Rules for Significant Figures

The significant figure rule for addition and subtraction can be stated as follows ... 

Then perform the division, applying the multiplication/division significant-figure rule. For the addition, we obtain... 

Using the significant figure rule for multiphcation/division when rounding off an addition or subtraction result... 

As we can see, since the significant figure rules for addition limit the answer to two decimal places, the amount of H3O contributed by HCHO2 is completely negligible. The amount of H3O contributed by the autoionization of water is even smaller and therefore similarly negligible. 

The determination of logarithms and inverse logarithms (antilogarithms) is discussed in Appendix A. Significant figure rules for logarithms are also presented there. 

For many mole conversions, you need to look up atomic masses on the periodic table (see Chapter 4). The atomic masses you see in different periodic tables may vary slightly, so for consistency, we ve rounded all atomic mass values to two decimal places before plugging them into the equations. We round answers according to significant figure rules (see Chapter 1 for details). 

Compare and contrast the multiplication/division significant figure rule to the significant figure rule applied for addition/subtraction mathematical operations. Explain how density can be used as a conversion factor to convert the volume of an object to the mass of the object, and vice versa. 

Calculate the volume and density for each sample and the average density of the six samples. Be sure to use significant figure rules. 

Arden P. Zipp, "A Simple but Effective Demonstration for Illustrating Significant Figure Rules When Making Measurements and Doing Calculations," ]. Chem. Educ., Vd. 69,1992, 291. 

Compare and contrast the multiplication/division significant figure rule to the significant figure rule applied for addition/subtraction in mathematical operations. 

A more exact rule on multiplication/division is that the result should have about the same relative error—for example, expressed as parts per hundred (percent) or parts per thousand—as the least precisely known quantity. Usually the significant figure rule conforms to this requirement occasionally, it does not (see Exercise 67). 

The integral of the Gaussian distribution function does not exist in closed form over an arbitrary interval, but it is a simple matter to calculate the value of p(z) for any value of z, hence numerical integration is appropriate. Like the test function, f x) = 100 — x, the accepted value (Young, 1962) of the definite integral (1-23) is approached rapidly by Simpson s rule. We have obtained four-place accuracy or better at millisecond run time. For many applications in applied probability and statistics, four significant figures are more than can be supported by the data. 

Some other varieties of behavior are shown in figure 8.22 and 8.23. Figures 8.22-a and 8.22-b are representative of the class of link rules for which the induced structural change is only minimal. Such systems evolve essentially as a CA system on a mildly perturbed underlying lattice. Other rules may have a much stronger effect on the lattice and can significantly alter the manner in which the pure value propagation proceeds in the absence of any link operators. 

The rules for significant figures involving natural logarithms and inverse logarithms are somewhat more complex than those for base-10 logs. However, for simplicity we will assume that the rules listed above apply here as well. Thus... 

In order of increasing mass, the items are iron bar < aluminum foil < water. Realize, however, that the rules for significant figures do not allow us to distinguish between the masses of aluminum and water. 

Rules for Determining the Number of Significant Figures in a Given Number... 

Rules for Determining Significant Figures in the Answer to a Calculation... 

Know how to determine the number of significant figures in a number, the rules for how many significant figures are to be shown in the final answer, and the round-off rules. 

We ve rounded molar masses to the hundredths place before doing the calculations. Answers have been rounded according to the rules for significant figures (see Chapter 1 for details). 

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