Measured numbers, significant

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. 

The bacterial and mammalian cell assays for gene mutation were developed to measure statistically significant increases in the numbers of mutant colonies derived from rare events many millions of exposed cells must be plated out to allow the assessment of mutation frequency. The Salmonella typhimurium reverse mutation assay ( Ames test) is carried out in a variety of different mutant strains selected to identify the various classes of mutation. The test generates many hundreds of Petri dishes for counting and is not practical for profiling. 

In addition to the rules cited above, there is another full set of rules to be followed for significant figures when two or more measured numbers are subtracted, added, divided, or multiplied. These rules are summarized in the appendix of the Conceptual Chemistry Laboratory Manual. 

The external electric field is in the direction of the pore axis. The particle is driven to move by the imposed electric field, the electroosmotic flow, and the Brownian force due to thermal fluctuation of the solvent molecules. Unlike the usual electroosmotic flow in an open slit, the fluid velocity profile is no longer uniform because a pressure gradient is built up due to the presence of the closed end. The probability of the particle position is obtained by solving the Fokker-Planck equation. The penetration depth is found to be dependent upon the Peclet number, which is a measure of significance of the convective electroosmotic flow relative to the Brownian diffusion, and the Damkohler number, which is a ratio of the characteristic diffusion-to-deposition times. 

Round off the measured number 2,997,215.548 to nine significant digits. 

Round off the measured number in problem 15 to eight, seven, six, five, four, three, two, and one significant digits. 

Significant figures Digits that indicate the precision of measurements— digits of a measured number that have uncertainty only in the last digit. 

If the characteristic linear dimension of the flow field is small enough, then the measured hydrodynamic data differ from those predicted by the Navier-Stokes equations [79]. With respect to the value in macrocharmels, in microchannels (around 50 microns of section) (i) the friction factor is about 20-30% lower, (ii) the critical Reynolds number below which the flow remains laminar is lower (e.g., the change to turbulent flow occurs at lower linear velocities) and (iii) the Nusselt number, for example, heat transfer characteristics, is quite different [80]. The Nusselt number for the microchannel is lower than the conventional value when the flow rate is small. As the flow rate through the microchannel is increased, the Nusselt number significantly increases and exceeds the value for the fully developed flow in the conventional channel. These effects have been investigated extensively in relation to the development of more efficient cooling devices for electronic applications, but have clear implications also for chemical applications. 

Recording numerical data - write down only those numbers that can be justified by your measurement technique (significant figures). 

Feret s Diameter A statistical particle diameter the length of a line drawn parallel to a chosen direction and taken between parallel planes drawn at the extremities on either side of the particle. This diameter is thus the maximum projection of the particle onto any plane parallel to the chosen direction. The value obtained depends on the particle orientation thus, these measurments have significance only when a large enough number of measurements are averaged together. See also Martin s Diameter. 

Three of the burner settings were varied in the experiments air distribution between primary and secondary ducts (air ratio, AR, expressed as frachon of secondary air over the total air flow rate) and the swirl numbers of both air streams (SI and S2, respectively both reported here as a percentage with respect to maximum swirl level). Detailed in-flame measurements revealed significant changes in the distribution of species and temperatures inside the flame when AR, SI, or S2 were varied... 

A continuous 26-day unattended run with diesel containing 20 mg/kg sulfur was performed to test the long term stability. No calibration checks or recalibrations were done. Figure 5 shows the plot obtained of sulfur readout versus measurement number. It is seen that the long term stability is excellent, with no significant up or down drift. Since drift is negligibly small, the standard deviation of all the measurements (sigma = 0.17 mg/kg S) is another indicator of the precision at 20 mg/kg sulfur. 

Rule 1 applies here. Every nonzero digit of a measured number is significant. We must assume that the last digit is an estimate and reflects the uncertainty of the measurement. 

NOE studies predict long residence times, of the order of 300-500 ps, for water molecules in the hydration layer. Such long residence times can be appropriate only for water molecules strongly bound to the cavity of a protein. In fact, these initial estimates from NOE have not been properly explained even today. It was pointed out recently by Halle that all earlier NOE measurements derived significant contributions from distant water molecules as well, because the number of contributing water molecules increases as and the characteristic time for orientational modulation of the intemuclear vector also increases as 1. Thus, earlier estimates from NOE might not be reliable for the residence time of the water molecules. 

For those experimental techniques that yield rate constants, it is important to establish, for each measurement, the significance of the measured rate constant, namely the conditions under which it can be expected to be valid. The fact that a number has been obtained for a rate constant for a particular set of conditions does not necessarily imply that it can be applied willy-nilly to any other set of conditions. For example, rate constants measured by high-pressure mass spectrometry can differ from those obtained by low-pressure measurements (see Section 3.4.2). 

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