Subtraction significant figure rules

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. 

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. 

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. 

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

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

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

EXAMPLE 1-6 Applying Significant Figure Rules Addition/Subtraction... 

In addition to the rules cited above, there is another full set of rules to be followed for significant figures when two or more measured numbers are subtracted, added, divided, or multiplied. These rules are summarized in the appendix of the Conceptual Chemistry Laboratory Manual. 

Different rounding off rules are needed for addition (and its reverse, subtraction) and multiplication (and its reverse, division). In both procedures we round off the answers to the correct number of significant figures. 

The rules for significant figures are slightly different for addition, subtraction, multiplication, and division. 

The rule for addition and subtraction concerns the position of the last significant figure in the sum—that is, the location of this figure relative to the decimal point. The rule is When two or more numbers are added or subtracted, the positions of the last significant figures of each number relative to the decimal point should be compared. Of these positions, the one farthest to the left is the position of the last permissible significant figure of the sum or difference. 

Remember that the rules for determining the number of significant figures in multiplication and division problems are different from the rules for determining the number of significant figures in addition and subtraction problems. 

We first check to see that the quantities to be added or subtracted are expressed in the same units. We carry out the addition or subtraction. Then we follow Rule 4 for significant figures to express the answer to the correct number of significant figures. 

We have subtracted 0.045% from exactly 100%. We have therefore not violated the rules for significant figures. 

Check Note that in parts (a) and (c) we made the energy units in free energy changes (kJ) consistent with those in R (J). Based on the rules for significant figures in addition and subtraction, we retain one digit to the right of the decimal place in part (c). 

Rules for Significant Figures in Addition and Subtraction Calculations... 

When carrying measured quantities through calculations, the least certain measurement limits the certainty of the calculated quantity and thereby determines the number ofsign -cant figures in the final answer. The final answer should be reported with only one uncertain digit. To keep track of significant figures in calculations, we will make frequent use of two rules, one for addition and subtraction, and another for multiplication and division. 

A second set of rules specifies how to handle significant figures in calculations. In addition and subtraction, the answer cannot have more digits to the right of the decimal point than either of the original numbers. Consider these examples ... 

We use the subtraction rule to determine that the intermediate answer (3.37) has only one significant decimal place. To avoid small errors, it is best not to round at this point instead, we xmderline the least significant figure as a reminder. 

When a calculation contains both addition/subtraction and multiplication/division, you must apply each individual rule for significant figures separately. If two numbers... 

Strategy This problem requires two steps subtraction to determine the mass of the gas, and division to determine its density. Apply the corresponding rule regarding significant figures to each step. 

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