Answer:
[tex]5.000 \frac{g}{cm^3}[/tex]
Explanation:
We can obtain our answer using conversion factors.
We know that 1 kilogram is 1000 grams, this is
[tex]1 \ kg = 1000 \ g[/tex]
Now, we can divide both sides by 1 kg
[tex]\frac{1 \ kg}{1 \ kg } = \frac{1000 \ g}{ 1 \ kg} [/tex]
[tex]1 = \frac{1000 \ g}{ 1 \ kg} [/tex]
The left side of the equations is 1, this means that our conversion factor is dimensionless, and can be multiplied in any equation, without changing the physical meaning of it.
same as before, we know that 1 m equals 100 cm
[tex]1 \ m = 100 \ cm[/tex]
Now, lets take the cube on both side of the equation
[tex](1 \ m)^3 = (100 \ cm)^3[/tex]
[tex]1^3 \ m^3 = 100^3 \ cm^3[/tex]
[tex]1 \ m^3 = (10^2)^3 \ cm^3[/tex]
[tex]1 \ m^3 = 10^{(2*3)} \ cm^3[/tex]
[tex]1 \ m^3 = 10^6 \ cm^3[/tex]
Now, we can divide both sides by 10^6 \ cm^3 to obtain
[tex] \frac{ 1 \ m^3 }{ 10^6 \ cm^3 } = 1 [/tex]
Now, we can simply multiply the density for our conversion factors
[tex]5000 \frac{kg}{m^3} * \frac{ 1 \ m^3 }{ 10^6 \ cm^3 } * \frac{1000 \ g}{ 1 \ kg} =5 \frac{g}{cm^3}[/tex]
We are allowed to do this, as our conversion factors are dimensionless and equal to one.
