Knowledge (XXG)

Scientific notation

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It is customary in scientific measurement to record all the definitely known digits from the measurement and to estimate at least one additional digit if there is any information at all available on its value. The resulting number contains more information than it would without the extra digit, which
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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
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means that too much money is put into circulation, perhaps by printing banknotes, chasing too few goods. It is sometimes defined as inflation of 50% or more in a single month. In such conditions, money rapidly loses its value. Some countries have had events of inflation of 1 million percent or more
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Conversion between different scientific notation representations of the same number with different exponential values is achieved by performing opposite operations of multiplication or division by a power of ten on the significand and an subtraction or addition of one on the exponent part. The
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is usually read to have five significant figures: 1, 2, 3, 0, and 4, the final two zeroes serving only as placeholders and adding no precision. The same number, however, would be used if the last two digits were also measured precisely and found to equal 0 – seven significant figures.
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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
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Another similar convention to denote base-2 exponents is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal. This notation can be produced by implementations of the
2216: 2084: 2607: 2699:(using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes 1470:
Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation. None of these alter the actual number, only how it's expressed.
2672:) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E", a shorthand notation originally proposed by 1955: 3957:
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).
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supporting scientific notation appeared in 1972. The displays of pocket calculators of the 1970s did not display an explicit symbol between significand and exponent; instead, one or more digits were left blank (e.g.
448:. This form allows easy comparison of numbers: numbers with bigger exponents are (due to the normalization) larger than those with smaller exponents, and subtraction of exponents gives an estimate of the number of 1962: 2481: 595:
When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the placeholding zeroes are no longer required. Thus
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Additional information about precision can be conveyed through additional notation. It is often useful to know how exact the final digit or digits are. For instance, the accepted value of the mass of the
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may be considered a significant digit because it conveys some information leading to greater precision in measurements and in aggregations of measurements (adding them or multiplying them together).
2488: 468:). The 10 and exponent are often omitted when the exponent is 0. For a series of numbers that are to be added or subtracted (or otherwise compared), it can be convenient to use the same value of 1173:
for the scientific-notation exponent to distinguish it from "normal" exponents, and suggested the letter "D" as a separator between significand and exponent in typewritten numbers (for example,
3535:. 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). 3187: 1207:
In 1962, Ronald O. Whitaker of Rowco Engineering Co. proposed a power-of-ten system nomenclature where the exponent would be circled, e.g. 6.022 × 10 would be written as "6.022③".
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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.
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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 "
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exponents like 10 can be inconvenient to display or type, the letter "E" or "e" (for "exponent") is often used to represent "times ten raised to the power of", so that the notation
539:| < 10. Though similar in concept, engineering notation is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their corresponding 3832: 2387: 1859: 581:. Leading and trailing zeroes are not significant digits, because they exist only to show the scale of the number. Unfortunately, this leads to ambiguity. The number 3229: 4367: 3423:(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.) 3517:" which is technically incorrect, and the letter D to separate the "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example, 475:
Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such as
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A significant figure is a digit in a number that adds to its precision. This includes all nonzero numbers, zeroes between significant digits, and zeroes
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typically present very large or small numbers using scientific notation, and some can be configured to uniformly present all numbers that way. Because
3688: 2394: 1177:); these gained some currency in the programmable calculator user community. The letters "E" or "D" were used as a scientific-notation separator by 1441:
in a single month, which usually results in the rapid abandonment of the currency. For example, in November 2008 the monthly inflation rate of the
1766: 941:. While common in computer output, this abbreviated version of scientific notation is discouraged for published documents by some style guides. 2616:
While base ten is normally used for scientific notation, powers of other bases can be used too, base 2 being the next most commonly used one.
4307: 4008: 2947: 2893: 1483:, to put the number's value within a desired range, between 1 and 10 for normalized notation. If the decimal was moved to the left, append 2807:
I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since
3836: 3960:"The IAU 2009 system of astronomical constants: The report of the IAU working group on numerical standards for Fundamental Astronomy" 2942:(3rd ed.). Washington, DC : Oxford ; New York: American Chemical Society ; Oxford University Press. p. 210. 519:
Engineering notation (often named "ENG" on scientific calculators) differs from normalized scientific notation in that the exponent
2211:{\displaystyle {\frac {2.34\times 10^{2}}{5.67\times 10^{-5}}}\approx 0.413\times 10^{2-(-5)}=0.413\times 10^{7}=4.13\times 10^{6}} 1231:
before and after "×" or in front of "E" is sometimes omitted, though it is less common to do so before the alphabetical character.
