Significant Figures Calculation Challenge

Question 1: What is the result of the following calculation, reported with the correct number of significant figures?

(0.92 mL + 0.08 mL + 0.01 mL) x (0.590 g/mL)

Option 1: 069

Option 2: 0509

Option 3: 0.59599

Option 4: 05959

Final answer:

The calculation result is 0.5959 g, which must be rounded to two significant figures, resulting in 0.60 g. The provided options do not include this answer, but Option 4: 05959 appears to be a typo and closest to the correct result.

Explanation:

The result of the following calculation (0.92 mL + 0.08 mL + 0.01 mL) x (0.590 g/mL) should be reported with the correct number of significant figures. When we sum the volumes, we get a total of 0.92 + 0.08 + 0.01 = 1.01 mL. Given that all the volume measurements have two significant figures, the sum is also reported to two significant figures. Now, we proceed to multiply this total volume by the density of 0.590 g/mL, which has three significant figures. The multiplication of 1.01 mL by 0.590 g/mL yields 0.5959 g.

However, we must report our final answer with the same number of significant figures as the measurement with the least number of significant figures, which is two in this case. Therefore, the correct answer needs to be rounded to two significant figures. Consequently, the correct answer is 0.60 g, which does not correspond to any of the provided options. However, if we consider that there might be a typographical error in the options, Option 4: 05959 seems to be closest to the calculated result after correcting for the significant figures.

Question 2: What is a significant figure, and why is it important in scientific calculations?

A significant figure is a digit that carries meaning contributing to the precision or accuracy of a value. It is crucial in scientific calculations because it helps in determining the certainty of the measurement and the reliability of the results obtained. By considering significant figures, scientists can properly report their findings and ensure that the data is presented accurately and with the correct level of precision.