Quotients significant figures

Count the number of significant figures in the numerator and in the denominator the smaller of these two numbers is the number of significant figures in the quotient... 

Multiplying or dividing Round the product or quotient so that it has the same number of significant figures as the least-precise measurement — the measurement with the fewest significant figures. 

Following the rules of significant-figure math, the first step yields 24.4 feet-1-5.02 feet-1.348 feet. Each product or quotient contains the same number of significant figures as the number in the calculation with the fewest number of significant figures. 

Multiplication or division. The product or quotient should be rounded off to the same number of significant figures as the least accurate number involved in the calculation. Thus, 0.00296 x 5845 = 17.3, but 0.002960 x 5845 = 17.30. However, this rule should be applied with some discretion. For example, consider the following multiplication ... 

Multiplication and division The product or quotient can have no more significant figures than the number with the smallest number of significant figures used in the calculation. 

This equation says that the ratio of the proportions of nucleophilicity that are present in the A and B parameters may be obtained from the parameters for any solvent by subtracting the contribution of ionizing power from each (A and B) and dividing. Although the y values depend on the assigned value of the ratio, R, as do the yly ratios (equation 6), the quotient in equation 7 is, remarkably, independent of the y values, within the error limits posed by significant figures. Sample calculations have confirmed this result. A proof that this statement is correct comes from an alternative way to get the ratio. 

Divide the first dividend by the first trial divisor, and the first significant figure in the quotient will be the second significant of the root. Thus starting from the old equation (1), whose root-we know to be about 1. 

However, since the least number of significant figures in the data is two in 0.0021, the product and quotient should be rounded to two significant figures. 

Most calculators would say 0.66666666. If the 2 and 3 were experimentally determined numbers, this quotient would imply far too many significant figures, none... 

In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. The following examples illustrate this rule ... 

The first uncertain figure of the answer is the last significant figure. For example, in the quotient... 

Figure 3.9 Mass-volume data for a sample of cooking oil. (a) The third column is the result of dividing the measured mass by the measured volume. All quotients are rounded to the number of significant figures justified by the data, (b) The slope of the line between any two points, A and B, on the line, Am/AV, is the density of the oil. Notice that the slope of the line of the plot in part (b) is the same as the mass/volume ratio in the third data column in part (a). 

In multiplication and division, the following rule should be used to determine the number of significant figures in the answer The product or quotient should contain the number of significant digits that are contained in the number with the fewest significant digits. For example, the product... 

This is a good time to remind ourselves of the significance of the reaction quotient, Q, for a system that is not at equilibrium. (Section 15.6) Recall that when Q < K, there is an excess of reactants relative to products and the reaction proceeds spontaneously in the forward direction to reach equilibrium, as noted in Figure 19.17. When Q > K, the reaction proceeds spontaneously in the reverse direction. At equilibrium Q = K. 

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