A system of units is coherent with respect to a system of quantities and equations if the system of units is chosen in such a way that the equations between numerical values have exactly the same form (including the numerical factors) as the corresponding equations between the quantities. In such a coherent system, no numerical factor other than the number 1 ever occurs in the expressions for the derived units in terms of the base units. For example, the $newton$ and the $joule$. These two are, respectively, the force that causes one kilogram to be accelerated at 1 metre per (1) second per (1) second, and the work done by 1 newton acting over 1 metre. Being coherent refers to this consistent use of 1. In the old c.g.s. system , with its base units the centimetre and the gram, the corresponding coherent units were the dyne and the erg, respectively the force that causes 1 gram to be accelerated at 1 centimetre per (1) second per (1) second, and the work done by 1 dyne acting over 1 centimetre. So $1\\,newton = 10^5 dyne$, $1 joule = 10^7 erg$, making each of the four compatible in a decimal sense within its respective other system, but not coherent therein.
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