Significant figures number

Significant figures are used to specify the uncertainty in a measured number or in a number calculated using measured numbers. Significant figures must be carried through calculations such that the implied uncertainty in the final answer is reasonable. 

Exact numbers, such as the stoichiometric coefficients in a chemical formula or reaction, and unit conversion factors, have an infinite number of significant figures. A mole of CaCb, for example, contains exactly two moles of chloride and one mole of calcium. In the equality... 

Indicate how many significant figures are in each of the following numbers. 

Round each of the following to the stated number of significant figures. 

Report results for the following calculations to the correct number of significant figures. 

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. 

Note that for now we keep enough significant figures to match the number of decimal places to which the signal was measured. The resulting calibration curve is shown in Figure 5.10. 

Note that seven figures are retained in the calculation until the final stage, when the numbers are rounded to six significant figures. 

Be careful to use the necessary number of significant figures for the molar masses.) For... 

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 ... 

Note that five significant figures have been retained for the reciprocals of the squares of the quantum numbers because, as you can see in the calculation, two of these figures are lost when the reciprocals are subtracted. 

Note that the values given for Wq limit the number of significant figures to four for H2 and to three for F2 and I2. 

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... 

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.)... 

For releases to any medium that amount to 1,000 pounds or more forthe year, you must provide an estimate in pounds per year in column A.2. Any estimate provided in column A.2 should be reported to no more than two significant figures. This estimate should be in whole numbers. Do not use decimal points. 

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. 

Frequently we need to know the number of significant figures in a measurement reported by someone else (Example 1.2). 

The number of significant figures is the number of digits shown when a quantity is expressed in exponential notation. 

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. 

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... 

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