Contents 1 Renard numbers 2 1-2-5 series 3 Convenient numbers 4 E-series 5 Paper documents, envelopes, and drawing pens 6 Computer engineering 7 Retail packaging 8 Photography 9 See also 10 References 11 Further reading


Renard numbers[edit] Main article: Renard series In 1870 Charles Renard proposed a set of preferred numbers.[2] His system was adopted in 1952 as international standard ISO 3.[3] Renard's system divides the interval from 1 to 10 into 5, 10, 20, or 40 steps, leading to the R5, R10, R20 and R40 scales, respectively. The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.


1-2-5 series[edit] In applications for which the R5 series provides a too fine graduation, the 1-2-5 series is sometimes used as a cruder alternative. It is effectively an R3 series rounded to one significant digit: … 0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1000 … This series covers a decade (1:10 ratio) in three steps. Adjacent values differ by factors 2 or 2.5. Unlike the Renard series, the 1-2-5 series has not been formally adopted as an international standard. However, the Renard series R10 can be used to extend the 1-2-5 series to a finer graduation. This series is used to define the scales for graphs and for instruments that display in a two-dimensional form with a graticule, such as oscilloscopes. The denominations of most modern currencies, notably the euro and British pound, follow a 1-2-5 series. The United States and Canada follow the approximate 1-2-5 series 1, 5, 10, 25, 50, 100 (cents), $1, $2, $5, $10, $20, $50, $100. The ¼-½-1 series (… 0.1 0.25 0.5 1 2.5 5 10 …) is also used by currencies derived from the former Dutch gulden (Aruban florin, Netherlands Antillean gulden, Surinamese dollar), some Middle Eastern currencies (Iraqi and Jordanian dinars, Lebanese pound, Syrian pound), and the Seychellois rupee. However, newer notes introduced in Lebanon and Syria due to inflation follow the standard 1-2-5 series instead.


Convenient numbers[edit] Main article: Convenient numbers In the 1970s the National Bureau of Standards (NBS) defined a set of convenient numbers to ease metrication in the United States. This system of metric values was described as 1-2-5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10), excluding linear dimensions above 100 mm.[1]


E-series[edit] Main article: E-series of preferred numbers The E-series is another system of preferred numbers. It consists of the E3, E6, E12, E24, E48, E96 and E192 series. Based on some of the existing manufacturing conventions, the International Electrotechnical Commission (IEC) began work on a new international standard in 1948.[4] The first version of this IEC 63 (renamed into IEC 60063 in 2007) was released in 1952.[4] It works similarly to the Renard series, except that it subdivides the interval from 1 to 10 into 3, 6, 12, 24, 48, 96 or 192 steps. These subdivisions ensure that when some arbitrary value is replaced with the nearest preferred number, the maximum relative error will be on the order of 40%, 20%, 10%, 5%, etc. Use of the E-series is mostly restricted to electronic parts like resistors, capacitors, inductors and Zener diodes. Commonly produced dimensions for other types of electrical components are either chosen from the Renard series instead or are defined in relevant product standards (for example wires).


Paper documents, envelopes, and drawing pens[edit] Main article: Paper size Standard metric paper sizes use the square root of two (√2) as factors between neighbouring dimensions rounded to the nearest mm (Lichtenberg series, ISO 216). An A4 sheet for example has an aspect ratio very close to √2 and an area very close to 1/16 square metre. An A5 is almost exactly half an A4, and has the same aspect ratio. The √2 factor also appears between the standard pen thicknesses for technical drawings (0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00 mm). This way, the right pen size is available to continue a drawing that has been magnified to a different standard paper size.


