To convert the density of mercury from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we need to use the given conversion factors: [tex]\(1 kg = 1000 g \)[/tex] and [tex]\(1 m³ = 10^6 cm³\)[/tex].
The steps for this conversion process are as follows:
1. Start with the original density: [tex]\( \frac{13.6 \, g}{cm^3} \)[/tex].
2. Convert grams to kilograms by using the factor [tex]\( \frac{1 \, kg}{1000 \, g} \)[/tex].
3. Convert cubic centimeters to cubic meters by using the factor [tex]\( \frac{10^6 \, cm^3}{1 \, m^3} \)[/tex].
When we apply these conversion factors, the equation becomes:
[tex]\[
\frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13600 \, kg}{m^3}
\][/tex]
Therefore, plugging the appropriate labels into the equation, we get:
[tex]\[
\frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13600 \, kg}{m^3}
\][/tex]
