If we start with
[tex]\dfrac{3\text{ kg}}{1\text{ m}^2}[/tex]
we can convert the fraction recalling that
[tex]1\text{ kg}=1000\text{ g},\quad 1\text{ m}^2=10000\text{ cm}^2[/tex]
So, we have
[tex]\dfrac{3\text{ kg}}{1\text{ m}^2} = \dfrac{3000\text{ g}}{10000\text{ cm}^2} =\dfrac{30\text{ g}}{100\text{ cm}^2}[/tex]