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वैज्ञानिक संकेतन

मुक्त ज्ञानकोश विकिपीडिया से

वैज्ञानिक अंकन (अंग्रेज़ी: Scientific notation) उन संख्याओं को व्यक्त करने का एक तरीका है जो दशमलव रूप में सुविधाजनक रूप से लिखने के लिए बहुत बड़ी या बहुत छोटी होती हैं, क्योंकि ऐसा करने पर बहुत लंबी अंक-श्रंखला लिखनी पड़ती। इसे वैज्ञानिक रूप, स्टैंडर्ड इंडेक्स रूप या यूनाइटेड किंगडम में मानक रूप भी कहा जाता है। यह दशाधारित अंकन वैज्ञानिकों, गणितज्ञों और अभियंताओं द्वारा आमतौर पर उपयोग किया जाता है क्योंकि इससे कुछ अंकगणितीय क्रियाएँ सरल हो जाती हैं। वैज्ञानिक परिकलित्रों में इसे सामान्यतः एससीआई प्रदर्शन मोड कहा जाता है।

दशमलव अंकन वैज्ञानिक अंकन
२ २ x १००
३०० ३ x १०२
४,३२१.७६८ ४.३२१ ७६८ x १०३
-५३,०० -५.३ x १०४
६,७२,००,००,००० ६.७२ x १०९
०.२ २ x १०-१
९८७ ९.८७ x १०२
०.००००००००७५१ ७.५१ x १०-९

वैज्ञानिक अंकन में, शून्य से भिन्न संख्याएँ निम्न रूप में लिखी जातीं हैं:

m × १०ⁿ 

अर्थात् m गुना दस की घात n, जहाँ n एक पूर्णांक होता है और गुणांक m एक शून्य से भिन्न वास्तविक संख्या होती है (अमूमन इसका परिमाण १ और १० के बीच होता है तथा प्रायः इसे समाप्त होने योग्य दशमलव के रूप में लिखा जाता है)। पूर्णांक n को घातांक कहा जाता है और वास्तविक संख्या m को संकेतांक या मानांक कहा जाता है। यदि संख्या ऋणात्मक हो तो मानक दशमलव अंकन की तरह m के आगे ऋण चिह्न लगाया जाता है। मानकीकृत अंकन में घातांक इस प्रकार चुना जाता है कि संकेतांक m का परिमाण कम से कम १ और १० से कम हो।

दशमलव चल-बिंदु एक संगणक अंकगणित प्रणाली है जो वैज्ञानिक अंकन के निकट सम्बन्धी है।

