CSA 2234.3-89 pdf download – Guide for the Selection and Use of Preferred Numbers.
4.4 Derived Series Derived series are distinguished by the symbol of the corresponding basic series followed by a solidus and the appropriate number (2,3,4, …p). Mention must be made of at least one of the terms to avoid ambiguity. Example: R10/3 means any of three possible R10/3 derived series. R10/3 (…80…) designates that which includes the number 80. 4.5 Shifted Series A shifted series is designated in the same way as a basic or more-rounded series with the addition (in parentheses) of one of its terms, eg, R5 (…2.24…). 5. Characteristics of Preferred Numbers 5.1 General In any calculations involving preferred numbers it must be kept in mind that preferred numbers deviate slightly from their theoretical values. To minimize the buildup of errors, it is recommended that the theoretical values be used in order to keep the result within the required range. values but to go back to the theoretical values, manipulate as required, and then round the results. Note: See Appendix A for further treatment of rounding and precision. In performing mathematical operations, the user is advised not to base calculations on rounded 5.2 Significant Characteristics Significant characteristics include the following: (a) Each term in a series differs from the term preceding it by a constant factor. (b) The logarithms of the terms in a series form an arithmetic series; that is, their terms differ by a constant increment. The mantissae of the theoretical values of the terms in the R5 series differ by 2000, in the R10 series by 1000, in the R20 series by 0500, in the R40 series by 0250, and in the R80 series by 0125. 5.3 Sums In general, the sum or difference of two preferred numbers will not be a preferred number. When it is a preferred number, it will usually be found only in a higher series than the one in which the addends first appear. 5.4 Products The product or quotient of two or more preferred numbers is also a preferred number: it will be an exact value if theoretical values are used and an approximate value if preferred numbers or more-rounded values are used. 5.5 Powers The integral positive or negative power of a preferred number will be another preferred number. 5.6 Some Other Characteristics 5.6.1 The series I31013 (…0.125,0.25,0.5, 1 ,2,4,8, 1 6,31 .5 …) is very nearly the series of the negative and positive integral powers of 2.
5.6.2 Just as the terms of the R10 series approximately double every three terms, the terms of the R20 series double every six terms, and those of the R40 series double every 12 terms. 5.6.3 For the R10 series, it should be noted that ‘,%is equal to , E, to an accuracy closer than 1 in 1000. Therefore the cube of a number of this series is approximately equal to double the cube of the preceding number. In other words, the nfh term is approximately double the (n – 3)fh term. Owing to rounding, they are usually related by a factor of 2 exactly. 5.6.4 Squaring the terms of the R1 0 series produces an R5 series (approximately; it is exact for the theoretical values). This relationship also holds true for R20 to R10, R40 to R20, etc. 5.6.5 In all but the R5 series, the number 3.15, which is equal to the value of z, to an accuracy better than 0.3%0, can be found among the preferred numbers. It follows that if a circle’s diameter is a preferred number, its circumference and area may also be expressed with good accuracy by preferred numbers. This also applies to peripheral speeds, cutting speeds, cylindrical areas and volumes and spherical areas and volumes. It should be noted that 3.15 is also closer than 0.4% to the value of G.CSA 2234.3-89 pdf download.
