Question

four research teams measured the density of a new alloy, and what each team wrote in its team notebook is shown in the table below. suppose a later and more reliable measurement gives 3.60 g/cm³ for the density of the same alloy. decide which of the earlier measurements was the most accurate, and which was the most precise.

team	what was written in the notebook	most accurate measurement	most precise measurement
b	\4.10 g/cm³ ± 1.0%\
c	\2.6 g/cm³ ± 0.5 g/cm³\
d	\3.70 g/cm³\

Explanation:

Step1: Understand accuracy and precision

Accuracy refers to how close a measurement is to the true value. Precision refers to how close repeated - measurements are to each other.

Step2: Analyze Team A's measurement

Team A: "between 4.35 g/cm³ and 4.85 g/cm³". This is a range, so it is not very precise. And without knowing the true value, we can't say it's very accurate.

Step3: Analyze Team B's measurement

Team B: "4.10 g/cm³ ± 1.0%". The relative uncertainty of 1.0% gives an uncertainty of \(4.10\times0.01 = 0.041g/cm³\). The range is \(4.10 - 0.041=4.059g/cm³\) to \(4.10 + 0.041 = 4.141g/cm³\). It has a relatively small uncertainty, so it is precise. But we still don't know accuracy without the true - value.

Step4: Analyze Team C's measurement

Team C: "2.6 g/cm³ ± 0.5 g/cm³". The uncertainty is 0.5 g/cm³, and the range is \(2.6 - 0.5=2.1g/cm³\) to \(2.6 + 0.5 = 3.1g/cm³\). This is a large uncertainty, so it is neither very accurate nor very precise.

Step5: Analyze Team D's measurement

Team D: "3.70 g/cm³". There is no uncertainty given. But compared to the others, if we assume a small implicit uncertainty (since it is given to two decimal places), it could be considered relatively precise. And if the true value is close to 3.70 g/cm³, it could be accurate. Since the later more reliable measurement is 3.60 g/cm³, Team D's value of 3.70 g/cm³ is closer to 3.60 g/cm³ than the other earlier measurements. So Team D's measurement is the most accurate among the earlier ones. And Team B's measurement has the smallest relative uncertainty among the earlier ones, so it is the most precise.

Answer:

Most accurate measurement: D. "3.70 g/cm³"
Most precise measurement: B. "4.10 g/cm³ ± 1.0%"