To convert the density of acetone from [tex]\( 790 \, \text{kg/m}^3 \)[/tex] to [tex]\( \text{g/cm}^3 \)[/tex], we start with the given conversion factors: [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex] and [tex]\( 1 \, \text{m}^3 = 10^6 \, \text{cm}^3 \)[/tex].
1. First, we convert mass from kilograms to grams:
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
2. Next, we convert volume from cubic meters to cubic centimeters:
[tex]\[
1 \, \text{m}^3 = 10^6 \, \text{cm}^3
\][/tex]
3. Combining these conversions, we have:
[tex]\[
\frac{1 \, \text{kg}}{1 \, \text{m}^3} = \frac{1000 \, \text{g}}{10^6 \, \text{cm}^3}
\][/tex]
4. Simplifying this conversion factor:
[tex]\[
\frac{1000 \, \text{g}}{10^6 \, \text{cm}^3} = 0.001 \, \text{g/cm}^3
\][/tex]
5. Now, we multiply the given density by this conversion factor:
[tex]\[
790 \, \text{kg/m}^3 \times 0.001 = 0.79 \, \text{g/cm}^3
\][/tex]
So, the correct steps and resulting value are as follows:
- We use [tex]\( 1000 \)[/tex] (for mass) and [tex]\( 10^6 \)[/tex] (for volume).
- These operations reveal that the density of acetone in [tex]\( \text{g/cm}^3 \)[/tex] is [tex]\( 0.79 \)[/tex].
