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