Verified answer

1 gm = 10^-3 kg. Replace "g" by "10^-3 kg"

0.0028 * 10^-3 kg/mm^3

1 mm^3 = 10^-9 m^3.

0.0028 * 10^-3 kg/mm^3 = 0.0028 * 10^-3 kg/10^-9 m^3

Start with 0.00028 g/mm³

Multiply by "1 kg / 1000g". This cancels out the "g" and replaces it with "kg".

Multiply by "1000000000 mm³ / 1 m³". This cancels out the "mm³" and replaces it with "m³"