a. A student wants to determine the volume of \(27.2 \mathrm{~g}\) of a
substance. He looks up the density of the material in a reference book, where
it is reported to be \(2.4451 \mathrm{~g} / \mathrm{cm}^{3} .\) He performs the
calculation in the following manner:
$$
27.2 \mathrm{~g} \times 1.0 \mathrm{~cm}^{3} / 2.4 \mathrm{~g}=11.3
\mathrm{~cm}^{3}
$$
Is the calculated answer correct? If not, explain why it is not correct.
b. Another student performs the calculation in the following manner:
$$
27.2 \mathrm{~g} \times 1.00 \mathrm{~cm}^{3} / 2.45 \mathrm{~g}=11.1
\mathrm{~cm}^{3}
$$
Is this a "better" answer than that of the first student? Is this the "best"
answer, or could it be "improved"? Explain.
C. Say that you have ten ball bearings, each having a mass of \(1.234
\mathrm{~g}\) and a density of \(3.1569 \mathrm{~g} / \mathrm{cm}^{3}\).
Calculate the volume of these ten ball bearings. In performing the
calculation, present your work as unit conversions, and report your answer to
the correct number of significant figures.
d. Explain how the answer that you calculated in part \(\mathrm{c}\) is the
"best" answer to the problem?