Sure, let's break down the conversion step-by-step:
1. We start with the given density [tex]\( \frac{13.6 \, g}{cm^3} \)[/tex].
We need to convert grams to kilograms and cubic centimeters to cubic meters.
2. Convert grams to kilograms:
[tex]\[ 1 \, kg = 1000 \, g \][/tex]
[tex]\[ \frac{1 \, kg}{1000 \, g} \][/tex]
3. Convert cubic centimeters to cubic meters:
[tex]\[ 1 m^3 = 10^6 \, cm^3 \][/tex]
[tex]\[ \frac{10^6 \, cm^3}{1 \, m^3} \][/tex]
4. Now, we multiply these conversions with the given density:
[tex]\[ \frac{13.6 \, g}{cm^3} \times \frac{1 \, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13.6 \times 10^6}{1000} \frac{kg}{m^3} \][/tex]
5. Simplify the expression:
[tex]\[ \frac{13.6 \times 10^6}{1000} = 13,600 \, kg/m^3 \][/tex]
So, the step-by-step filled in equation would be:
[tex]\[ \frac{13.6 \, g}{cm^3} \times \frac{1\, kg}{1000 \, g} \times \frac{10^6 \, cm^3}{1 \, m^3} = \frac{13,600 \, kg}{m^3} \][/tex]
