Multiplication significant figures 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 multiplication and division is as follows ... 

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

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). 

EXAMPLE 1-5 Applying Significant Figure Rules Multiplication/Division... 

Multiplication or division. The product or quotient should be rounded off to the same number of significant figures as the least accurate number involved in the calculation. Thus, 0.00296 x 5845 = 17.3, but 0.002960 x 5845 = 17.30. However, this rule should be applied with some discretion. For example, consider the following multiplication ... 

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. 

In nearly all practical chemical calculations, a precision of only two to four significant figures is required. Therefore the student need not perform multiplications and divisions manually. Even if an electronic calculator is not available, an inexpensive 10-in slide rule is accurate to three significant figures, and a table of 4-place logarithms is accurate to four significant figures. 

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

There are five basic rules for determining whether or not digits are significant. These rules are important to know to earn all possible points during the free-response section of the test. Significant figures do not appear in the multiple-choice portion. 

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. 

The Solutions Manual section contains solutions and answers to the odd-numbered exercises in the textbook, including the Fundamentals sections. To display intermediate results we have disregarded rules concerning significant figures, but have adhered to them in reporting the final answers. In exercises with multiple parts, the properly rounded values are used for subsequent calculations. Student answers may differ slightly if only the final values are rounded, a method recommended by some instructors and the text, but not readily implemented in a printed Manual. 

The weak link for multiplication and division is the number of significant figures in the number with the smallest number of significant figures. Use this rule of thumb with caution. 

Rules for Significant Figures in Multiplication and Division Calculations... 

RULE 6. In multiplication or division, the calculated result cannot contain more significant figures than the least well-known measurement. 

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. 

To keep track of significant figures in calculations, we will make frequent use of two rules. The first involves multiplication and division, and the second... 

We use the multiplication rule to determine that the intermediate answer (11.758) rounds to two significant figures (12) because it is limited by the two significant figures in 3.37. 

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