Decimation

Common Block (Decimal Words) System Type Key N=2 N=3 N=4 N=6... 

Density is generally measured at 15°C using a hydrometer in accordance with the NF T 60-101 method it is expressed in kg/1 with an error of 0.0002 to 0.0005 according to which category of hydrometer is utilized. However, in practice only three decimal places are usually retained. 

D-CTViewer allows to create up to three different Isosurfaces inside the data volume with each having different color and transparency value. The number of polygons inside the Isosurface hull can be decimated using a special polygon reduction tool (Fig. 5). 

The calculation proceeds as illustrated in Table 2.2, which shows the variation in the coefficients of the atomic orbitals in the lowest-energy wavefunction and the energy for the first four SCF iterations. The energy is converged to six decimal places after six iterations and the charge density matrix after nine iterations. 

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

The format markers in Eile 4-lb are at intervals of five spaces each. Thus the entire file might be thought of as a 10 x 67 matrix with row 1 containing the integers 6 and 4 in columns 65 and 67 and zeros elsewhere. (In EORTRAN, a blank is read as a zero.) Row 5 has the floating point number 2. in columns 4 and 5. Both the 2 and the. (decimal point) occupy a column. Row 5 column 35 contains the integer 2 and so on. 

Though individual atoms always have an integer number of amus, the atomic mass on the periodic table is stated as a decimal number because it is an average of the various isotopes of an element. Isotopes can have a weight either more or less than the average. The average number of neutrons for an element can be found by subtracting the number of protons (atomic number) from the atomic mass. 

Twaddell Hydrometer. This hydrometer, which is used only for liquids heavier than water, has a scale such that when the reading is multiplied by 5 and added to 1000 the resulting number is the specific gravity with reference to water as 1000. To convert specific gravity at 60°/60°F to Twaddell degrees, take the decimal portion of the specific gravity value and multiply it by 200 thus a specific gravity of 1.032 = 0.032 X 200 = 6.4° Tw. See also special table for conversion to density and Baume scale. 

A common logarithm, in general, consists of an integer, which is called the characteristic, and a decimal (usually endless), which is called the mantissa. The characteristic of any number may be determined from the following rules ... 

Rule I. The characteristic of any number greater than 1 is one less than the number of digits before the decimal point. 

Rule II. The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing —10 after the result. 

Mantissa of a Common Logarithm of a Number. An important consequence of the use of base 10 is that the mantissa of a number is independent of the position of the decimal point. Thus 93 600, 93.600, 0.000 936, all have the same mantissa. Hence in Tables of Common Logarithms only mantissas are given. A five-place table gives the values of the mantissa correct to five places of decimals. 

When connecting numbers to logarithms, use as many decimal places in the mantissa as there are significant digits in the number. 

When finding the antilogarithm, keep as many significant digits as there are decimal places in the mantissa. 

Molecular Identification. In the identification of a compound, the most important information is the molecular weight. The mass spectrometer is able to provide this information, often to four decimal places. One assumes that no ions heavier than the molecular ion form when using electron-impact ionization. The chemical ionization spectrum will often show a cluster around the nominal molecular weight. 

A saturated aqueous solution in contact with an excess of a definite solid phase at a given temperature will maintain constant humidity in an enclosed space. Table 11.4 gives a number of salts suitable for this purpose. The aqueous tension (vapor pressure, in millimeters of Hg) of a solution at a given temperature is found by multiplying the decimal fraction of the humidity by the aqueous tension at 100 percent humidity for the specific temperature. For example, the aqueous tension of a saturated solution of NaCl at 20°C is 0.757 X 17.54 = 13.28 mmHg and at 80°C it is 0.764 X 355.1 = 271.3 mmHg. 

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. 

The standard deviation about the regression, Sr, suggests that the measured signals are precise to only the first decimal place. For this reason, we report the slope and intercept to only a single decimal place. 

Much of modem life revolves around the use of the decimal system of numbers, although for many purposes it is far from ideal. This system (dec = ten) takes 10 as the basic unit of operation, and we say that we are working to base 10. However, the base 10 is not the only one possible the previous British and many other countries coinage was founded on a base of 12. The meaning of a base for purposes of calculation is illustrated in Figure 42.1. 

