". $\endgroup$ – HDE 226868 Jan 8 '16 at 1:27

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