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is coherent unit of system

A coherent unit of measurement for a unit system is a defined unit that may be expressed as a product of powers of the system's base units with the proportionality factor of one. 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. For example, the 'newton' and the 'joule'. These two are, respectively, the force that causes one kilogram to be accelerated at 1 metre per second per 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 second per 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.