वैज्ञानिक संकेतन

वैज्ञानिक संकेतन फ़रवरी 2026 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 अंकनवैज्ञानिक अंकन२२ x १००३००३ x १०२४,३२१.७६८४.३२१ ७६८ x १०३ -५३,०० -५.३ x १०४६,७२,००,००,०००६.७२ x १०९०.२२ x १०-१९८७९.८७ x १०२०.००००००००७५१७.५१ 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 Caliò Franca Lazzari Alessandro Elements of Mathematics with Numerical Applications Società Editrice Esculapio 30–32 September 2017 978-8-89385052-0 Edwards John 2009 Submission Guidelines for Authors: HPS 2010 Midyear Proceedings Health Physics Society McLean, VA 5 http://hps.org/documents/2010_midyear_author-submission-guidelines.pdf 2013-03-30 However, E notation was not included in the preliminary specification of Fortran, as of 1954. Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN Preliminary report John Warner Backus John Warner Backus Harlan L. Herrick Robert A. Nelson Irving Ziller 0 John Warner Backus John Warner Backus Programming Research Group, Applied Science Division, International Business Machines Corporation New York 1954-11-10 https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf 2022-07-04 (29 pages) The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual Applied Science Division and Programming Research Department, International Business Machines Corporation New York 1956-10-15 David Sayre David Sayre John Warner Backus John Warner Backus Robert J. Beeber Sheldon F. Best Richard Goldberg Richard Goldberg Harlan L. Herrick Robert A. Hughes Lois B. Mitchell (Haibt) Lois B. Mitchell Robert A. Nelson Roy Nutt Roy Nutt David Sayre David Sayre Peter B. Sheridan Harold Stern Irving Ziller 0 9, 27 http://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf 2022-07-04 (2+51+1 pages) The SHARE 709 System: Input-Output Translation Vincent J. DiGri Jane E. King Journal of the ACM 6 2 April 1959 1958-06-11 10.1145/320964.320969 19660148 141–144 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. free (4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.) 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. Jim Davidson Richard J. Nelson 65 Notes Santa Ana, CA January 1976 3 1 4 V3N1P4 (([title unknown])) Richard C. Vanderburgh Decapower 52-Notes – Newsletter of the SR-52 Users Club 1 6 1 November 1976 V1N6P1 Dayton, OH http://www.claudiolarini.altervista.org/pdf/52NOTES.pdf 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|−45 123×10−45 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). 28 मई 2017 https://web.archive.org/web/20170528031508/http://www.claudiolarini.altervista.org/pdf/52NOTES.pdf dead Decapower 1 6 1 November 1976 52-Notes – Newsletter of the SR-52 Users Club Dayton, OH http://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html 2018-05-07 (NB. The term decapower was frequently used in subsequent issues of this newsletter up to at least 1978.) http://www.math.hawaii.edu/lab/197/fortran/fort3.htm#double UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc. Math.hawaii.edu 2012-02-12 2012-03-06 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 de SHARP Pocket Computer Model PC-1280 Operation Manual 1987 Sharp Corporation 7M 0.8-I(TINSG1123ECZZ)(3) 56–60 http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1280-de.pdf 2017-03-06 6 मार्च 2017 https://web.archive.org/web/20170306145930/http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1280-de.pdf dead SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung de SHARP Pocket Computer Model PC-1475 Operation Manual 105–108, 131–134, 370, 375 1987 Sharp Corporation http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf 2017-02-25 dead https://web.archive.org/web/20170225090805/http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf 2017-02-25 SHARP Pocket Computer Model PC-E500 Operation Manual Sharp Corporation 1989 9G1KS(TINSE1189ECZZ) SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung de SHARP Pocket Computer Model PC-E500S Operation Manual Sharp Corporation 1995 6J3KS(TINSG1223ECZZ) http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf 2017-02-24 dead https://web.archive.org/web/20170224235944/http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf 2017-02-24 ja:電言板5 PC-1490UII PROGRAM LIBRARY Telephone board 5 PC-1490UII program library University Co-op ja 1991 5 ja:電言板6 PC-U6000 PROGRAM LIBRARY Telephone board 6 PC-U6000 program library University Co-op ja 1993 6 For instance, DEC FORTRAN 77 (f77), Intel Fortran, Compaq/Digital Visual Fortran, and GNU Fortran (gfortran) DEC Fortran 77 Manual Double Precision, REAL**16 Digital Equipment Corporation https://wwwth.mpp.mpg.de/members/hahn/decfortman.html 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 2005 2003 Intel Corporation 253261-003 3-7–3-8, 3-10 https://www.ehu.eus/sgi/ARCHIVOS/lang_for.pdf 2022-12-22 (858 pages) Compaq Visual Fortran – Language Reference August 2001 Compaq Computer Corporation Houston https://jp.xlsoft.com/documents/intel/cvf/cvf_lref.pdf 2022-12-22 (1441 pages) The GNU Fortran Compiler 6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter 2014-06-12 https://gcc.gnu.org/onlinedocs/gcc-4.7.4/gfortran/_003ccode_003eQ_003c_002fcode_003e-exponent-letter.html#_003ccode_003eQ_003c_002fcode_003e-exponent-letter 2022-12-21 Report on the Algorithmic Language ALGOL 60 Communications of the ACM Peter Naur Peter Naur Copenhagen 1960 3 5 299–311 10.1145/367236.367262 https://dl.acm.org/doi/10.1145/367236.367262 Computer Arithmetic