संदर्भ

[संपादित करें]
  1. Caliò, Franca; Alessandro, Lazzari (September 2017). Elements of Mathematics with Numerical Applications. Società Editrice Esculapio. pp. 30–32. ISBN 978-8-89385052-0.
  2. Edwards, John (2009). Submission Guidelines for Authors: HPS 2010 Midyear Proceedings (PDF). McLean, VA: Health Physics Society. p. 5. अभिगमन तिथि: 2013-03-30.
  3. However, E notation was not included in the preliminary specification of Fortran, as of 1954.
    Backus, John Warner, ed. (1954-11-10). Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN (PDF) (Preliminary report). New York: Programming Research Group, Applied Science Division, International Business Machines Corporation. अभिगमन तिथि: 2022-07-04. (29 pages)
    Sayre, David, ed. (1956-10-15). The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual (PDF). New York: Applied Science Division and Programming Research Department, International Business Machines Corporation. pp. 9, 27. अभिगमन तिथि: 2022-07-04. (2+51+1 pages)
  4. DiGri, Vincent J.; King, Jane E. (April 1959) [1958-06-11]. "The SHARE 709 System: Input-Output Translation". Journal of the ACM. 6 (2): 141–144. डीओआई:10.1145/320964.320969. एस2सीआईडी 19660148. It tells the input translator that the field to be converted is a decimal number of the form ~X.XXXXE ± YY where E implies that the value of ~x.xxxx is to be scaled by ten to the ±YY power. (4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.)
  5. Jim Davidson coined decapower and recommended the "D" separator in the 65 Notes newsletter for Hewlett-Packard HP-65 users, and Richard C. Vanderburgh promoted these in the 52-Notes newsletter for Texas Instruments SR-52 users.
    Davidson, Jim (January 1976). Nelson, Richard J. (ed.). "[title unknown]". 65 Notes. 3 (1). Santa Ana, CA: 4. V3N1P4.
    Vanderburgh, Richard C., ed. (November 1976). "Decapower" (PDF). 52-Notes – Newsletter of the SR-52 Users Club. 1 (6). Dayton, OH: 1. V1N6P1. मूल से (PDF) से 28 मई 2017 को पुरालेखित।. अभिगमन तिथि: 2017-05-28. Decapower – In the January 1976 issue of 65-Notes (V3N1p4) Jim Davidson (HP-65 Users Club member #547) suggested the term "decapower" as a descriptor for the power-of-ten multiplier used in scientific notation displays. I'm going to begin using it in place of "exponent" which is technically incorrect, and the letter D to separate the "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example, 123−45 [sic] which is displayed in scientific notation as 1.23 -43 will now be written 1.23D-43. Perhaps, as this notation gets more and more usage, the calculator manufacturers will change their keyboard abbreviations. HP's EEX and TI's EE could be changed to ED (for enter decapower). "Decapower". 52-Notes – Newsletter of the SR-52 Users Club. Vol. 1, no. 6. Dayton, OH. November 1976. p. 1. अभिगमन तिथि: 2018-05-07. (NB. The term decapower was frequently used in subsequent issues of this newsletter up to at least 1978.)
  6. "UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc". Math.hawaii.edu. 2012-02-12. अभिगमन तिथि: 2012-03-06.
  7. Specifically, models PC-1280 (1987), PC-1470U (1987), PC-1475 (1987), PC-1480U (1988), PC-1490U (1990), PC-1490UII (1991), PC-E500 (1988), PC-E500S (1995), PC-E550 (1990), PC-E650 (1993), and PC-U6000 (1993).
    SHARP Taschencomputer Modell PC-1280 Bedienungsanleitung [SHARP Pocket Computer Model PC-1280 Operation Manual] (PDF) (जर्मन भाषा में). Sharp Corporation. 1987. pp. 56–60. 7M 0.8-I(TINSG1123ECZZ)(3). मूल से (PDF) से 6 मार्च 2017 को पुरालेखित।. अभिगमन तिथि: 2017-03-06.
    SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung [SHARP Pocket Computer Model PC-1475 Operation Manual] (PDF) (जर्मन भाषा में). Sharp Corporation. 1987. pp. 105–108, 131–134, 370, 375. मूल से (PDF) से 2017-02-25 को पुरालेखित।. अभिगमन तिथि: 2017-02-25.
