Dimensions of interaction/radiation length

[Kara386]

I've been given that in an electromagnetic calorimeter the radiation length of a material consisting of a single nucleus is:
$X_0 = \frac{716.4A}{Z(Z+1)\ln(287/\sqrt{74}}$

Where $X_0$ is in g $cm^{-2}$. How can it be in those units when everything in that expression is dimensionless? It's possible I'm meant to use density to calculate $X_0$ in the correct units somehow.

Thanks for any help!

 

[Kara386]

Ok, change of question. Assuming $X_0$ is originally calculated in g$cm^{-2}$, can I use density to somehow calculate the value in cm instead? cm seems like a more sensible unit for a length. And dimensionally dividing a quantity in g$cm^{-2}$ by g$cm^{-3}$ gives cm, is there any justification for why $\frac{X_0}{\rho}$ would give $X_0$ in cm? Rather than some quantity completely different to radiation length?