Number exact

Exact numbers have an unlimited number of significant figures. Exact mmibers originate from three somces  

100cm = 1 m means 100.00000... cm = 1.0000000... m Note that some conversion factors are defined quantities whereas others are not. 

The 3 and the 5 are significant (rule 1). The leading zeros only mark the decimal place and are not significant (rule 5). SOLUTION (a) 0.0035 two significant figures 

The interior zero is significant (rule 2), and the trailing zero is significant (rule 3). The 1 and the 8 are also significant (rule 1). (b) 1.080 four significant figures 

All digits are significant (rule 1). (c) 2371 four significant figures 

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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... 

Chemical compounds having odor and taste number in the thousands. In 1969 a description of the odor characteristics of more than three thousand chemical compounds used in the flavor and perfume industries were described (41). The Hst of volatile compounds found in food that may contribute to odor and taste is even larger (42), and the Hst of all possible flavor compounds, including those that have yet to be synthesized, is greater than a thousand. Many different compounds have the same flavor character or quaUty, differing perhaps in their relative intensity but indistinguishable in the type of flavor they ehcit. The exact number of different flavor quaUties is not known, but it appears to be much less than the total number of compounds with flavor. 

Many organisms are exposed to some of the thermal, chemical, and physical stresses of entrainment by being mixed at the discharge with the heated water this is plume entrainment. The exact number exposed depends on the percentage of temperature decline at the discharge that is attributed to turbulent mixing rather than to radiative or evaporative cooling to the atmosphere. 

Temperature and pressure represent two of the major parameters measured and evaluated in a monitoring system. All gas turbine engines are equipped with sensors of this type however, the exact number as well as their location varies considerably among manufacturers. 

The neuraminidase molecule is a homotetramer made up of four identical polypeptide chains, each of around 470 amino acids the exact number varies depending on the strain of the virus. If influenza virus is treated with the proteolytic enzyme pronase, the head of the neuraminidase, which is soluble, is cleaved off from the stalk projecting from the viral envelope. The soluble head, comprising four subunits of about 400 amino acids each, can be crystallized. 

Since we need to find both triplet and singlet excited states, we ve included the 50-50 option to the CIS keyword. We ve asked for two states of each type, the exact number we require for this well-studied system. When examining new systems, however, it s often a good idea to request slightly more states than you initially want to. allow for degenerate states and other unexpected results. 

Some typical errors in heat of formation for the MNDO, AMI and PM3 methods are given in Table 3.1. The exact numbers of course depend on which, and how many, compounds have been selected for comparison, thus the numbers should only be taken as a guideline for the accuracy expected. Some typical errors in bond distances are given in Table 3.2. 

Blending catalyst, dye or additive into a viscous fluid Laminar Usually 10-14. The exact number of elements will depend on the viscosity ratio. 

The previous discussion has shown us how to calculate the total number of possible cyclic states. We also know, from Lemma 2, that all cycle lengths must divide the maximal cycle length Hiv obtain the exact number of distinct cycles and their lengths takes a little bit more work. If flw prime, we know that the only possible cyclic lengths are 1 and It can then be shown that only the null configuration is a fixed point unless N is some multiple of 3, it which case there are exactly four distinct cycles of length one. If Hat i ot prime, there can exist as many cycles as there are divisors of Although there is no currently known closed form... 

A different type of exact number arises in certain calculations. Suppose you are asked to determine the amount of heat evolved when one kilogram of coal burns. The implication is that because one is spelled out, exactly one kilogram of coal bums. The uncertainty in the answer should be independent of the amount of coaL... 

Stoichiometric coefficients are exact numbers so they do not limit the significant figures of stoichiometric calculations (see Appendix 1C). 

Integers and exact numbers In multiplication or division by an integer or an exact number, the uncertainty of the result is determined by the measured value. Some unit conversion factors are defined exactly, even though they are not whole numbers. For example, 1 in. is defined as exactly 2.54 cm and the 273.15 in the conversion between Celsius and Kelvin temperatures is exact so 100.000°C converts into 373.150 K. 

When exact numbers are used, their presence has no effect on the significant figures in the result. For example, we can convert 1.855 hours into seconds. 

While an exact number of site clusters has not been proposed, the authors consider from approximately 3 to 10 clusters of sites to be appropriate. These clusters should represent different ecoregions with different ecological characteristics as well as different loadings (both in amount and source) of mercury deposition. Care should be taken to monitor different types of water bodies and watersheds (e.g., seepage lakes, drainage lakes, old reservoirs, rivers, and estuaries). Areas that should be considered as potential cluster site locations include lakes in northern New England/the Adirondacks, lakes in the upper Midwest, rivers and streams in the southeastern coastal plain, lakes in south-central and southeastern Canada, western... 

Although it is desirable to collect the sample from as many locations as possible in order to obtain a representative value, the exact number of sampling points can be determined in context with a field size or a waterway width. 

While no exact numbers are available, conjunctivitis, which is also known as red eye, is one of the most common ophthalmic complaints seen by general clinicians. An inflamed conjunctiva is the most common cause of red eye.10 Use the differential diagnosis algorithm shown in Fig. 60-1 to determine the proper treatment or need for referral. 

Anisotropic materials have different properties in different directions (1-7). 1-Aamples include fibers, wood, oriented amorphous polymers, injection-molded specimens, fiber-filled composites, single crystals, and crystalline polymers in which the crystalline phase is not randomly oriented. Thus anisotropic materials are really much more common than isotropic ones. But if the anisotropy is small, it is often neglected with possible serious consequences. Anisoiropic materials have far more than two independent clastic moduli— generally, a minimum of five or six. The exact number of independent moduli depends on the symmetry in the system (1-7). Anisotropic materials will also have different contractions in different directions and hence a set of Poisson s ratios rather than one. 

Alternatively, shorter, discrete crosslinkers containing PEG spacers of known chain length are now available (Thermo Fisher, Quanta BioDesign see Chapter 18). These reagents are designed to contain an exact number of PEG units, typically from between 2 repeating units... 

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