Same percentage rule

A similar false rejection problem arises when multichannel instrument systems are controlled using the I2J rule on each of several channels. For one control material being analyzed by 4, 8, 12, and 20 channels, the chances that the control value on at least one channel exceeds its 2s limits are 18%, 33%, 46%, and 64%, respectively. Such a high rate of values exceeding the control limits may cause the same percentage of work to be routinely repeated, obviously compromising the efficiency of the laboratory and increasing its costs. 

If Q = a - b, then the same rule applies for calculating the possible error, i.e., the total possible error in Q is the possible error in a plus the possible error in b. Thus, if we wished to estimate the height of the pot lid from the difference between the total height of the vessel plus lid and the vessel alone, it would be 0.5 0.2 cm, which represents a significant percentage error ( 40%), and demonstrates that this is a poor way of estimating the height of the lid. 

The CMC of this new surfactant is several orders of magnitude lower than the CMC of its parent species. Figure 15 indicates a typical CMC plot versus the composition of the anionic-cationic (e.g., dodecyl sulfate-tetradecyl trimethyl ammomnium chloride) mixture in water. It can be seen that the CMCs of the anionic and cationic species are quite high, e.g., around 0.1 wt. %. As soon as a very small percentage of cationic is added to an anionic solution, the CMC falls several orders of magnitude. The same happens when a very small amount of anionic is added to a cationic solution. In both cases it seems that an equimolar catanionic species forms, and that its very low CMC dominates the mixing rule [84]. 

By the approximate rule, the answer should be 1.1 (two significant figures). However, a difference of 1 in the last place of 9.3 (9.3 0.1) results in an error of about 1 percent, while a difference of 1 in the last place of 1.1 (1.1 0.1) yields an error of roughly 10 percent. Thus the answer 1.1 is of much lower percentage accuracy than 9.3. Hence in this case the answer should be 1.06, since a difference of 1 in the last place of the least exact factor used in the calculation (9.3) yields a percentage of error about the same (about 1 percent) as a difference of 1 in thelastplaceof 1.06 (1.06 0.01). Similarly, 0.92 x 1.13 = 1.04. 

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