Significant figures value expression

I Apply rules for significant figures to express uncertainty in measured and calculated values. 

In addition and subtraction, all values must first be converted to numbers that have the same exponent of 10. The result is the sum or the difference of the first factors, multiplied by the same exponent of 10. Finally, the result should be rounded to the correct number of significant figures and expressed in scientific notation. 

In each example, the initial values of the factors are expressed in U.S. customary units, and the dimensionless value is calculated. Then the factors are converted to SI units, and the dimensionless value is recalculated. The two dimensionless values will be approximately the same. (Small variations occur due to the number of significant figures carried in the solution.)... 

In a sequence of computations, adjusting the number of significant figures in intermediate results can lead to errors in the final value. Instead, wait until the computations are complete, and then express the final value with the appropriate number of significant figures. 

This is a large value for a molar mass, but it is reasonable because biological molecules often are quite large. As in any calculation, be careful to express all data in appropriate units. The osmotic pressure was measured to two significant figures, so the result has two significant figures. 

Chemical equilibria often involve pure liquids and solids in addition to gases and solutes. The concentration of a pure liquid or solid does not vary significantly. Figure 16-4 shows that although the amount of a solid or liquid can vary, the number of moles per unit volume remains fixed. In other words, the concentrations of pure liquids or solids are always equal to their standard concentrations. Thus, division by standard concentration results in a value of 1 for any pure liquid or solid. This allows us to omit pure liquids and solids from equilibrium constant expressions. For a general reaction (2A + iBt= C D-l-. S where S is a pure solid or liquid ... 

Rather than solve this mathematically, one can solve this by successive approximation. Simply pick a value for x, plug into the above expression and see if you get the value of the Ksp. If your value is different (which it probably is), pick a higher or lower number. Keep going until you find x, in this case, to one significant figure. Start with x = 6 x 10-8. 

The numerical values of a, b, and c can be found by direct substitution in the algebraic expressions if care is taken to carry an apparently excessive number of significant figures through the calculations, which involve taking small differences between large numbers. Alternatively, the determinants in Equations (A.9)-(A.ll) can be evaluated by methods described in the references, or the linear equations, (A.6)-(A.8) can be solved by matrix methods (2). 

A modest value of E° produces a large equilibrium constant. The value of K is correctly expressed with one significant figure, because E° has three digits. Two are used for the exponent (14), and only one is left for the multiplier (4). 

A student weighs a beaker on a triple-beam balance, finding values of 50.32 g, 50.31 g, and 50.31 g in successive weighings. Express the average weight to the proper number of significant figures. 

The conversion factor for cubic feet to cub ic meters is normally 35.31. However, SCF is measured at 21.1 °C and Nm3 is measured at 0°C. Therefore the conversion factor must be adjusted for temperature. All values are rounded to the nearest four or five significant figures. Gas values are expressed in the stable hydrogen condition 75% ortho, 25% para 4I. 

Significant Figures When tolerance limits are expressed numerically, the values are significant to the number of digits... 

The factor 6 is a pure integer. Estimate the value of R without using a calculator, following the procedure outlined in Section 2.5b. Then calculate R, expressing your answer in both scientific and decimal notation and making sure it has the correct number of significant figures. 

The answer is correctly expressed to two significant figures. The solubility decreased as expected. The pressure on the solution was reduced from 4.0 atm to 1.0 atm, so the solubility should be reduced to one-fourth its original value, which it is. 

Because only a small mass of sodium chloride is dissolved per 100.0 g of water, the percent by mass should be a small value, which it is. The mass of sodium chloride was given with two significant figures, therefore, the answer also is expressed with two significant figures. 

The Kjp value has two significant figures, so the answer is correctly expressed with two digits. As predicted, the molar solubility of CUCO3 is approximately 10 mol/L. 

Values for pH are expressed with as many decimal places as the number of significant figures in the H+ ion concentration. Thus, the pH is correctly stated with two decimal places. As predicted, the pH value is 7.00. 

The values of pH and pOH are correctly expressed with two decimal places because the given concentration has two significant figures. As predicted, pOH is close to 3 and pH is close to 12. 

The purity and assay values are typically expressed with three significant figures. 

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