The Early Days of Hexadecimal John J. G. Savard 2018 2005 quadibloc http://www.quadibloc.com/comp/cp02.htm 2018-07-16 ALGOL W – Notes For Introductory Computer Science Courses Henry R. Bauer Sheldon Becker Susan L. Graham January 1968 Stanford University, Computer Science Department http://i.stanford.edu/pub/cstr/reports/cs/tr/68/86/CS-TR-68-86.pdf 2017-04-08 Revised Report on the Algorithmic Language Algol 68 Acta Informatica 5 1–236 September 1973 1–3 10.1007/BF00265077 10.1.1.219.3999 2490556 cs2 Working Group Document Revised proposal to encode the decimal exponent symbol Broukhis Leonid 2008-01-22 unicode.org https://www.unicode.org/L2/L2008/08030r-subscript10.pdf L2/08-030R https://www.unicode.org/versions/Unicode7.0.0/ The Unicode Standard v. 7.0.0 2018-03-23 Numerical Prefixes Ronald O. Whitaker 1962-06-15 Electronics Crosstalk 4 http://www.bitsavers.org/magazines/Electronics/Electronics_V35_N24_19620615.pdf 2022-12-24 (1 page) Also see TI calculator character sets. http://education.ti.com/downloads/guidebooks/sdk/83p/sdk83pguide.pdf TI-83 Programmer's Guide 2010-03-09 SIMULA standard as defined by the SIMULA Standards Group – 3.1 Numbers http://prosjekt.ring.hibu.no/simula/Standard/chap_1.htm 2009-10-06 August 1986 Samples of usage of terminology and variants: A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB WHOI Document Collection Donald A. Moller June 1976 Technica Report Woods Hole Oceanographic Institution WHOI-76-59 Woods Hole, MA http://darchive.mblwhoilibrary.org/bitstream/1912/665/1/WHOI-76-59.pdf 2015-08-19 http://www.brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html https://web.archive.org/web/20071019061437/http://brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html 2007-10-19 Cengage – the Leading Provider of Higher Education Course Materials http://www.brynmawr.edu/nsf/tutorial/ss/ssnot.html 2007-04-07 Bryn Mawr College: Survival Skills for Problem Solving – Scientific Notation http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html 2007-04-07 Scientific Notation http://www.ttinet.com/doc/language_v44_003.html#heading_3.2.4.2 https://web.archive.org/web/20150503005623/http://www.ttinet.com/doc/language_v44_003.html 2015-05-03 INTOUCH 4GL a Guide to the INTOUCH Language Mohr Peter J. Newell David B. Taylor Barry N. July–September 2016 CODATA recommended values of the fundamental physical constants: 2014 http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=920687 Reviews of Modern Physics 88 3 035009 10.1103/RevModPhys.88.035009 1507.07956 2016RvMP...88c5009M 10.1.1.150.1225 1115862 Luzum Brian Capitaine Nicole Fienga Agnès Folkner William Fukushima Toshio Hilton James Hohenkerk Catherine Krasinsky George Petit Gérard Pitjeva Elena Soffel Michael Wallace Patrick 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 August 2011 293–304 2011CeMDA.110..293L 10.1007/s10569-011-9352-4 free Various David R. Lide 2000 Handbook of Chemistry and Physics 81st CRC 978-0-8493-0481-1 http://allafrica.com/stories/200810090256.html Zimbabwe: Inflation Soars to 231 Million Percent The Herald Harare, Zimbabwe Martin Kadzere 2008-10-09 2008-10-10 http://news.bbc.co.uk/1/hi/world/africa/7660569.stm Zimbabwe inflation hits new high 9 October 2008 https://web.archive.org/web/20090514123525/http://news.bbc.co.uk/1/hi/world/africa/7660569.stm 2009-05-14 BBC News 2009-10-09 electronic hexadecimal calculator/converter SR-22 Texas Instruments Incorporated 1974 7 Revision A 1304-389 Rev A http://www.datamath.net/Manuals/SR-22_US.pdf 2017-03-20 (NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.) Letters to the editor: On binary notation Bruce Alan Martin Communications of the ACM 11 10 October 1968 658 10.1145/364096.364107 28248410 free HP16C Emulator Library for the HP48S/SX Jake Schwartz Rick Grevelle 2003-10-20 April 1993 1 1.20 http://www.pahhc.org/mul8r.htm 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.) HP16C Emulator Library for the HP48 – Addendum to the Operator's Manual Jake Schwartz Rick Grevelle 2003-10-21 1 1.20 http://www.pahhc.org/mul8r.htm 2015-08-15 Rationale for International Standard – Programming Languages – C 5.10 April 2003 52, 153–154, 159 http://www.open-std.org/jtc1/sc22/wg14/www/C99RationaleV5.10.pdf 2010-10-17 dprintf, fprintf, printf, snprintf, sprintf – print formatted output The Open Group Base Specifications Issue 7, IEEE Std 1003.1, 2013 2013 2001 The IEEE and The Open Group http://pubs.opengroup.org/onlinepubs/9699919799/functions/printf.html 2016-06-21 Nelson H. F. Beebe The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library 2017-08-22 Salt Lake City Springer 1 2017947446 978-3-319-64109-6 10.1007/978-3-319-64110-2 30244721 cppreference.com floating point literal http://en.cppreference.com/w/cpp/language/floating_literal 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. The Swift Programming Language (Swift 3.0.1) Lexical Structure Guides and Sample Code: Developer: Language Reference Apple Corporation https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/LexicalStructure.html 2017-03-11 Such as the TI SR-10. Texas Instruments electronic slide rule calculator SR-10 1973 Texas Instruments Incorporated Dallas 1304-739-266 https://www.sliderulemuseum.com/Calculators/SR-10_US.pdf 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.) श्रेणी:संख्या पद्धति श्रेणी:मापन श्रेणी:गणितीय अंकन श्रेणी:सीएस1 जापानी-भाषा स्रोत (ja) श्रेणी:सीएस1 जर्मन-भाषा स्रोत (de)