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Chapter 1: Problem 11

Why is it incorrect to say that the results of a measurement were accurate but not precise?

Short Answer

Expert verified
It is incorrect to say that the results of a measurement were accurate but not precise because accuracy refers to how closely a measurement matches the true or accepted value, and precision refers to the consistency of repeated measurements. To be accurate, a measurement must match the true value closely, which means that repeated measurements would have to be consistent and precise. Therefore, it is impossible for a measurement to be accurate without being precise.

Step by step solution

01

1. Definition of Accuracy

Accuracy is the degree to which the result of a single measurement or multiple measurements match the true value or the accepted value. If the results match the true value well, then that measurement is considered accurate. This term refers to the close measurement compared to the standard or real value.
02

2. Definition of Precision

Precision refers to how close the results of multiple replicated measurements are to one another. The more repeatable and consistent the measurements, the higher the precision. This term refers to the consistency and repeatability of the measuring system.
03

3. Relationship between Accuracy and Precision

It is crucial to understand the relationship between accuracy and precision to address the problem. For measurements to be accurate, they must be close to the true value. For measurements to be precise, they must give consistent results when repeated. It is possible to have measurements that are both accurate and precise, but it is impossible to say that a measurement is accurate and not precise.
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4. Explanation of Incorrect Statement

If the result of a measurement were accurate, this would mean that the result closely matched the true or accepted value. However, to determine precision, we need to look at repeated measurements. If the repeated measurements are inconsistent and vary significantly, this would mean that the measurement is not precise. So, it is incorrect to say that the results of a measurement were accurate but not precise because to be accurate implies that the measurement result closely matched the true or accepted value - and if that were the case, repeated measurements must be consistent and therefore precise.

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Most popular questions from this chapter

Perform the following mathematical operations and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

The world record for the hundred meter dash is \(9.74 \mathrm{~s}\). What is the corresponding average speed in units of \(\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}, \mathrm{ft} / \mathrm{s}\), and \(\mathrm{mi} / \mathrm{h}\) ? At this speed, how long would it take to run \(1.00 \times 10^{2}\) yards?

Would a car traveling at a constant speed of \(65 \mathrm{~km} / \mathrm{h}\) violate a 40\. mi/h speed limit?

Explain the fundamental steps of the scientific method.

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(6.022 \times 10^{23} \times 1.05 \times 10^{2}\) b. \(\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}\) c. \(1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}\) d. \(\frac{(1.00866-1.00728)}{6.02205 \times 10^{2.3}}\) e. \(\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100(100\) is exact) f. \(\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}(3\) is exact)
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