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require the numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted:
1693: 1633: 4049: 4454: 4087: 3869: 3411: 2677: 2079:{\displaystyle 5.67\times 10^{-5}\times 2.34\times 10^{2}\approx 13.3\times 10^{-5+2}=13.3\times 10^{-3}=1.33\times 10^{-2}} 3119: 1382: 957: 38: 1409:. Using scientific notation, this value can be uniformly expressed to any desired precision, from the nearest tenth of a 3752: 2816: 3865: 3171: 1184:
released between 1987 and 1995, "E" used for 10-digit numbers and "D" used for 20-digit double-precision numbers. The
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if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as
2976: 318:. The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the 3003: 3783: 2292: 2232: 4171: 3894: 2781: 1114: 636:. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous. 31: 2602:{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}} 77:
notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain
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Similar to "B" (or "b"), the letters "H" (or "h") and "O" (or "o", or "C") are sometimes also used to indicate
949: 3822:(Technica Report). WHOI Document Collection. Woods Hole, MA: Woods Hole Oceanographic Institution. WHOI-76-59 3662: 3617: 61:, since to do so would require writing out an inconveniently long string of digits. It may be referred to as 1162: 3706: 2860:– a Chinese numeral system formerly used in commerce, with order of magnitude written below the significand 2854:– an international standard which guides the use of physical quantities and units of measurement in science 3921: 3817:"A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB" 3791: 3307: 2692: 1756: 969: 524: 345: 82: 3816: 2910: 4265: 4152: 4029: 2624: 964:– use this "E" notation, which comes from Fortran and was present in the first version released for the 491: 78: 4409: 4404: 4399: 4292:
The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library
3758: 2673: 1125: 4459: 3971: 3913: 3270: 2834: 514: 476: 3926: 3854: 3576: 3312: 4240: 4099:(NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.) 3580: 3572: 3277: 2846: 1216: 985: 715: 578: 572: 449: 3873: 4430: 4321: 4190: 3939: 3903: 3325: 3223: 3060: 3041: 2972: 2352: 1499:
in normalized scientific notation, the decimal separator would be moved 6 digits to the left and
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However, E notation was not included in the preliminary specification of Fortran, as of 1954.
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would have its decimal separator shifted 3 digits to the right instead of the left and yield
1011:. This presented a challenge for computer systems which did not provide such a character, so 4295: 4180: 3979: 3931: 3592: 3317: 3050: 1445:
reached 79.6 billion percent; the approximate value with three significant figures would be
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would likely be read out as "one-point-two-five times ten-to-the-negative-eight metres".
3975: 3917: 3113: 1157:), or a pair of smaller and slightly raised digits were reserved for the exponent (e.g. 490:
is not restricted to the range 1 to 10 (as in engineering notation for instance) and to
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The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual
2714: 1760: 1752: 1437: 711: 481: 423: 357: 335: 4414: 4057: 3538: 2984:(Preliminary report). New York: Programming Research Group, Applied Science Division, 2866:– a notation to specify resistor and capacitor values, with symbols for powers of 1000 4448: 3842: 3608: 3604: 3596: 3541: 3186:"6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter". 3103: 2851: 2820: 1020: 924: 460:
is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as
4436: 4325: 4194: 3064: 1950:{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}} 3943: 3329: 1534:
Converting a number from scientific notation to decimal notation, first remove the
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In normalized scientific notation, in E notation, and in engineering notation, the
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separating the numbers. It is also the form that is required when using tables of
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was frequently used in subsequent issues of this newsletter up to at least 1978.)
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scientific notation (called "standard form" in the United Kingdom), the exponent
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in scientific notation in addition to the usual decimal floating-point numbers.)
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numbers in scientific notation, and newer Fortran compilers use "Q" to signify
4375: 4299: 3984: 3959: 3843:"Bryn Mawr College: Survival Skills for Problem Solving – Scientific Notation" 3211: 2812: 1410: 1224: 1196: 1058: 977: 961: 869: 4419: 4151:, this package also supports calculations for binary, octal, and hexadecimal 2937: 2936:
Coghill, Anne M.; Garson, Lorrin R.; American Chemical Society, eds. (2006).
