Units of the wavelet scale

What are the units of the wavelet scale- a ? I always thought that it would be non-dimentional due to mathworks wavelet help: (copy/paste) "If we accept to associate the frequency Fc to the wavelet function then, when the wavelet is dilated by a factor a, this center frequency becomes Fc/a"

However (again in the matworks site: " Lastly, if the underlying sampling period is delta, it is natural to associate to the scale a the frequency Fa=Fc/(a*delta)"

Now being delta de samplinfg period ( thus in seconds), in order to Fa to be in Hertz a-the scale, as got to be in 1/sec Is this right? Thank you