/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 103 A rule of thumb in designing exp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 103

A rule of thumb in designing experiments is to avoid using a result that is the small difference between two large measured quantities. In terms of uncertainties in measurement, why is this good advice?

Short Answer

Expert verified
In summary, using a result that is a small difference between two large measured quantities in experiments is not advisable due to the propagation of uncertainties. The uncertainties in each of the individual measurements combined can lead to a disproportionately large uncertainty in the difference itself. This makes the result less reliable and more prone to inaccuracies. Therefore, avoiding such scenarios helps minimize the impact of uncertainties in measurement, resulting in more accurate and reliable experimental conclusions.

Step by step solution

01

Understanding uncertainties in measurement

Uncertainties in measurement are inherent in any experimental process and are a result of various factors, such as the accuracy and precision of measuring instruments or human error. When interpreting experimental results, it is important to consider these uncertainties to ensure that the conclusions drawn from the results are valid and reliable.
02

Considering the small difference between two large values

When a result is given as the small difference between two large measured quantities (e.g., A - B, where A and B are large values), the uncertainties in both A and B come into play. This is because the uncertainty in the difference depends on the uncertainties in both of the individual measurements.
03

The propagation of uncertainties

The propagation of uncertainties is the process through which the uncertainties of individual measurements affect the uncertainty of the overall result. In the case of the small difference between two large measured quantities, we can analyze the propagation of uncertainties through the formula for the difference: \( \Delta(A - B) = \sqrt{(\Delta A)^2 + (\Delta B)^2} \) Here, 螖(A - B) represents the uncertainty in the difference, while 螖A and 螖B represent the uncertainties in the individual measurements A and B, respectively.
04

Analyzing the impact of the small difference between large values on uncertainty

From the propagation of uncertainties formula, we can see that if A and B are large values with significant uncertainties, then the combined uncertainty in their difference is even larger. Consequently, the ratio of the uncertainty in the difference to the difference itself becomes large, leading to a less reliable result. Essentially, the small difference between two large measured quantities will have a disproportionately large uncertainty, making it difficult to draw accurate conclusions from the result due to higher levels of uncertainty. In conclusion, avoiding the use of results that are small differences between two large measured quantities in experiments is good advice because it helps minimize the impact of uncertainties in measurement. By following this rule of thumb, experiment designers can ensure that the overall uncertainty in the result is kept low, leading to more reliable and accurate conclusions from the experiment.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The density of pure silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). If \(5.25 \mathrm{~g}\) of pure silver pellets is added to a graduated cylinder containing \(11.2 \mathrm{~mL}\) of water, to what volume level will the water in the cylinder rise?

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost \(2.45\) euros per kilogram. Given that 1 euro is equivalent to approximately \(\$ 1.46\), calculate what a pound of peaches will cost in dollars.

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)

Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by 100 . Percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100\) Calculate the percent error for the following measurements. a. The density of an aluminum block determined in an experiment was \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). (True value \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\).) b. The experimental determination of iron in iron ore was \(16.48 \%\). (True value \(16.12 \% .)\) c. A balance measured the mass of a \(1.000-\mathrm{g}\) standard as \(0.9981 \mathrm{~g}\)

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation. a. \(0.00034159\) to three digits b. \(103.351 \times 10^{2}\) to four digits c. \(17.9915\) to five digits d. \(3.365 \times 10^{5}\) to three digits
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.