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"Derived units are defined as products of powers of the base units. When the product of powers includes no numerical factor other than one, the derived units are called coherent derived units"

I know that units for quantity such as area (meter squared), volume (meter cubed), velocity (distance per time),..... are coherent. But is there, by any chance, existing a unit that is not coherent ?

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    $\begingroup$ Yes, there are, but not within the SI. $\endgroup$ – Massimo Ortolano Mar 12 '17 at 5:08
  • $\begingroup$ Consider if you want to express area in acres (or hectares for that matter), volume in quarts, or velocity in miles per hour. $\endgroup$ – The Photon Mar 12 '17 at 5:36
  • $\begingroup$ @MassimoOrtolano, how about the liter? Not equal to 1 ${\rm m^3}$. $\endgroup$ – The Photon Mar 12 '17 at 5:37
  • $\begingroup$ @ThePhoton The liter is not an SI unit, even though it's tolerated in the SI. $\endgroup$ – Massimo Ortolano Mar 12 '17 at 5:41
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    $\begingroup$ @ProtonUpUpDown $1\,\mathrm{L} = 10^{-3}\,\mathrm{m}^3$, so the numerical factor is not one. $\endgroup$ – Massimo Ortolano Mar 12 '17 at 6:26
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To condense the answers that have been provided in the comments:

  • A base unit in the SI is one of the seven established base units (kg, m, s, A, K, cd and mol).
  • A coherent derived unit is a product of powers of those base units with no added frills: m/s, N, C, J/mol, F, H, and so on.
  • Derived units can also have non-unity factors in front of them: kJ/mol, cm/s, pF, g/m$^3$, and so on. These are derived units that are not part of the coherent set.
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