a. Consider three masses that you wish to add together: 3 g, 1.4 g, and 3.3 g. These numbers represent measured values. Add the numbers together and report your answer to the correct number of significant figures.
b. Now perform the addition in a stepwise fashion in the following manner. Add 3 g and 1.4 g, reporting this sum to the correct number of significant figures. Next, take the number from the first step and add it to 3.3 g, reporting this sum to the correct number of significant figures.
c. Compare your answers from performing the addition in the two distinct ways presented in parts a and b. Does one of the answers represent a “better” way of reporting the results of the addition? If your answer is yes, explain why your choice is better.
d. A student performs the calculation (5.0 × 5.143 g) + 2.80 g and, being mindful of significant figures, reports an answer of 29 g. Is this the correct answer? If not, what might this student have done incorrectly?
e. Another student performs the calculation (5 × 5.143 g) + 2.80 and reports an answer of 29 g. Is this the correct answer? If not, what might this student have done incorrectly?
f. Yet another student performs the calculation (5.00 × 5.143 g) + 2.80 and reports an answer of 28.5 g. Is this the correct answer? If not, what did this student probably do incorrectly?
g. Referring to the calculations above, outline a procedure or rule(s) that will always enable you to report answers using the correct number of significant figures.
Part 2
a. A student wants to determine the volume of 27.2 g of a substance. He looks up the density of the material in a reference book, where it is reported to be 2.4451 g/cm3. He performs the calculation in the following manner:
27.2 g × 1.0 cm3/2.4 g × 11.3 cm3
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 g × 1.00 cm3/2.45 g × 11.1 cm3
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 g and a density of 3.1569 g/cm3. 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 c is the “best” answer to the problem?