To find the density of the object, we start with the given mass and volume.
The formula for density [tex]\( (\rho) \)[/tex] is:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
Given:
[tex]\[
\text{mass} = 32.1 \text{ grams}
\][/tex]
[tex]\[
\text{volume} = 41.25 \text{ milliliters}
\][/tex]
We need to divide the mass by the volume:
[tex]\[
\rho = \frac{32.1 \text{ grams}}{41.25 \text{ milliliters}}
\][/tex]
Performing this division, we get the density:
[tex]\[
\rho = 0.7778787878787879 \text{ grams per milliliter}
\][/tex]
However, we need to report the density to the correct number of significant figures. To determine the number of significant figures in our result, we look at the given values:
- The mass [tex]\(32.1 \text{ grams}\)[/tex] has 3 significant figures.
- The volume [tex]\(41.25 \text{ milliliters}\)[/tex] has 4 significant figures.
The result must be reported to the least number of significant figures in the given values, which is 3 in this case. Therefore, we round [tex]\(0.7778787878787879\)[/tex] to 3 significant figures.
So, the correct density is:
[tex]\[
\rho = 0.778 \text{ grams per milliliter}
\][/tex]
Thus, the density of the object reported to the correct number of significant figures is:
[tex]\[
\boxed{0.778 \frac{\text{grams}}{\text{milliliter}}}
\][/tex]
