four research teams measured the density of a new alloy, and what each team wrote in its team notebook is…

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.\n| team | a | b | c | d |\n| ---- | ---- | ---- | ---- | ---- |\n| what was written in the notebook | \between 4.35g/cm³ and 4.85g/cm³\ | \4.10g/cm³ ± 1.0%\ | \2.6g/cm³ ± 0.5g/cm³\ | \3.70g/cm³\ |\n| most accurate measurement | | | | |\n| most precise measurement | | | | |

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.\n| team | a | b | c | d |\n| ---- | ---- | ---- | ---- | ---- |\n| what was written in the notebook | \between 4.35g/cm³ and 4.85g/cm³\ | \4.10g/cm³ ± 1.0%\ | \2.6g/cm³ ± 0.5g/cm³\ | \3.70g/cm³\ |\n| most accurate measurement | | | | |\n| most precise measurement | | | | |

Answer

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

Team A has a range of values between $4.35g/cm^{3}$ and $4.85g/cm^{3}$.

Step3: Analyze Team B

Team B has a measurement of $4.10g/cm^{3}\pm1.0%$. The uncertainty is $4.10\times0.01 = 0.041g/cm^{3}$, so the range is from $4.10 - 0.041=4.059g/cm^{3}$ to $4.10 + 0.041 = 4.141g/cm^{3}$.

Step4: Analyze Team C

Team C has a measurement of $2.6g/cm^{3}\pm0.5g/cm^{3}$, range is from $2.6 - 0.5=2.1g/cm^{3}$ to $2.6+0.5 = 3.1g/cm^{3}$.

Step5: Analyze Team D

Team D has a measurement of $3.70g/cm^{3}$.

Step6: Compare accuracy

The later and more reliable measurement is $3.60g/cm^{3}$. Team B's measurement ($4.10g/cm^{3}$) is closest to $3.60g/cm^{3}$ among the earlier measurements, so Team B has the most accurate measurement.

Step7: Compare precision

Precision is related to the smallest uncertainty. Team B has a percentage - based uncertainty of $1.0%$ which is relatively small compared to the absolute uncertainties of other teams. Team B also has a relatively narrow range of possible values, so Team B has the most precise measurement.

Answer:

Most accurate measurement: Team B Most precise measurement: Team B