A box has a volume of 1.01 m^3. Two students measure the box. The first says the volume is 1m^3, while the second says the volume is 1.23m^3. Assuming they are reporting the correct number of significant figures for the measuring devices used, which student used the more precise device? Which student provided the more accurate answer?

Question

A box has a volume of 1.01 m^3. Two students measure the box.  The first says the volume is 1m^3, while the second says the volume is 1.23m^3. Assuming they are reporting the correct number of significant figures for the measuring devices used,  which student used the more precise device? Which student provided the more accurate answer?

GPT-4o mini · Answer

To assess the precision and accuracy of the measurements provided by the two students, we need to analyze their reported values and the original volume of the box (1.01 m³).

Significant Figures:

First Student: Reports the volume as 1 m³.
- This value has 1 significant figure.
Second Student: Reports the volume as 1.23 m³.
- This value has 3 significant figures.

Precision:

Precision refers to the consistency and resolution of measurements. The second student, who reported 1.23 m³, used a device that can measure to a finer resolution (at least to the hundredths place), thus demonstrating a more precise measurement.

Accuracy:

Accuracy refers to how close a measured value is to the true value. In this case, the true volume of the box is 1.01 m³.

The first student's measurement of 1 m³ is only 0.01 m³ from the true value, which provides a reasonable approximation but is not very close.
The second student's measurement of 1.23 m³ is 0.22 m³ away from the true value, which is further off from the actual volume.

Conclusion:

Precision: The second student (1.23 m³) used the more precise device due to greater significant figures.
Accuracy: The first student (1 m³) provided the more accurate answer as it is closer to the true value of 1.01 m³.