Error significant figures

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

Limits of error were in the following ranges k 1-3% or less Ej 0.3-0.5 kcal mole i, except for reference 487 (0.3-1.0) JS +1-1.5 cal mole i deg logioA 0.2-0.5. Values for idS are usually reported with more significant figures than is justified. 

The values for K, listed here have been calculated from pK, values with more significant figures than shown so as to minimize rounding errors. Values for polyprotic acids—those capable of donating more than one proton—refer to the first deprotonation. 

In a sequence of computations, adjusting the number of significant figures in intermediate results can lead to errors in the final value. Instead, wait until the computations are complete, and then express the final value with the appropriate number of significant figures. 

In practice, in numerical calculations with a computer, both rational and imtiooal numbers are represented by a finite number of digits. In both cases, then, approximations are made and die errors introduced in the result depend on the number of significant figures carried by the computer - the machine precision. In die case of irrational numbers such errors cannot be avoided. 

Note Exact conversions 1 m = 100 cm, 1 km = 1000 m. Inexact conversion 1 mile = 1.609 km to 4 significant figures. The number of significant figures in the answer is set by the data (4 sig. figs.) but the answer has extra source of error since the conversion from kilometers to miles is only good to 4 sig. figs. 

Note To minimize rounding errors, keep all your numbers in your calculator until the end, then round to the appropriate number of significant figures. 

Note The answers to each step were rounded to the correct number of significant figures. However, the entire number has been kept in the calculator and used throughout the entire calculation to minimize rounding errors. 

Note when doing calculations step-wise, it is critical that you keep the entire number in your calculator and don t round between steps. Otherwise, major rounding errors can develop. Rounding was done in this manual at every step only to illustrate the concept of significant figures. 

Note In the following calculations, the answers that are in parentheses contain too many significant figures, but are the ones used in the progressive calculation in order to minimize rounding errors. 

For the second sample, parallel calculations give 0.001200 mol NaCsHs, 0.093 g C4H8, x =1.1. There is rounding error in this second calculation because it is limited to two significant figures. The best answer is from the first run x -1.02 or 1. The formula is NaC5H5(THF),. 

One point deduction for error in significant figures (maximum once per question) number of significant figures must be correct within +/- one digit... 

B.2.1 Statistical treatment of finite samples 3B.2.2 Distribution of random errors 3B.2.3 Significant figures 3B.2.4 Comparison of results 3B.2.5 Method of least squares... 

Solving the quadratic equation gives a value of x, correct to one decimal place. As a result, [H2] can have only one significant figure. The calculated value of is equal to the given value, within the error introduced by rounding. 

Check your answers. Try to finish a little early so that you can read through your answers. Make sure your answers are complete. It is easy to make simple errors. Check for any missing answers to parts of questions, especially multiple-choice questions. Make sure your answers make scientific sense, and in numerical answers check that you have included units and considered significant figures. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

First let us deal with deconvolution in general. We have a few admonitions to the reader of a literature report on a new method. They should ask, does the writer deal fairly with noise Even the most volatile of the linear methods can produce a reasonable restoration when noise is limited to roundoff error in the seventh significant figure of the data. A method s capability of yielding acceptable restorations in the presence of realistic noise is critical to its practicality. 

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