    SHARP Pocket Computer Model PC-E500 Operation Manual. Sharp Corporation. 1989. 9G1KS(TINSE1189ECZZ).
    SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung [SHARP Pocket Computer Model PC-E500S Operation Manual] (PDF) (जर्मन भाषा में). Sharp Corporation. 1995. 6J3KS(TINSG1223ECZZ). मूल से (PDF) से 2017-02-24 को पुरालेखित।. अभिगमन तिथि: 2017-02-24.
    電言板5 PC-1490UII PROGRAM LIBRARY [Telephone board 5 PC-1490UII program library] (जापानी भाषा में). Vol. 5. University Co-op. 1991.
    電言板6 PC-U6000 PROGRAM LIBRARY [Telephone board 6 PC-U6000 program library] (जापानी भाषा में). Vol. 6. University Co-op. 1993.
  8. For instance, DEC FORTRAN 77 (f77), Intel Fortran, Compaq/Digital Visual Fortran, and GNU Fortran (gfortran)
    "Double Precision, REAL**16". DEC Fortran 77 Manual. Digital Equipment Corporation. अभिगमन तिथि: 2022-12-21. Digital Fortran 77 also allows the syntax Qsnnn, if the exponent field is within the T_floating double precision range. […] A REAL*16 constant is a basic real constant or an integer constant followed by a decimal exponent. A decimal exponent has the form: Qsnn […] s is an optional sign […] nn is a string of decimal digits […] This type of constant is only available on Alpha systems.
    Intel Fortran: Language Reference (PDF). Intel Corporation. 2005 [2003]. pp. 3-7 – 3-8, 3–10. 253261-003. अभिगमन तिथि: 2022-12-22. (858 pages)
    Compaq Visual Fortran – Language Reference (PDF). Houston: Compaq Computer Corporation. August 2001. अभिगमन तिथि: 2022-12-22. (1441 pages)
    "6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter". The GNU Fortran Compiler. 2014-06-12. अभिगमन तिथि: 2022-12-21.
  9. Naur, Peter, ed. (1960). "Report on the Algorithmic Language ALGOL 60". Communications of the ACM. 3 (5). Copenhagen: 299–311. डीओआई:10.1145/367236.367262.
  10. Savard, John J. G. (2018) [2005]. "Computer Arithmetic". quadibloc. The Early Days of Hexadecimal. अभिगमन तिथि: 2018-07-16.
  11. Bauer, Henry R.; Becker, Sheldon; Graham, Susan L. (January 1968). "ALGOL W – Notes For Introductory Computer Science Courses" (PDF). Stanford University, Computer Science Department. अभिगमन तिथि: 2017-04-08.
  12. "Revised Report on the Algorithmic Language Algol 68". Acta Informatica. 5 (1–3): 1–236. September 1973. CiteSeerX 10.1.1.219.3999. डीओआई:10.1007/BF00265077. एस2सीआईडी 2490556.
  13. Broukhis, Leonid (2008-01-22), "Revised proposal to encode the decimal exponent symbol" (PDF), unicode.org (Working Group Document), L2/08-030R
    "The Unicode Standard" (v. 7.0.0 ed.). अभिगमन तिथि: 2018-03-23.
  14. Whitaker, Ronald O. (1962-06-15). "Numerical Prefixes" (PDF). Crosstalk. Electronics. p. 4. अभिगमन तिथि: 2022-12-24. (1 page)
  15. Also see TI calculator character sets.
    "TI-83 Programmer's Guide" (PDF). अभिगमन तिथि: 2010-03-09.
  16. "SIMULA standard as defined by the SIMULA Standards Group – 3.1 Numbers". August 1986. अभिगमन तिथि: 2009-10-06.
  17. Samples of usage of terminology and variants:
    Moller, Donald A. (June 1976). "A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB" (PDF) (Technica Report). WHOI Document Collection. Woods Hole, MA: Woods Hole Oceanographic Institution. WHOI-76-59. अभिगमन तिथि: 2015-08-19.
    "Cengage – the Leading Provider of Higher Education Course Materials". मूल से से 2007-10-19 को पुरालेखित।.
    "Bryn Mawr College: Survival Skills for Problem Solving – Scientific Notation". अभिगमन तिथि: 2007-04-07.
    "Scientific Notation". अभिगमन तिथि: 2007-04-07.
    "INTOUCH 4GL a Guide to the INTOUCH Language". मूल से से 2015-05-03 को पुरालेखित।.
