Significant figures, effects

Note that, since 5q is given, effectively, to six significant figures, the calculation has been done to seven figures and rounded to six at the final stage. 

The osmotic coefficient is often used as a measure of the activity of the solvent instead of a because a is nearly unity over the concentration range where 7 is changing, and many significant figures are required to show the effect of solute concentration on a. The osmotic coefficient also becomes one at infinite dilution, but deviates more rapidly with concentration of solute than does a. ... 

From analysis of the data in Figure 5 it is clear that the rate of PAC formation is fairly constant for the first 9 h to approx. 180 mM PAC and subsequently declines after this to reach a maximum value of 300 mM in 54 h. Unpublished studies by our group have shown no significant inhibition effects of PAC up to concentrations of 154 mM [13]. However, it is possible that appreciable inhibition could occur at higher PAC concentrations. Byproducts acetoin and acetaldehyde may also be inhibitory in the latter stages of the biotransformation although both concentrations were below 5 mM at 9 h. 

When exact numbers are used, their presence has no effect on the significant figures in the result. For example, we can convert 1.855 hours into seconds. 

Figure 6.3 Histamine release measured from the posterior hypothalamus of freely behaving cats across the sleep-wakefulness cycle. The histamine release was higher during wakefulness compared with non-REM and REM sleep in each experiment, producing a highly significant group effect. Each experiment is represented by a single line (n = 5). Adapted from Strecker et al. (2002), to which the reader is referred for more details.

Various blend ratios of polycarbonate and PBT polyester were flame retarded with the three flame retardants. These data are shown graphically in Figure 3. Brominated phosphate is the most efficient and brominated polycarbonate the least efficient flame retardant. At a 50/50 ratio of polycarbonate/PBT, brominated phosphate is significantly more effective than brominated polystyrene. 

We have expressed each result with an additional significant figure, written as a subscript, so that we can see the effect of rounding. With the beads available, we can produce 163 necklaces, since we are unable to produce a fraction of a necklace. 

In order to effectively utilize the stoichiometry of the reaction involved in a titration, both the titrant and the substance titrated need to be measured exactly. The reason is that one is the known quantity, and the other is the unknown quantity in the stoichiometry calculation. The buret is an accurate (if carefully calibrated) and relatively high-precision device because it is long and narrow. If a meniscus is read in a narrow graduated tube, it can be read with higher precision (more significant figures) than in a wider tube. Thus a buret provides the required precise measurement of the titrant. 

Polyacrylamide gel (PAG) electrophoresis is performed either in cylindrical glass tubes or in flat beds (Figure 3.27). The method is comparable with other electrophoretic techniques but care must be taken to keep the current low to prevent any significant heating effect. 

The reduced mass ratios agree exactly with Aston s to the five significant figures reported by Aston. An interesting result obtained in this study, where there was no longer any question abut zero-point energy, is the electronic isotope effect reported as 0.33 0.08 cm-1, a result which appears much more satisfactory than that obtained earlier by Mulliken. 

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