Question

the very last report question is f2flab 2: density had you calculate a density for a solid. the report question stated: discussion question 6) a solid had a measured mass of 4.15 g. when added to water, the volume of the water changed from 15.40 ml to 21.2 ml. what is the density of the solid?\
the work for that question is shown here:
volume: 21.2 ml - 15.40 ml = 5.8 ml
density: d = 4.15 g + 5.8 ml = 7.16 g/ml which rounds to 7.2 g/ml.
why is the correct answer the 2 significant figure 7.2 g/ml and not the 3 sig fig. answer 7.16 g/ml?
a) since most values provided in the question are 3 significant figures, the final density should be 3 significant figures.
b) the division rule for significant figures is to use the great number and density divides a 3 sig. fig. value by a 2 sig. fig. value and is reported as 3 sig. figs.
c) the subtraction rule results in the volume getting reported with one after the decimal. this results in a volume that is only 2 significant figures. the division for density divides a 3 sig. fig. value by a 2 sig. fig. value and is reported as 2 sig. figs.
d) the volume subtraction rule results gives a volume of 5.80 ml. this results in a volume that is 3 significant figures. the division for density divides a 3 sig. fig. value by a 3 sig. fig. value and is reported as 3 sig. figs.

Explanation:

• For subtraction: When subtracting \(21.2 - 15.40\), the rule is that the result should be rounded to the least number of decimal places. \(21.2\) has one decimal place and \(15.40\) has two decimal places. So, \(21.2-15.40 = 5.8\) (one decimal place), and \(5.8\) has two significant figures.
• For division: The rule for division of significant figures is that the result should have the same number of significant figures as the least - precise measurement. The mass \(m = 4.15\ g\) (three significant figures) and the volume \(V=5.8\ mL\) (two significant figures). When calculating density \(d=\frac{m}{V}=\frac{4.15}{5.8}\), the result should be reported with two significant figures.

Answer:

C. The subtraction rule results in the volume getting reported with one after the decimal. This results in a volume that is only 2 significant figures. The division for density divides a 3 sig. fig. value by a 2 sig. fig. value and is reported as 2 sig. figs.