Here's the neat, cool way to convert units like this:
-- 1 kilogram = 1,000 grams
-- 1 meter = 100 centimeters
So . . . . .
(1000 kg/m³) x (1000 g/kg) x (1 m/100 cm)³ =
(1,000 kg/m³) x (1,000 g/kg) x (1 m³/1,000,000 cm³) =
(1,000 x 1,000 x 1 / 1,000,000) (kg-g-m³ / m³-kg-cm³) = 1 g/cm³
