# Consistent values for density of galaxies between degree squared and steradian

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 $$\Delta z$$ ?