Computer engineering[edit] When dimensioning computer components, the powers of two are frequently used as preferred numbers: 1 2 4 8 16 32 64 128 256 512 1024 … Where a finer grading is needed, additional preferred numbers are obtained by multiplying a power of two with a small odd integer: 1 2 4 8 16 32 64 128 256 512 1024 … (×3) 3 6 12 24 48 96 192 384 768 1536 … (×5) 5 10 20 40 80 160 320 640 1280 … (×7) 7 14 28 56 112 224 448 896 1792 … Preferred aspect ratios 16: 15: 12:  :8 2:1 3:2  :9 16:9 5:3 4:3  :10 8:5 3:2  :12 4:3 5:4 1:1 In computer graphics, widths and heights of raster images are preferred to be multiples of 16, as many compression algorithms (JPEG, MPEG) divide color images into square blocks of that size. Black-and-white JPEG images are divided into 8×8 blocks. Screen resolutions often follow the same principle. Preferred aspect ratios have also an important influence here, e.g., 2:1, 3:2, 4:3, 5:3, 5:4, 8:5, 16:9.


Retail packaging[edit] In some countries, consumer-protection laws restrict the number of different prepackaged sizes in which certain products can be sold, in order to make it easier for consumers to compare prices. An example of such a regulation is the European Union directive on the volume of certain prepackaged liquids (75/106/EEC[5]). It restricts the list of allowed wine-bottle sizes to 0.1, 0.25 (1/4), 0.375 (3/8), 0.5 (1/2), 0.75 (3/4), 1, 1.5, 2, 3, and 5 litres. Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors 2/3 or 3/4, in some cases even 1/2, 4/5, or some other ratio of two small integers.


Photography[edit] In photography, aperture, exposure, and film speed generally follow powers of 2: The aperture size controls how much light enters the camera. It is measured in f-stops: f/1.4, f/2, f/2.8, f/4, etc. Full f-stops are a square root of 2 apart. Digital cameras often subdivide these into thirds, so each f-stop is a sixth root of 2, rounded to two significant digits: 1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, etc. The film speed is a measure of the film's sensitivity to light. It is expressed as ISO values such as "ISO 100". Measured film speeds are rounded to the nearest preferred number from a modified Renard series including 100, 125, 160, 200, 250, 320, 400, 500, 640, 800… This is the same as the R10′ rounded Renard series, except for the use of 6.4 instead of 6.3, and for having more aggressive rounding below ISO 16. Film marketed to amateurs, however, uses a restricted series including only powers of two multiples of ISO 100: 25, 50, 100, 200, 400, 800, 1600 and 3200. Some low-end cameras can only reliably read these values from DX encoded film cartridges because they lack the extra electrical contacts that would be needed to read the complete series. Some digital cameras extend this binary series to values like 12800, 25600, etc. instead of the modified Renard values 12500, 25000, etc. The shutter speed controls how long the camera records light. These are expressed as fractions of a second, roughly but not exactly based on powers of 2: 1 second, ​1⁄2, ​1⁄4, ​1⁄8, ​1⁄15, ​1⁄30, ​1⁄60, ​1⁄125, ​1⁄250, ​1⁄500, ​1⁄1000 of a second.


See also[edit] Nominal size Convenient number Nominal impedance Preferred metric sizes


References[edit] ^ a b Milton, Hans J. (December 1978). "The Selection of Preferred Metric Values for Design and Construction" (PDF). U.S. Government Printing Office. Washington, USA: The National Bureau of Standards (NBS). NBS Technical Note 990 (Code: NBTNAE). Archived (PDF) from the original on 2017-11-01. Retrieved 2017-11-01.  ^ "preferred numbers". Sizes, Inc. 2014-06-10 [2000]. Archived from the original on 2017-11-01. Retrieved 2017-11-01.  ^ ISO 3:1973-04 - Preferred numbers - Series of preferred numbers. International Standards Organization (ISO). April 1973. Archived from the original on 2017-11-02. Retrieved 2017-11-02.  (Replaced: ISO Recommendation R3-1954 - Preferred Numbers - Series of Preferred Numbers. July 1954.  (1953)) ^ a b IEC 60063:1952 - Series of preferred values and their associated tolerances for resistors and capacitors (1.0 ed.). International Electrotechnical Commission (IEC). 2007 [1952-01-01]. Archived from the original on 2017-11-01. Retrieved 2017-07-11.  ^ "COUNCIL DIRECTIVE of 19 December 1974 on the approximation of the laws of the Member States relating to the making-up by volume of certain prepackaged liquids (75/106/EEC)" (PDF). 2004-05-01 [1974-12-19]. Archived from the original (PDF) on 2013-05-16. 


