To convert the density of acetone from [tex]\(790 \, \text{kg/m}^3\)[/tex] to [tex]\(\text{g/cm}^3\)[/tex], follow these steps:
1. First, recall the relationship between kilograms and grams: [tex]\(1 \, \text{kg} = 1000 \, \text{g}\)[/tex].
2. Also, note the relationship between cubic meters and cubic centimeters: [tex]\(1 \, \text{m}^3 = 10^6 \, \text{cm}^3\)[/tex].
Given these conversions, here is the step-by-step process:
1. Convert kilograms to grams: Since [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex], we need to convert the density from [tex]\(\text{kg}\)[/tex] to [tex]\(\text{g}\)[/tex]. Thus, multiply the density by [tex]\(1000\)[/tex]:
[tex]\[
790 \, \text{kg/m}^3 \times 1000 \, \frac{\text{g}}{\text{kg}} = 790,000 \, \text{g/m}^3
\][/tex]
2. Convert cubic meters to cubic centimeters: Since [tex]\(1 \, \text{m}^3 = 10^6 \, \text{cm}^3\)[/tex], we need to convert the volume from [tex]\(\text{m}^3\)[/tex] to [tex]\(\text{cm}^3\)[/tex]. Thus, for the volume conversion, we divide by [tex]\(10^6\)[/tex]:
[tex]\[
790,000 \, \text{g/m}^3 \div 10^6 \, \frac{\text{cm}^3}{\text{m}^3} = 0.79 \, \text{g/cm}^3
\][/tex]
Finally, the density of acetone in [tex]\( \text{g/cm}^3 \)[/tex] is [tex]\( 0.79 \)[/tex].
Therefore, the correct choices for the blanks are:
- Divide 790 by 1,000 and
- Multiply by [tex]\(10^6\)[/tex]
- The density of acetone in [tex]\( \text{g/cm}^3 \)[/tex] is [tex]\( 0.79 \)[/tex]
