J.R. S. answered • 02/15/20

Ph.D. University Professor with 10+ years Tutoring Experience

Dimensional analysis: set up so the units you don't want cancel, and you are left with the units you do want.

5.52 ~~g~~/~~cm~~^{3} x 1 kg/10^{3} ~~g~~ x 1~~cm~~^{3}/10^{-6} m^{3} = 5.52 x10^{3} kg/m^{3}

Do the same using 454 g = 1 lb and 1 cm^{3} = 3.5x10-5 ft^{3}