Significant figures calculation with

Finally, it is important to note that the precision of quantities is often not arbitrary. Measuring tools have limits on the precision of measurement. Such measures will have a particular number of significant figures. Calculations with measurements may not result in an increase in the number of significant figures. There are two rules to follow to determine the number of significant figures in the result of calculations ... 

The mass accuracy of LSIMS for measurement of the unresolved isotopic cluster is typically within 100 p.p.m. of the calculated average [M+H]+ mass. The accuracy of the observed masses listed in Tables I and II for the MALDI mass spectra benefited from the use of a reflectron instrument which generally reduced the deviation observed between spectra measured under different experimental conditions (e.g. different matrix or laser power) from 1000 p.p.m. to 300 p.p.m. Reflecting this level of mass accuracy we present the MALDI measurements with only 4 significant figures, compared with 5 significant figures for the LSIMS measurements. 

Step 6 Calculate your answer and report it to the correct significant figures and with the correct unit. 

Steps 5 and 6 If the units do not cancel to yield the desired unit, we do the necessary unit conversions to make them cancel. In this example, we need to convert 75 mL to L so that the volume units cancel. We finish the problem by calculating the answer and reporting it with the correct significant figures and with the correct unit. 

Careful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers also must be expressed in the desired units. The procedure we will use to convert between units in solving chemistry problems is called the factor-label method, or dimensional analysis. A simple technique requiring little memorization, the factor-label method is based on the relationship between different units that express the same physical qnan-tity. 

The results in.the following figure calculated with Eq. 15.3-7 show a significant decrease of thymine solubility with increasing pH until about pH = 4, beyond which the solubility remains approximately constant at 4.0 g/kg. 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

At 25°C, the Mark-Houwink exponent for poly(methyl methacrylate) has the value 0.69 in acetone and 0.83 in chloroform. Calculate (retaining more significant figures than strictly warranted) the value of that would be obtained for a sample with the following molecular weight distribution if the sample were studied by viscometry in each of these solvents ... 

Question. Calculate, to three significant figures, the wavelength of the first member of each of the series in the spectrum of atomic hydrogen with the quantum number (see Section f.2) n" = 90 and 166. In which region of the electromagnetic spectrum do these transitions appear ... 

Much of the additional material is taken up by what 1 have called Worked examples . These are sample problems, which are mostly calculations, with answers given in some detail. There are seventeen of them scattered throughout the book in positions in the text appropriate to the theory which is required. 1 believe that these will be very useful in demonstrating to the reader how problems should be tackled. In the calculations, 1 have paid particular attention to the number of significant figures retained and to the correct use of units. 1 have stressed the importance of putting in the units in a calculation. In a typical example, for the calculation of the rotational constant B for a diatomic molecule from the equation... 

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a quantitative sense, some degree of doubt. For example, a measurement of 8.12 inches implies tliat Uie actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantihes quantities tliat are known exactly (e.g., pure integers) have an infinite number of significant figures. 

Most measured quantities are not end results in themselves. Instead, they are used to calculate other quantities, often by multiplication or division. The precision of any such derived result is limited by that of the measurements on which it is based. When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. 

Atomic masses calculated in this manner, using data obtained with a mass spectrometer can in principle be precise to seven or eight significant figures. The accuracy of tabulated atomic masses is limited mostly by variations in natural abundances. Sulfur is an interesting case in point. It consists largely of two isotopes, fiS and fgS. The abundance of sulfur-34 varies from about 4.18% in sulfur deposits in Texas and Louisiana to 4.34% in volcanic sulfur from Italy. This leads to an uncertainty of 0.006 amu in the atomic mass of sulfur. 

The values for K, listed here have been calculated from pK, values with more significant figures than shown so as to minimize rounding errors. Values for polyprotic acids—those capable of donating more than one proton—refer to the first deprotonation. 

We ll see how they compare in time response simulations when we come back to this problem later in Example 5.7C. A point to be made is that empirical tuning is a very imprecise science. There is no reason to worry about the third significant figure in your tuning parameters. The calculation only serves to provide us with an initial setting with which we begin to do field or computational tuning. 

In practice, in numerical calculations with a computer, both rational and imtiooal numbers are represented by a finite number of digits. In both cases, then, approximations are made and die errors introduced in the result depend on the number of significant figures carried by the computer - the machine precision. In die case of irrational numbers such errors cannot be avoided. 

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