Dimensionless units in the SI

@article{Mohr2015DimensionlessUI,
  title={Dimensionless units in the SI},
  author={Peter J. Mohr and William D. Phillips},
  journal={Metrologia},
  year={2015},
  volume={52},
  pages={40-47}
}
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit 'one', and suggest how to… 

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