Question

the average density of a planet is 4.133 g/cm³. what is its density in kg/m³? be sure your answer has the correct number of significant figures. note: reference the si prefixes table for additional information.

Explanation:

Step1: Recall unit - conversion factors

We know that \(1\ m = 100\ cm\), so \(1\ m^{3}=(100\ cm)^{3}=10^{6}\ cm^{3}\) and \(1\ kg = 1000\ g\).

Step2: Set up the conversion

The density \(
ho = 4.133\frac{g}{cm^{3}}\). To convert to \(\frac{kg}{m^{3}}\), we use the following conversion:
\[

$$\begin{align*} ho&=4.133\frac{g}{cm^{3}}\times\frac{1\ kg}{1000\ g}\times\frac{(100\ cm)^{3}}{1\ m^{3}}\\ &=4.133\times\frac{1\ kg}{1000\ g}\times\frac{10^{6}\ cm^{3}}{1\ m^{3}}\\ &=4.133\times10^{3}\frac{kg}{m^{3}} \end{align*}$$

\]

Answer:

\(4.133\times 10^{3}\frac{kg}{m^{3}}\)