To solve the given problem, we will convert the volume from liters to milliliters, find the mass in grams using the density, and then convert the mass from grams to kilograms. Here are the detailed steps:
1. Convert the volume from liters to milliliters:
- We start with 0.48 liters.
- We know that 1 liter is equal to [tex]\(10^3\)[/tex] milliliters.
- To convert 0.48 liters to milliliters, we multiply by [tex]\(10^3\)[/tex]:
[tex]\[
0.48 \, \text{L} \times \frac{10^3 \, \text{mL}}{1 \, \text{L}} = 480 \, \text{mL}
\][/tex]
2. Calculate the mass in grams:
- Density ([tex]\( \rho \)[/tex]) is given as 0.80 g/mL.
- We have 480 milliliters of the fluid.
- To find the mass, we multiply the volume by the density:
[tex]\[
480 \, \text{mL} \times 0.80 \frac{\text{g}}{\text{mL}} = 384 \, \text{g}
\][/tex]
3. Convert the mass from grams to kilograms:
- We know that 1 kilogram is equal to [tex]\(10^3\)[/tex] grams.
- To convert 384 grams to kilograms, we divide by [tex]\(10^3\)[/tex]:
[tex]\[
384 \, \text{g} \div 10^3 = 0.384 \, \text{kg}
\][/tex]
So, the final results after these conversions and calculations are:
- Volume in milliliters: [tex]\( 480 \, \text{mL} \)[/tex]
- Mass in grams: [tex]\( 384 \, \text{g} \)[/tex]
- Mass in kilograms: [tex]\( 0.384 \, \text{kg} \)[/tex]
Thus, the solution to the problem is:
[tex]\[
(0.48 \, \text{L}) \left(\frac{1 \, \text{mL}}{10^{-3} \, \text{L}}\right)\left(0.80 \frac{\text{g}}{\text{mL}}\right)\left(\frac{1 \, \text{kg}}{10^3 \, \text{g}}\right) = 0.384 \, \text{kg}
\][/tex]
