Significant figures calculation involving both

Do the following calculations and use the correct number of significant figures in your answers. Assume aU numbers are the results of measurements. In calculations involving both addi-tion/subtraction and multiphcation/division, it is usually better to do additions/subtractions first. 

In calculations involving both multiplication/division and addition/subtraction, we do the steps in parentheses first determine the correct number of significant figures in the intermediate answer then do the remaining steps. 

SKILLBUILDER 2.7 Significant Figures in Calculations Involving Both Multiplication/Division and Addition/Subtraction... 

What limits the munber of significant digits in a calculation involving only addition and subtraction How are significant figures determined in calculations involving both addition/subtraction and multiplication/ division ... 

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. 

Thus, the 2.54 in the equation should not be interpreted as a measured number with three significant figures, hi calculations involving conversion between in and cm, we treat both 1 and 2.54 as having an infinite number of significant figures. Similarly, if an object has a mass of 5.0 g, then the mass of nine such objects is... 

Figure 5 presents an example of the excitation probability S (v) and the VDOS D (v) for the iron atom in the molecule Fe(TPP)(l-MeIm)(CO), as determined from measurements on a polycrystalline sample. Sharp features in both representations of the experimental data clearly identify vibrational frequencies above 100 cm, although low-frequency vibrational features are more apparent in the VDOS representation. The VDOS also provides the most convenient estimate of the mode composition factor ej, since the area of each feature directly yields the sum of values for all contributing vibrations. This avoids the need to remove the additional factors in equation (5) that contribute to the area of a feature in S (v), with the subtleties associated with determining an appropriate value for the recoilless fraction Z. However, calculation of D (v) from S (v) involves implicit assumptions that may not be valid in some situations, for example, when more than one molecular species contributes to the experimental signal or when vibrational anisotropy is significant. 

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