Digits, rounded significant

Not all the digits are significant. They are given to minimize round-off errors). 

Even in carefully designed and conducted experiments, there is no realistic possibility of determining PZCs/IEPs with accuracy better than 0.1 pH unit. This is due to the intrinsic properties of pH electrodes on the one hand and of dispersed systems on the other. Surface charging is always accompanied by other phenomena that affect the pH and that are unavoidable and difficult to control. Several authors (e.g., [23,71,100,232-234]) report their PZCs/IEPs with two decimal digits. This gives a false impression that the second digit is significant. Such results are rounded to the nearest one-tenth of pH unit in the present compilation. 

If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up the last significant figure. 

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. 

Previously published and 1994 data aie rounded off by the U.S. Bureau of Mines to three significant digits and may not add to totals shown. Table includes data available through July 5, 1995. 

The analyst can then calculate the total probability of failure (Ft) by summing the probability of all failure paths (Fi-s). The probability of a specific path is calculated by multiplying the probabilities of each success and failure limb in that path. Note The probabilities of success and failure sum to 1.0 for each branch point. For example, the probability of Error B is 0.025 and the probability of Success b is 0.975.) Table 5.2 summarizes the calculations of the HRA results, which are normally rounded to one significant digit after the intermediate calculations are completed. 

Table 6-1 lists the experimental quantities, k, T, ct, the transformed variables x, y, and the weights w. (It is necessary, in least-squares calculations, to carry many more digits than are justified by the significant figures in the data at the conclusion, rounding may be carried out as appropriate.) The sums required for the solution of the normal equations are... 

If the digits to be discarded are less than- -500. . . .leave the last digit unchanged. Masses of 23.315 g and 23.487 g both round off to 23 g if only two significant digits are required. 

The second significant digit in (underlined) corresponds to the third decimal place of Xmean- In reporting this result, one should round as follows ... 

Notice that a result of this type, in order to be interpretable, must comprise three numbers the mean, the (relative) standard deviation, and the number of measurements that went into the calculation. All calculations are done using the full precision available, and only the final result is rounded to an appropriate precision. The calculator must be able to handle >4 significant digits in the standard deviation. (See file SYS SUITAB.xls.)... 

Example 48 The result is thus CL(/4) = 7.390 0.028 mM/g, and should be either left as given or rounded to one significant digit in C1 7.39 0.03 The %-variance contributions are given in parentheses (Eq. (4.24)). Note that the analytical method with the best precision (titrimetry), because of the particular numerical constellation, here gives rise to the largest contribution (77%). 

The programmable calculator or PC that is to be used must be able to work with the number of significant digits required by the algorithm rounding the coefficients can appreciably alter the results of an approximation. 

Round, Column Width) permits the raw data presentation to be adjusted by choosing the number of significant digits to which the numbers are rounded to, see Presentation of Numbers below the column width is automatically adjusted. 

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