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Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN
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Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (July–September 2016).
3055: 3036: 3011:. New York: Applied Science Division and Programming Research Department, 2717:
representation commonly used in computer arithmetic, and the usage of IEC
2668:(or shorter: 1.001E11) with the letter "E" now standing for "times two (10 1560:
would have its decimal separator shifted 6 digits to the right and become
17: 4053: 3514: 3506: 3466: 3438: 3244: 2863: 2220: 1241: 1028: 1019:, and some Soviet Algol variants allowed the use of the Cyrillic letter " 301: 74: 42: 3381:"SIMULA standard as defined by the SIMULA Standards Group – 3.1 Numbers" 2808: 2800: 348:
is a computer arithmetic system closely related to scientific notation.
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This article is about a numeric notation. For the musical notation, see
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HP16C Emulator Library for the HP48 – Addendum to the Operator's Manual
4140: 3890:"CODATA recommended values of the fundamental physical constants: 2014" 3321: 1062: 1012: 973: 965: 945: 293: 278: 4266:"dprintf, fprintf, printf, snprintf, sprintf – print formatted output" 3072:(4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.) 2939:
The ACS style guide: effective communication of scientific information
37:"E notation" redirects here. For the series of preferred numbers, see 4148: 4136: 3833:"Cengage – the Leading Provider of Higher Education Course Materials" 2772: 1082: 989: 650: 3908: 3269:
Bauer, Henry R.; Becker, Sheldon; Graham, Susan L. (January 1968).
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would have its decimal separator moved 3 digits to the left and be
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in 1956. The E notation was already used by the developers of
953: 4317: 4241:"Rationale for International Standard – Programming Languages – C" 3510: 3459: 3446: 3083:"UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc" 2788: 2734: 2730: 2726: 2722: 1351: 1303: 1154: 1124: 996: 4214: 4121: 2657:
if binary context is obvious). In E notation, this is written as
543:, which facilitates reading and oral communication. For example, 486:– although the latter term is more general and also applies when 256:
In scientific notation, nonzero numbers are written in the form
2476:{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}} 1399: 1307: 3548:. Vol. 1, no. 6. Dayton, OH. November 1976. p. 1 2912:
Submission Guidelines for Authors: HPS 2010 Midyear Proceedings
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is added to (or subtracted from) the exponent, as shown below.
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that are too large or too small to be conveniently written in
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binary floating-point standard. Example: 1.3DEp42 represents
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can be read as "twelve-point-five nanometres" and written as
479:, is desired. Normalized scientific notation is often called 3464:
Davidson, Jim (January 1976). Nelson, Richard J. (ed.). "".
1849:{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}} 1081:
Some programming languages use other symbols. For instance,
992:
programming language supports the use of either "E" or "D".
3661:. 1987. pp. 105–108, 131–134, 370, 375. Archived from 3271:"ALGOL W – Notes For Introductory Computer Science Courses" 3131:
decimal digits This type of constant is only available on
2691:(or shorter: 1.001B11). For comparison, the same number in 2619:
For example, in base-2 scientific notation, the number 1001
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First, move the decimal separator point sufficient places,
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An exercise in converting to and from scientific notation
3740:] (in Japanese). Vol. 6. University Co-op. 1993. 3729:] (in Japanese). Vol. 5. University Co-op. 1991. 3690:
SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung
3646:
SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung
3619:
SHARP Taschencomputer Modell PC-1280 Bedienungsanleitung
3449:
users, and Richard C. Vanderburgh promoted these in the
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Texas Instruments electronic slide rule calculator SR-10
3345:"Revised proposal to encode the decimal exponent symbol" 326:. If the number is negative then a minus sign precedes 3298:"Revised Report on the Algorithmic Language Algol 68". 27:
Method of writing numbers with a large amount of digits
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programming language provided a choice of characters:
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Guides and Sample Code: Developer: Language Reference
3695:
SHARP Pocket Computer Model PC-E500S Operation Manual
2884:
Caliò, Franca; Alessandro, Lazzari (September 2017).
