To convert the density of a liquid from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we need to follow a few steps:
1. Understand the given value: The density of the liquid is provided as [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex].
2. Know the conversion factor: We need to convert grams to kilograms and cubic centimeters to cubic meters.
- [tex]\( 1 \, \text{g} = 0.001 \, \text{kg} \)[/tex]
- [tex]\( 1 \, \text{cm}^3 = 1 \times 10^{-6} \, \text{m}^3 \)[/tex] because [tex]\( 1 \, \text{m}^3 = (100 \, \text{cm})^3 = 1,000,000 \, \text{cm}^3 \)[/tex]
3. Perform the conversion:
- Since 1 g/cm³ = 1000 kg/m³ (this is because converting the mass from grams to kilograms multiplies by [tex]\( 0.001 \)[/tex] and converting the volume from cubic centimeters to cubic meters divides by [tex]\( 1\times10^{-6} \)[/tex], so the conversion factor is [tex]\( 0.001 / 1\times10^{-6} = 1000 \)[/tex])
4. Apply the conversion factor to the given density:
[tex]\[ 13.6 \, \text{g/cm}^3 \times 1000 = 13600 \, \text{kg/m}^3 \][/tex]
Thus, the density of the liquid in SI units is [tex]\( 13600 \, \text{kg/m}^3 \)[/tex].