  18. Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (July–September 2016). "CODATA recommended values of the fundamental physical constants: 2014". Reviews of Modern Physics. 88 (3): 035009. आर्काइव:1507.07956. बिबकोड:2016RvMP...88c5009M. CiteSeerX 10.1.1.150.1225. डीओआई:10.1103/RevModPhys.88.035009. एस2सीआईडी 1115862.
  19. Luzum, Brian; Capitaine, Nicole; Fienga, Agnès; Folkner, William; Fukushima, Toshio; Hilton, James; Hohenkerk, Catherine; Krasinsky, George; Petit, Gérard; Pitjeva, Elena; Soffel, Michael; Wallace, Patrick (August 2011). "The IAU 2009 system of astronomical constants: The report of the IAU working group on numerical standards for Fundamental Astronomy". Celestial Mechanics and Dynamical Astronomy. 110 (4): 293–304. बिबकोड:2011CeMDA.110..293L. डीओआई:10.1007/s10569-011-9352-4.
  20. Various (2000). Lide, David R. (ed.). Handbook of Chemistry and Physics (81st ed.). CRC. ISBN 978-0-8493-0481-1.
  21. Kadzere, Martin (2008-10-09). "Zimbabwe: Inflation Soars to 231 Million Percent". Harare, Zimbabwe: The Herald. अभिगमन तिथि: 2008-10-10.
  22. "Zimbabwe inflation hits new high". BBC News. 9 October 2008. मूल से से 2009-05-14 को पुरालेखित।. अभिगमन तिथि: 2009-10-09.
  23. electronic hexadecimal calculator/converter SR-22 (PDF) (Revision A ed.). Texas Instruments Incorporated. 1974. p. 7. 1304-389 Rev A. अभिगमन तिथि: 2017-03-20. (NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.)
  24. Martin, Bruce Alan (October 1968). "Letters to the editor: On binary notation". Communications of the ACM. 11 (10): 658. डीओआई:10.1145/364096.364107. एस2सीआईडी 28248410.
  25. Schwartz, Jake; Grevelle, Rick (2003-10-20) [April 1993]. HP16C Emulator Library for the HP48S/SX. 1.20 (1 ed.). अभिगमन तिथि: 2015-08-15. (NB. This library also works on the HP 48G/GX/G+. Beyond the feature set of the HP-16C, this package also supports calculations for binary, octal, and hexadecimal floating-point numbers in scientific notation in addition to the usual decimal floating-point numbers.)
  26. Schwartz, Jake; Grevelle, Rick (2003-10-21). HP16C Emulator Library for the HP48 – Addendum to the Operator's Manual. 1.20 (1 ed.). अभिगमन तिथि: 2015-08-15.
  27. "Rationale for International Standard – Programming Languages – C" (PDF). 5.10. April 2003. pp. 52, 153–154, 159. अभिगमन तिथि: 2010-10-17.
  28. The IEEE and The Open Group (2013) [2001]. "dprintf, fprintf, printf, snprintf, sprintf – print formatted output". The Open Group Base Specifications (Issue 7, IEEE Std 1003.1, 2013 ed.). अभिगमन तिथि: 2016-06-21.
  29. Beebe, Nelson H. F. (2017-08-22). The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library (1 ed.). Salt Lake City: Springer. डीओआई:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. LCCN 2017947446. एस2सीआईडी 30244721.
  30. "floating point literal". cppreference.com. अभिगमन तिथि: 2017-03-11. The hexadecimal floating-point literals were not part of C++ until C++17, although they can be parsed and printed by the I/O functions since C++11: both C++ I/O streams when std::hexfloat is enabled and the C I/O streams: std::printf, std::scanf, etc. See std::strtof for the format description.
  31. "The Swift Programming Language (Swift 3.0.1)". Guides and Sample Code: Developer: Language Reference. Apple Corporation. Lexical Structure. अभिगमन तिथि: 2017-03-11.
  32. Such as the TI SR-10.
    Texas Instruments electronic slide rule calculator SR-10 (PDF). Dallas: Texas Instruments Incorporated. 1973. 1304-739-266. अभिगमन तिथि: 2023-01-01. (1+1+45+1 pages) (NB. Although this manual is dated 1973, presumably version 1 of this calculator was introduced in November 1972 according to other sources.)
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