Convention of units for densities in cosmology

[fab13]

TL;DR Summary

I would like to know the Convention of units for densities in cosmology : I wonder if consistent units are used by multiplying or dividing with Delta_z

I have a table of densities of galaxies :

Expected number density of galaxies for photometric survey per unit area and redshift intervals, $\mathrm{d} N / \mathrm{d} \Omega \mathrm{d} z\left[\mathrm{sr}^{-1}\right]$ and the corresponding density of galaxies per $\operatorname{arcmin}^2$ for each redshift

I wonder if the second row values are correct : indeed, I hesitate between both calculus, for example for the bin :

- case 1

3 / 11818102.860 * 0.119 = 4219062.72 (rounded to 4219063) in units $\text{d}N/\text{d}\Omega\text{d}z$

OR should I set rather :

- case 2

3 / 11818102.860 / 0.119 = 297935366.218 (rounded to 297935366) in units $\text{d}N/\text{d}\Omega\text{d}z$

One of both is wrong since I don't know if the units are $\text{d}N/\text{d}\Omega\text{d}z$ or $\text{d}N/\text{d}\Omega/\text{d}z$.

Could anyone help me what is the convention for the units of the writing $\text{d}N/\text{d}\Omega\text{d}z$ that causes some confusions ( we don't know if we have to multiply or divide by $\Delta z$ ?