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Chapter 1: Problem 10

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

Expert verified
(3) Y is more accurate than X.

Step by step solution

01

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.
02

Understand Significant Figures

Significant figures indicate the precision of a measurement. The more significant figures a measurement has, the more precise it is.
03

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.
04

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.
05

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈥攊t'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.

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Most popular questions from this chapter

Which of the following statements is incorreet? (1) \Lambdall clements are homogencous (2) Compounds made up of a number of elements are hetcrogencous (3) \(\Lambda\) mixture is not always heterogencous (4) \Lambdair is an heterogencous mixture

Suppose that \(\Lambda\) and \(\mathrm{B}\) are two clements which form compounds \(\mathrm{B}_{2} \Lambda_{3}\) and \(\mathrm{B}_{2} \Lambda\), respectively. If \(0.05 \mathrm{~mole}\) of \(\mathrm{B}_{2} \Lambda_{3}\) weighs \(9.0 \mathrm{~g}\) and \(0.10 \mathrm{~mole}\) of \(\mathrm{B}_{2} \Lambda\) weighs \(10 \mathrm{~g}\), then the atomic weight of \(\Lambda\) and \(\mathrm{B}\), respectively is (1) 30 and 40 (2) 40 and 30 (3) 20 and 5 (4) 15 and 20

Element \(\Lambda\) (atomic weight \(12.01)\) and element \(\mathrm{B}\) (atomic weight 16 ) combine to form a new substance \(\mathrm{X}\). If two moles of \(\mathrm{B}\) combines with one mole of \(\Lambda\), then the weight of one mole of \(\mathrm{X}\) is (1) \(28.01 \mathrm{~g}\) (2) \(44.01 \mathrm{~g}\) (3) \(40.02 \mathrm{~g}\) (4) \(56.02 \mathrm{~g}\)

\(4.4\) g of an unknown gas occupies \(2.24\) litres of volume at STP. The gas may be (1) carbon dioxide (2) carbon monoxide (3) oxygen (4) sulphur dioxide

\(\mathrm{II}_{2} \mathrm{~S}\) contain \(5.88 \%\) hydrogen, \(\mathrm{I}_{2} \mathrm{O}\) contain \(11.11 \%\) hydrogen while \(\mathrm{SO}_{2}\) contains \(50 \%\) sulphur. The data illustrate the law of (1) Conservation of mass (2) Constant proportions (3) Multiple proportions (4) Reciprocal proportions
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