June 1, 2015
      
                  
        
  Author(s)
  Peter J. Mohr,   William D. Phillips
 
       
            
    
    
        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