Further reading[edit] Hirshfeld, Clarence Floyd; Berry, C. H. (1922-12-04). "Size Standardization by Preferred Numbers". Mechanical Engineering. New York, USA: The American Society of Mechanical Engineers. 44 (12): 791–.  [1] Hazeltine, Louis Alan (January 1927) [December 1926]. "Preferred Numbers". Proceedings of the Institute of Radio Engineers (IRE). 14 (4): 785–787. doi:10.1109/JRPROC.1926.221089. ISSN 0731-5996.  Van Dyck, Arthur F. (February 1936). "Preferred Numbers". Proceedings of the Institute of Radio Engineers (IRE). 24 (2): 159–179. doi:10.1109/JRPROC.1936.228053. ISSN 0731-5996. […] choice of series is influenced by the fact that these units are sold with different standard tolerances, namely five, ten and twenty per cent, and there is a desire to have every unit manufactured, regardless of what its value may be, fall into some standard size and tolerance […]  Van Dyck, Arthur F. (March 1951) [February 1951]. "Preferred Numbers". Proceedings of the Institute of Radio Engineers (IRE). IEEE. 39 (2): 115. doi:10.1109/JRPROC.1951.230759. ISSN 0096-8390. […] For example, some years ago, the Radio-Television Manufacturers Association found it desirable to standardize the values of resistors. The ASA Preferred Numbers Standard was considered, but judged not to suit the manufacturing conditions and the buying practices of the resistor field at the moment, whereas a special series of numbers suited better. The special series was adopted and, since it was an official RTMA list, it has been utilized by later RTMA committees for other applications than resistors, although adopted originally because of seeming advantages for resistors. Ironically, the original advantages have largely disappeared through changes in resistor manufacturing conditions. But the irregular standard remains… […]  ISO 17:1973-04 - Guide to the use of preferred numbers and of series of preferred numbers. International Standards Organization (ISO). April 1973. Archived from the original on 2017-11-02. Retrieved 2017-11-02.  (Replaced: ISO Recommendation R17-1956 - Preferred Numbers - Guide to the Use of Preferred Numbers and of Series of Preferred Numbers. 1956.  (1955) and ISO R17/A1-1966 - Amendment 1 to ISO Recommendation R17-1955. 1966. ) ISO 497:1973-05 - Guide to the choice of series of preferred numbers and of series containing more rounded values of preferred numbers. International Standards Organization (ISO). May 1973. Archived from the original on 2017-11-02. Retrieved 2017-11-02.  (Replaced: ISO Recommendation R497-1966 - Preferred Numbers - Guide to the Choice of Series of Preferred Numbers and of Series Containing More Rounded Values of Preferred Numbers. 1966. ) ANSI Z17.1-1973 - American National Standard for Preferred Numbers. American National Standards Institute (ANSI). 1973-09-05.  (9 pages) (Replaced: ASA Z17.1-1958 - American National Standard for Preferred Numbers. 1958.  Reaffirmed as USASI Z17.1-1958 in 1966 and named ANSI Z17.1-1958 since 1969.) Paulin, Eugen (2007-09-01). Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! [Logarithms, preferred numbers, decibel, neper, phon - naturally related!] (PDF) (in German). Archived (PDF) from the original on 2016-12-18. Retrieved 2016-12-18.  Kienzle, Otto Helmut (2013-10-04) [1950]. Written at Hannover, Germany. Normungszahlen [Preferred numbers]. Wissenschaftliche Normung (in German). 2 (reprint of 1st ed.). Berlin / Göttingen / Heidelberg, Germany: Springer-Verlag OHG. ISBN 978-3-642-99831-7. ISBN 3-642-99831-3. Retrieved 2017-11-01.  (340 pages) Bergtold, Fritz (1965). Mathematik für Radiotechniker und Elektroniker [Mathematics for Radio and Electronics Technicians] (in German) (3 ed.). München, Germany: Franzis-Verlag.  Bauer, Horst, ed. (1995). Kraftfahrtechnisches Taschenbuch (in German) (22 ed.). Düsseldorf, Germany: Bosch, VDI-Verlag (de). ISBN 3-18419122-2.  Ries, Clemens (1962). Normung nach Normzahlen [Standardization by preferred numbers] (in German) (1 ed.). Berlin, Germany: Duncker & Humblot Verlag (de). ISBN 3-42801242-9.  (135 pages) Berg, Siegfried (1949). Angewandte Normzahl - Gesammelte Aufsätze [Applied preferred number - Collected papers] (in German). Berlin / Köln, Germany: Beuth-Vertrieb GmbH. Retrieved 2017-11-01.  (191 pages) Tuffentsammer, Karl; Schumacher, P. (1953). "Normzahlen – die einstellige Logarithmentafel des Ingenieurs" [Preferred numbers - the engineer's single-digit logarithm table]. Werkstattechnik und Maschinenbau (in German). 43 (4): 156.  Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.  Strahringer, Wilhelm (1952). Zauberwelt der Normzahlen [Magic world of preferred numbers] (in German). Frankfurt a. Main, Germany: Verlags- und Wirtschaftsgesellschaft der Elektrizitätswerke m.b.H. (VWEW).  (95 pages) v t e ISO standards by standard number List of ISO standards / ISO romanizations / IEC standards 1–9999 1 2 3 4 5 6 7 9 16 31 -0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 128 216 217 226 228 233 259 269 302 306 428 518 519 639 -1 -2 -3 -5 -6 646 690 732 764 843 898 965 1000 1004 1007 1073-1 1413 1538 1745 1989 2014 2015 2022 2047 2108 2145 2146 2240 2281 2709 2711 2788 2848 2852 3029 3103 3166 -1 -2 -3 3297 3307 3602 3864 3901 3977 4031 4157 4217 4909 5218 5428 5775 5776 5800 5964 6166 6344 6346 6385 6425 6429 6438 6523 6709 7001 7002 7098 7185 7200 7498 7736 7810 7811 7812 7813 7816 8000 8178 8217 8571 8583 8601 8632 8652 8691 8807 8820-5 8859 -1 -2 -3 -4 -5 -6 -7 -8 -8-I -9 -10 -11 -12 -13 -14 -15 -16 8879 9000/9001 9075 9126 9293 9241 9362 9407 9506 9529 9564 9594 9660 9897 9899 9945 9984 9985 9995 10000–19999 10005 10006 10007 10116 10118-3 10160 10161 10165 10179 10206 10218 10303 -11 -21 -22 -28 -238 10383 10487 10585 10589 10646 10664 10746 10861 10957 10962 10967 11073 11170 11179 11404 11544 11783 11784 11785 11801 11898 11940 (-2) 11941 11941 (TR) 11992 12006 12182 12207 12234-2 13211 -1 -2 13216 13250 13399 13406-2 13450 13485 13490 13567 13568 13584 13616 14000 14031 14224 14289 14396 14443 14496 -2 -3 -6 -10 -11 -12 -14 -17 -20 14644 14649 14651 14698 14750 14764 14882 14971 15022 15189 15288 15291 15292 15398 15408 15444 -3 15445 15438 15504 15511 15686 15693 15706 -2 15707 15897 15919 15924 15926 15926 WIP 15930 16023 16262 16612-2 16750 16949 (TS) 17024 17025 17100 17203 17369 17442 17799 18000 18004 18014 18245 18629 18916 19005 19011 19092 (-1 -2) 19114 19115 19125 19136 19439 19500 19501 19502 19503 19505 19506 19507 19508 19509 19510 19600:2014 19752 19757 19770 19775-1 19794-5 19831 20000+ 20000 20022 20121 20400 21000 21047 21500 21827:2002 22000 23270 23271 23360 24517 24613 24617 24707 25178 25964 26000 26300 26324 27000 series 27000 27001 27002 27006 27729 28000 29110 29148 29199-2 29500 30170 31000 32000 38500 40500 42010 55000 80000 -1 -2 -3 Category Retrieved from "https://en.wikipedia.org/w/index.php?title=Preferred_number&oldid=814634673" Categories: NumbersIndustrial designLogarithmic scales of measurementHidden categories: Use British English Oxford spelling from December 2011CS1 German-language sources (de)Interlanguage link template link number


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