Addition, significant digits

Note that the answers have been rounded to three significant digits. Since the even-tempered formula is only an approximation, this does not introduce any significant additional error. 

We must report the results of our calculations to the proper number of significant digits. We almost always use our measurements to calculate other quantities and the results of the calculations must indicate to the reader the limit of accuracy with which the actual measurements were made. The rules for significant digits as the result of additions or subtractions with measured quantities are as follows ... 

Estimating distances. For both the worst-case and alternative release scenarios, the source must estimate the distance to where the endpoint is no longer exceeded and estimate the population (rounded to two significant digits) within a circle defined by the distance and centered at the release point. U.S. Census data may be used and it does not have to be updated however, the presence of sensitive populations (e.g. hospitals, schools, etc.) must be noted. In addition, the source must identify and list the types of environmental receptors within the calculated worst-case distance and circle however,... 

This value must be rounded off to three total significant digits because this is the lower precision of the numerator and the denominator. The first insignificant digit is a 5. In this case there are additional non-zero digits after the 5, so rounding occurs upwards to 2.79 g/ml (answer B). 

If a problem has both addition or subtraction and multiplication or division, the part that is done first must have its significant digits noted before the next operation is performed, because the rules are different for determining which digits are retained. 

The rules for significant digits in addition and subtraction are different from those in multiplication and division. 

Addition and subtraction do not depend on the number of significant digits. Consider the following example ... 

Verify that S-Plus 5.1 performs a General Additive Model with Gaussian error Distribution and identity link problem correctly to 3 significant digits... 

We give the answer to four significant digits, because both the pressure and the amount of gas are specified to four significant digits. We can now make an additional conversion to express the volume in liters ... 

The doubtful digits are underlined in Example A-1. In addition or subtraction, the last significant digit in the answer is determined by the position of the least doubtful digit. In (a), this is the first digit after the decimal point. In (b),this is the second digit after the decimal point. 

What limits the munber of significant digits in a calculation involving only addition and subtraction How are significant figures determined in calculations involving both addition/subtraction and multiplication/ division ... 

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