By Arthur J. Lyon and W. Ashhurst (Auth.)
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For a number of years now i've been educating classes in machine algebra on the Universitat Linz, the college of Delaware, and the Universidad de Alcala de Henares. within the summers of 1990 and 1992 i've got equipped and taught summer time faculties in machine algebra on the Universitat Linz. progressively a suite in fact notes has emerged from those actions.
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Extra resources for Dealing with Data
1. Significant figures Beginners sometimes believe that what is important in a number for its degree of precision is the number of decimal places it has after the decimal point, and they will therefore round off indiscriminately, say to the second decimal place. So one number will be quoted as 247-85, but the number 0-024785 would be rounded off to 0-02 or possibly 0-025 (and 46 DEALING WITH DATA if the result came, say, from a division it would be carried no further than the second or third place) because the student would feel that places beyond the second or third place after the decimal point represent small and negligible quantities.
Hence we need the answer correct to the first decimal place, and retaining two uncertain digits we get x = 1569-3 + 2-8 (maximum error). (b) In the second gross mistake the student seems to think that all answers should be given to the second decimal place. Since the denominator, 67, has two significant figures we can expect that in fact the answer ought to be given to three or four significant figures. Straight division yields 0-035 . . , and the relative maximum error of this answer is approximately that in 67, namely 0-75%, or about 0-00026.
On the other hand, when we are concerned with relative accuracy it is rather the number of significant figures which is important, though this number does not define the relative accuracy precisely. If a value is correct to two significant figures its relative accuracy lies between 5% (for a value close to 10) and 0-5% (for a value close to 99). Similarly, a value correct to three significant figures has a relative accuracy between 0-5% and 0-05%, and so on. One can say, therefore, that with two significant figures the accuracy is of order 1%, with three it is of order 0-1%, with four of order 0*01%, and so on.