Significant figures definition

The integral of the Gaussian distribution function does not exist in closed form over an arbitrary interval, but it is a simple matter to calculate the value of p(z) for any value of z, hence numerical integration is appropriate. Like the test function, f x) = 100 — x, the accepted value (Young, 1962) of the definite integral (1-23) is approached rapidly by Simpson s rule. We have obtained four-place accuracy or better at millisecond run time. For many applications in applied probability and statistics, four significant figures are more than can be supported by the data. 

Note that the number of significant figures in the result is determined by the precision of the mass of 202Hg, because the mass of12C is established by definition as an exact number. 

By definition, the mole fraction of NaCl in this solution is = 0 2 35 2 = 0.0036. (Note the number of significant figures [see Section 13.4] reported here taking the density of the solution as 1, and calculating the weight of water therefore as 1000 g would not have affected this calculation. The density correction could, therefore, have been omitted. Also, as a rule of thumb, 1 liter of water can be approximated as 55 mol F O.)... 

We deal with two types of numbers in chemistry—exact and measured. Exact values are just that—exact, by definition. There is no uncertainty associated with them. There are exactly 12 items in a dozen and 144 in a gross. Measured values, like the ones you deal with in the lab, have uncertainty associated with them because of the limitations of our measuring instruments. When those measured values are used in calculations, the answer must reflect that combined uncertainty by the number of significant figures that are reported in the final answer. The more significant figures reported, the greater the certainty in the answer. 

Systematic Errors in Accurate Mass Measurements. 1. Problem Definitions The value of high resolution mass spectrometry is diminished if the mass measurements do not give unambiguous elemental compositions. Accurate mass measurements in FTMS require a precise measurement of ion frequencies and an accurate calibration law for converting ions frequencies to mass. The ion frequencies can be measured to nine significant figures with modern electronics however, the relationship between ion frequencies in the cubic cell and mass still requires further development. 

Some numerical values are exact to as many significant figures as necessary, by definition. Included in this category are the numerical equivalents of prefixes used in unit definition. For example, 1 cm = 0.01 m by definition, and the units conversion factor, 1.0 x 10-2 m/cm, is exact to an infinite number of significant figures. 

Exact numbers have no uncertainty and contain an infinite number of significant figures. These relationships are definitions. They are not measurements. 

Note that the centimeter units cancel to give inches for the result. This is exactly what we wanted to accomplish. Note also that the result has three significant figures, as required by the number 2.85. Recall that the 1 and 2.54 in the con- version factor are exact numbers by definition. 

Salinity and temperature are the primary factors that determine the density of seawater. The densities of most surface seawaters range from 1024 to 1028 kg m , and it is possible to evaluate density to about 0.01 of these units. In order to avoid writing numbers with many significant figures, density is usually presented as the Greek letter sigma, a, which has the following definition... 

The reciprocal of each of these is also a unit factor. Items in retail stores are frequently priced with unit factors, such as 39c/lb and 3.98/gal. When all the quantities in a unit factor come from definitions, the unit is known to an unlimited (infinite) number of significant figures. For instance, if you bought eight 1-gallon jugs of something priced at 3.98/gal, the total cost would be 8 X 3.98, or 31.84 the merchant would not round this to 31.80, let alone to 30. 

How do defined quantities affect significant figures Any quantity that comes from a deftnition is exact, that is, it is known to an unlimited number of significant figures. In Example 1-3, the quantities 5280 ft, 1 mile, 12 in., and 1 ft all come from definitions, so they do not limit the significant figures in the answer. 

The number of significant figures in the result is limited by the three significant figures in 97.6%. Because the definition of percentage involves exactly 100 parts, the number 100 is known to an infinite number of significant figures. 

Step 1 The table s length and the ant s velocity come from measurements, so 6.0 and 0.01 are not exact. The other numbers are exact because they are derived from definitions. Thus only 6.0 and 0.01 can limit our significant figures. 

The 10.5 comes from a measurement and has three significant figures. The 453.6 is calculated and rounded off. It has four significant figures. The 16 comes from a definition and is exact. We report three significant figures in our answer. 

Keep in mind that exact numbers obtained from definitions or by counting numbers of objects can be considered to have an infinite number of significant figures. If an object has a mass of 0.2786 g, then the mass of eight such objects is... 

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