The SI units of density are kg/m^3, but g/cm^3 is more commonly used. How many g/cm^3 are in 1 kg/m^3?

• A. 0.001 g/cm^3
• B. 0.1 g/cm^3
• C. 1 g/cm^3
• D. 0.01 g/cm^3

Answer: (A)

Verified step by step guidance

1. Understand that density is mass per unit volume, so the units kg/m^3 and g/cm^3 both represent mass divided by volume but in different unit systems.
2. Convert the mass unit from kilograms to grams: since 1 kg = 1000 g, multiply the mass by 1000 to convert kg to g.
3. Convert the volume unit from cubic meters to cubic centimeters: since 1 m = 100 cm, then 1 m^3 = (100 cm)^3 = 1,000,000 cm^3, so multiply the volume by 1,000,000 to convert m^3 to cm^3.
4. Combine these conversions to convert 1 kg/m^3 to g/cm^3 by dividing the converted mass by the converted volume, which is (1000 g) / (1,000,000 cm^3).
5. Simplify the fraction to find the equivalent density in g/cm^3, which will give you the numerical value corresponding to 1 kg/m^3 in g/cm^3 units.