In the next column, there are one seven (not one ten, as with decimal 17) and two sevens (from the 24), making a total of three sevens the total number of sevens is then 3 + 1 (carried from the previous column) = 4, and this is written down. Thus, the total obtained from the addition of 17 and 24 in the two systems is 41 in one and 44 in the other Which is correct In fact, we have cheated a little because 17 (decimal) written in the heptimal system should be two sevens and a... 

Addition of two decimal numbers. Note the carryover of one ten from the rightmost column into the left one. 

The above results appear most confusing, but only if the bases are mixed. Working with one base all the time (e.g., decimal), there is no confusion. 

Note The sequence of columns in binary runs 1,2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096 and so on, each column being two times greater than the previous one. Compare this with the decimal system where each column is 10 times greater than the previous one. 

To convert 1001 into a decimal number we have to take 1 x 8 plus 0 x 4 plus 0x2 plus 1 X 1 which is 9 (decimal). Conversion of 3265 into binary is a little more difficult the largest binary number near 3265 is 2048 (or 2") and there is only one of them with 1217 left over the next largest binary number is 1024 (or 2 °), leaving 193 the next binary number is 128 (or 2 ) and then 64 (2 ) and 1 (2°). Thus, the binary equivalent of 3265 is 110011000001. 

What is the binary equivalent of decimal 5 The largest power of 2 which fits 5 is 2 = 4. Therefore there is 1 x 2 in 5 with 1 left over 2 = 2 which is too big and so we write 0x21 finally we see that 1 x 2° = 1. The number 5 is made up from a 1 x 2 and a 1 X 2° = 1 but in binary we must not forget to put 0 x 2 in decimal we may write 304 meaning three hundred and four and if the 0 had been omitted then the number would have been thirty four (34). Thus, the binary equivalent of 5 is 101 and not 11. Other numbers may be converted into binary in an exactly similar fashion. Decimal 39 is ... 

To convert a decimal number into binary, it is necessary to look at the powers of 2 as described in Figure 42.3. Decimal numbers corresponding to ascending powers of 2 are shown here, up to 2 . Each number is just twice the previous one. 

There is an electronic circuit called a flip-flop. It consists of two transistors connected in such a way that, if a voltage is applied, one side of the circuit becomes active and the other side not if a second voltage is applied, the circuit flips so that the active side becomes inactive and vice versa. Thus, just as with a conventional switch for which one touch puts it on and a second touch turns it off, one touch of the flip-flop turns it on and a second touch turns it ojf. Addition of two binary numbers now becomes possible. Suppose we want to add 2 -(- 1 (= 3 decimal). First, the numbers must be converted into binary code (10 and 01) and these become switch settings in the machine, but we need four switches so that 10 becomes on, off and 01 becomes off, on (Figure 42.6). 

If the first pair of switches is examined, one is off and the other on, and the result of touching each must be a resulting on (off-on and on-off, giving a total of on). For the other pair, exactly the opposite sequence is present but the net result is on. As far as the machine is concerned, the result is on, on, which in binary code is 11 and in decimal code is 3, the correct answer. Therefore, to get the machine to add in binary, it is necessary to have a switch for each power of two that we want. The number 2 is 64 (decimal) and, to represent any number up to 63, we must have seven switches (seven flip-flop circuits), viz., 2, 2, 2, 2, 2 , and zero. In computer jargon, these... 

An electronic switching circuit can be on or ojf, and these positions are used to represent the two basic binary numbers 1 and 0, respectively. Decimal 2 is 10 in binary (switch settings on, off), and decimal 1 is 01 in binary (switch settings off, on). 

Two decimal numbers (17, 24) represented in binary bits in an x-register ((WlOOOl) and a y-register (0011000). Addition into the a-register gives OlOlOOl, which translates as 41 (decimal). 

A mass spectrometer that can measure mass accurately to several decimal places (rather than just to the nearest integer) can be used to measure such differences. 

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