By Arthur J. Lyon and W. Ashhurst (Auth.)
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Extra resources for Dealing with Data
And as before, we assume that the two pipette measurements of 25 ml and the normalities are essentially error-free. The maximum relative error in 25— p is ±5/24-06% or 0*2% approximately. Hence the maximum absolute error in x is ±0-2x0-09624/100 = ±0-0002 approximately. (b) N = 1-0 and p = 22-59. Hence or 25* = 2-41X1-0 x = 0-0964. The maximum relative error in 25— p is 5/2-41% or 2% approximately. The maximum absolute error in x is therefore 2% of 0-0964 or about ±0-002. Hence the two results are 0-0962 ±0-0002 and 0-096 ±0-002 and, clearly, the first result is ten times more precise than the second.
In other words, we have retained two guarding decimal places. Suppose that we have a larger number of terms, in fact a "generalized sum" of the form ±x±y±z±, .. ,in which there is considerable variation in the number of decimal places quoted. 4 that when all the values are correct to their last decimal place retention of two guarding places is still desirable, and in most cases adequate. e. that of the least accurate terms) ; let us say it is the kth decimal place after the point. If any terms contain digits beyond the (A:+2)th decimal place, then they should be rounded off correct to this place.
10. Calculations lead to the following values and possible errors. Round off according to the rules suggested in the text,t using powers of 10 where appropriate: (a) 54-37+0-0482. (b) 0-05638 + 0-0006. (c) 2-735 + 0-148. (d) 15,725 + 520. (e) 0-0003829 + 0-000027. (f) 7-82 + 0-074215. Answers 1. 2. 3. 4. 5. (a) +10%. (b) +0-1%. (c)+2%. (a) ±2g. (b) +8g. (c) +0-04 g. (a) + 5 V . (b) +0-01 V. (a) 12-5 + 0-1. (b) + 0-8%. (c) +0-8%. (d) + 3 Ω. (a) 5%. (b) No. (c) 5%. (d) 5%. (e) No. (f) 10%. (g) 10%.