Integers, rounding

Furthermore, due to integer round-up, it may be necessary to use an even smaller At as noted below. 

In the problem above, we determined the percentage data from the chemical formula. We can determine the empirical formula if we know the percent compositions of the various elements. The empirical formula tells us what elements are present in the compound and the simplest whole-number ratio of elements. The data may be in terms of percentage, or mass or even moles. However, the procedure is still the same—convert each element to moles, divide each by the smallest, and then use an appropriate multiplier if necessary. We can then determine the empirical formula mass. If we know the actual molecular mass, dividing the molecular formula mass by the empirical formula mass, gives an integer (rounded if needed) that we can multiply each of the subscripts in the empirical formula. This gives the molecular (actual) formula, which tells what elements are in the compound and the actual number of each. 

A solution of the equation xn=l, where n is a positive integer, round-off error... 

Since the degrees of freedom must be an integer, the value of V obtained using equation 4.22 is rounded to the nearest integer. 

Diameter. The nominal diameter shall he the inside diameter of the shell in inches, rounded off to the nearest integer. For kettle rehoders the nominal diameter shall he the port diameter followed hy the shell diameter, each rounded off to the nearest integer. 

Round upwards to the nearest integer all fractional turns in the results. Next multiply this result by the desired turns ratio to determine the number of... 

In addition to the type description code there is also a shorthand that is used for classifying heat exchangers. The first element of the shorthand is the nominal diameter, which is the inside diameter of the shell in inches, rounded off to the nearest integer. For kettle reboilers and chillers ii emember the kettle has a narrow end and a fat end), the nominal diame-tci is the port diameter (the narrow end) followed by the shell diameter, each rounded off to the nearest integer. 

Fractional numbers can pose a problem, but should be rounded to the next integer. 

ROUND Converts a real argument to an integer vaiue by rounding... 

Figure 3.5. Factorial space. Numbers in circles denote process yields actually measured (initial data set) all other numbers are extrapolated process yields used for planning further experiments (assuming that the repeatability Sy = 0.1 all values are rounded to the nearest integer) the estimated yield of 108% shows that the simple linear model is insufficient.

Intervals were calculated using a method equivalent to rounding numbers to Integer values before assignment to Intervals. 

You should read Technical Support Note TS-230 Dealing with Numeric Representation Error in SAS Applications to learn more about SAS floating-point numbers and storage precision in SAS. Another good resource for rounding issues is Ron Cody s SAS Functions by Example (SAS Press, 2004). In short, whenever you perform comparisons on numbers that are not integers, you should consider using the ROUND function. 

We have seen that we must sometimes reduce the number of digits in our calculated result to indicate the accuracy of the measurements that were made. To reduce the number, we round off numbers other than integer digits using the following rules. 

Dividing each by 1.425 yields 1.000mol Fe for every 1.333mol O. This ratio is still not integral. Multiplying these values by 3 yields integers. (We can round off when a value is within 1 or 2% of an integer, but not more.)... 

This is still not a whole number ratio, since 1.333 is much too far from an integer to round off. Since 1.333 is about l, multiply both numbers of moles by 3 ... 

Hint 2. There is a way of using all of the data to obtain these three constants by taking each of the two sets of data and plotting the appropriate straight line for each. Round off your values of m and n to the nearest half integer. 

Each sector has specific requirements in terms of the number of primary samples that should be taken. Simple empirical rules which have been used in the past to determine the number of samples to be taken from a lot include n = -JN and n = 3 x / N (in each case, N is the total number of items in the lot). In both cases, n is rounded to the nearest integer. 

The reaction orders obtained from nonlinear analysis are usually nonintegers. It is customary to round the values to nearest integers, half-integers, tenths of integers, etc. as may be appropriate. The regression is then repeated with order(s) specified to obtain a revised value of the rate constant, or revised values of the Arrhenius parameters. 

Nominal Mass Mass of an ion or molecule calculated using the mass of the most abundant isotope of each element rounded to the nearest integer value and equivalent to the sum of the mass numbers of all constituent atoms [1]. 

In real life, other problems involving discrete variables may not be so nicely posed. For example, if cost is a function of the number of discrete pieces of equipment, such as compressors, the optimization procedure cannot ignore the integer character of the cost function because usually only a small number of pieces of equipment are involved. You cannot install 1.54 compressors, and rounding off to 1 or 2 compressors may be quite unsatisfactory. This subject will be discussed in more detail in Chapter 9. 

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