Answer
First, to convert 5.52 g/$cm^{3}$ into kg/$m^{3}$, we need to know 1kg=1000g, and that $1m^{3}$=$(100cm)^{3}$=$10^{6}cm^{3}$.
Using these conversion factors, we can set up an equation so that our units cancel, and find the density in these terms to be $$\frac{5.52g}{cm^{3}}\times\frac{1kg}{1000g}\times\frac{10^{6}cm^{3}}{1m^{3}}=5520kg/m^{3}$$
Similarly, to convert to $ lb/ft^{3}$, we know that 2.204lb=1kg, and $1m^{3}=(3.28ft^{3})=35.3ft^{3}$
Setting up a conversion table and rounding to the correct number of significant figures gives us $$\frac{5520kg}{m^{3}}\times\frac{2.204lb}{1kg}\times\frac{1m^{3}}{35.3ft^{3}}=344lb/ft^{3} $$
Work Step by Step
First, to convert 5.52 g/$cm^{3}$ into kg/$m^{3}$, we need to know 1kg=1000g, and that $1m^{3}$=$(100cm)^{3}$=$10^{6}cm^{3}$.
Using these conversion factors, we can set up an equation so that our units cancel, and find the density in these terms to be $$\frac{5.52g}{cm^{3}}\times\frac{1kg}{1000g}\times\frac{10^{6}cm^{3}}{1m^{3}}=5520kg/m^{3}$$
Similarly, to convert to $ lb/ft^{3}$, we know that 2.204lb=1kg, and $1m^{3}=(3.28ft^{3})=35.3ft^{3}$
Setting up a conversion table and rounding to the correct number of significant figures gives us $$\frac{5520kg}{m^{3}}\times\frac{2.204lb}{1kg}\times\frac{1m^{3}}{35.3ft^{3}}=344lb/ft^{3} $$
