Significant Figures Rule

If we assume that the concentration of analyte in the original solvent is 0.060 M before extraction, then, after rounding the answer of the calculation according to significant figure rules, the concentration in the extraction solvent after extraction is also 0.060 M (a very large distribution coefficient, as in this problem, would indicate that virtually all the analyte is extracted). 

As in number 15 above, the distribution coefficient is very large and the calculation shows, after rounding according to significant figure rules, that virtually all of the analyte is extracted, 0.037 g. 

No problem. Follow the normal order of operations, doing multiplication and division first, followed by addition and subtraction. At each step, follow the simple significant-figure rules, and then move on to the next step. 

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). 

The experiment obviously requires careful weight, length, and width measurements using common laboratory measuring devices as well as subtraction and multiplication/division calculations in which significant figure rules need to be applied. 

Note Be sure to adhere to all significant figure rules in the calculations. 

Because 4.3 has the least number of significant figures (two), the result should have two significant figures (rule 1). 

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. 

Round the answer to the correct number of significant figures. Use the significant-figure rules from Sections 2.3 and 2.4. 

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... 

It is important to remember to follow the rules of significant figures in these unit conversion problems. Notice in this case that there are exactly three feet per yard (infinite number of significant figures—rule 5 in Table 2.1). Thus the answer to the calculation should have the same number of significant figures as in the number 15, which is two. The correct answer is therefore 5.0 yards, not 5 yards. 

What is the miles per gallon in each of the following Be sure to follow significant figure rules in expressing your answer. 

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. 

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