Uncertainty absolute

Recording a measurement provides information about both its magnitude and uncertainty. For example, if we weigh a sample on a balance and record its mass as 1.2637 g, we assume that all digits, except the last, are known exactly. We assume that the last digit has an uncertainty of at least 1, giving an absolute uncertainty of ... 

Thus, we report the volume and its absolute uncertainty as 19.984 0.008 mb. The relative uncertainty in the total delivered volume is... 

A propagation of uncertainty also helps in deciding how to improve the uncertainty in an analysis. In Example 4.7, for instance, we calculated the concentration of an analyte, obtaining a value of 126 ppm with an absolute uncertainty of 2 ppm and a relative uncertainty of 1.6%. How might we improve the analysis so that the absolute uncertainty is only 1 ppm (a relative uncertainty of 0.8%) Looking back on the calculation, we find that the relative uncertainty is determined by the relative uncertainty in the measured signal (corrected for the reagent blank)... 

Of these two terms, the sensitivity s uncertainty dominates the total uncertainty. Measuring the signal more carefully will not improve the overall uncertainty of the analysis. On the other hand, the desired improvement in uncertainty can be achieved if the sensitivity s absolute uncertainty can be decreased to 0.0015 ppm-i. 

Using Table 4.9, the absolute uncertainty in the concentration, Sc, is given as... 

The uncertainty in measured values expressed in units of the measurement. For example, a reaction velocity of 10.2 M/min is presumed to be valid to a tenth, and the absolute uncertainty is 0.1 M/min. See Relative Uncertainty... 

TRANSITION-STATE THEORY ABSOLUTE TEMPERATURE ABSOLUTE UNCERTAINTY RELATIVE UNCERTAINTY ABSOLUTE ZERO ABSORBANCE... 

The tools that we have to determine the age of the solar system and the chronology of early solar system materials are the long-lived and short-lived radiochronometers discussed in Chapter 8. The long-lived radionuclides tell us that the oldest objects in the solar system formed at -4.5-4.6 Ga (Fig. 9.8). But the precision of most of these measurements is not sufficient to investigate the details of those early times. In addition, there are uncertainties in the half-lives of the different radionuclides that translate into absolute uncertainties of several million to tens of millions of years. Short-lived radionuclides provide the time resolution necessary to unravel the details of early solar system history. 

Several isotope systems indicate that CAIs are the oldest objects to have formed in the solar system. Cosmochemists have adopted their formation age as the age of the solar system. Based on a combination of data from the Pb-Pb and 182H-182W systems (see below), we assign an age for the CAIs of 4568.2 0.5 Ma. To this precise age, we must add an absolute uncertainty of -0.2% (9 Myr at the age of the solar system) because of... 

Equation 6.34 shows that the absolute uncertainty in absorbance is proportional to the combination of relative uncertainties in the intensities I0 and I. 

Absolute uncertainty expresses the margin of uncertainty associated with a measurement. If the estimated uncertainty in reading a calibrated buret is 0.02 mL, we say that 0.02 mL is the absolute uncertainty associated with the reading. 

Relative uncertainty compares the size of the absolute uncertainty with the size of its associated measurement. The relative uncertainty of a buret reading of 12.35 0.02 mL is a dimensionless quotient ... 

For addition and subtraction, the uncertainty in the answer is obtained from the absolute uncertainties of the individual terms as follows ... 

First convert absolute uncertainties into percent relative uncertainties. 

For addition and subtraction, use absolute uncertainty. Relative uncertainty can be found at the end of the calculation. 

First work out the difference in the numerator, using absolute uncertainties. Thus,... 

The first digit of the absolute uncertainty is the last significant digit in the answer. Fo example, in the quotient... 

Convert absolute uncertainty info percent relative uncertainty for multiplication. 

You should not work with percent relative uncertainty [100 X (ejx)J in calculations with logs and antilogs, because one side of Equation 3-8 has relative uncertainty and the other has absolute uncertainty. 

Now consider y = antilog x, which is the same as saying y = 10 In this case, the relative uncertainty in y is proportional to the absolute uncertainty in x. 

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