Question

Two students, \(X\) and \(Y\), reported the mass of the same substance as \(7.0 \mathrm{~g}\) and \(7.00 \mathrm{~g}\), respectively. Which of the following statement is correct? (1) Both are equally accurate (2) \(\mathrm{X}\) is more accurate than \(\mathrm{Y}\) (3) \(\mathrm{Y}\) is more accurate than \(\mathrm{X}\) (4) Both are inaccurate scientifically

Short answer

(3) Y is more accurate than X.

Step-by-step solution

Understand the Problem

We have two students reporting measurements of a substance's mass: X reported 7.0 g and Y reported 7.00 g. We need to determine which statement regarding the accuracy of these measurements is correct.

Understand Significant Figures

Significant figures indicate the precision of a measurement. The more significant figures a measurement has, the more precise it is.

Compare the Number of Significant Figures

Student X's measurement (7.0 g) has 2 significant figures, while Student Y's measurement (7.00 g) has 3 significant figures.

Determine Accuracy Based on Significant Figures

Since Student Y's measurement has more significant figures (3 in total) compared to Student X's measurement (2 in total), Y's measurement is more precise. Higher precision generally indicates a higher accuracy assuming the instrument and technique are properly calibrated and executed.

Select the Correct Statement

Given that Y's measurement has more significant figures than X's measurement, the correct statement is: (3) Y is more accurate than X.

Key concepts

significant figures

In scientific measurements, significant figures are crucial for understanding how precise the measurement is. These figures consist of all the digits known with certainty, plus one digit that is estimated. For example, the number 7.0 has 2 significant figures, and 7.00 has 3 significant figures. The added zero in 7.00 indicates a higher level of precision. It's not just an extra zero—it's a confirmation that the measurement was more finely tuned.

measurement accuracy

Measurement accuracy refers to how close a measured value is to the actual or true value of the quantity being measured. Accuracy is dependent on the correctness and calibration of the measurement tools used. More significant figures usually indicate more precise measurement techniques, which can lead to higher accuracy. In our exercise, Student Y's measurement (7.00 g) is more accurate compared to Student X's measurement (7.0 g), assuming both measurements were obtained using properly calibrated instruments.

precision in scientific reporting

Precision in scientific reporting helps ensure that measurements reported are both reliable and replicable. Unlike accuracy, which focuses on closeness to the true value, precision looks at the consistency of repeated measurements. In our example, Student Y's reported value of 7.00 g (3 significant figures) demonstrates more precision than Student X's value of 7.0 g (2 significant figures). This implies that measurements are more consistent and reliable when the number of significant figures is higher. Always aim for higher precision to provide clear, consistent, and reproducible results.