2491: 2397: 2355: 2295: 2235: 2092: 1965: 1862: 1769: 1696: 1636: 3679:
SHARP Pocket Computer Model PC-E500 Operation Manual
3651:
SHARP Pocket Computer Model PC-1475 Operation Manual
3624:
SHARP Pocket Computer Model PC-1280 Operation Manual
1003:" character instead of the letter "E", for example: 4235: 4233: 3527:] which is displayed in scientific notation as 2886:
Elements of Mathematics with Numerical Applications
1174: 1110: 1106: 1098: 1090: 1086: 1044: 1040: 1036: 1032: 1024: 1015:(1966) replaced the symbol by a single quote, e.g. 976:in 1958. Later versions of Fortran (at least since 938: 934: 920: 916: 861: 845: 829: 813: 797: 781: 762: 746: 4026:"Zimbabwe: Inflation Soars to 231 Million Percent" 3634:. 1987. pp. 56–60. 7M 0.8-I(TINSG1123ECZZ)(3) 2837:can be viewed as a base-1000 scientific notation. 2601: 2475: 2381: 2341: 2281: 2210: 2078: 1949: 1848: 1742: 1682: 999:(1960) programming language uses a subscript ten " 4080:electronic hexadecimal calculator/converter SR-22 1759:are performed using the rules for operation with 702:. However it is still unclear whether the error ( 387:in many ways: for example, 350 can be written as 3037:"The SHARE 709 System: Input-Output Translation" 3035:DiGri, Vincent J.; King, Jane E. (April 1959) . 2819:supports it as well. It is also required by the 1588:decimal separator in the significand is shifted 1223:may be represented by a normal width space or a 3813:Samples of usage of terminology and variants: 2918:. McLean, VA: Health Physics Society. p. 5 944:Most popular programming languages – including 4368:"The Swift Programming Language (Swift 3.0.1)" 4120:Schwartz, Jake; Grevelle, Rick (2003-10-20) . 3478:Vanderburgh, Richard C., ed. (November 1976). 2888:. Società Editrice Esculapio. pp. 30–32. 4246:. 5.10. April 2003. pp. 52, 153–154, 159 4213:Schwartz, Jake; Grevelle, Rick (2003-10-21). 3870:"INTOUCH 4GL a Guide to the INTOUCH Language" 3546:52-Notes – Newsletter of the SR-52 Users Club 3487:52-Notes – Newsletter of the SR-52 Users Club 1540:on the end, then shift the decimal separator 1169:calculator user Jim Davidson coined the term 710:in this case) is the maximum possible error, 358:Exponentiation § History of the notation 356:For the history of exponential notation, see 85:, it is usually known as "SCI" display mode. 8: 4208: 4206: 4204: 4115: 4113: 4111: 4109: 4107: 4105: 3727:Telephone board 5 PC-1490UII program library 3705:. 1995. 6J3KS(TINSG1223ECZZ). Archived from 2342:{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} 2282:{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}} 1743:{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} 1683:{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}} 4167:"Letters to the editor: On binary notation" 3964:Celestial Mechanics and Dynamical Astronomy 3216:Report on the Algorithmic Language ALGOL 60 3151:. 2005 . pp. 3-7–3-8, 3–10. 253261-003 3013:International Business Machines Corporation 2986:International Business Machines Corporation 1373:. In engineering notation, this is written 1195:series of calculators (1996–present) use a 555:, while its scientific notation equivalent 374:Any real number can be written in the form 3738:Telephone board 6 PC-U6000 program library 3228:: CS1 maint: location missing publisher ( 3164:Compaq Visual Fortran – Language Reference 1630:Given two numbers in scientific notation, 1339:. In scientific notation, this is written 1285:. In scientific notation, this is written 1140:to three significant figures in E notation 527:of 3. Consequently, the absolute value of 4272:(Issue 7, IEEE Std 1003.1, 2013 ed.) 4184: 3983: 3925: 3907: 3436:and recommended the "D" separator in the 3311: 3054: 2590: 2568: 2546: 2524: 2502: 2490: 2465: 2460: 2444: 2431: 2415: 2402: 2396: 2373: 2360: 2354: 2331: 2326: 2313: 2300: 2294: 2271: 2266: 2253: 2240: 2234: 2202: 2183: 2149: 2124: 2106: 2093: 2091: 2067: 2045: 2017: 1998: 1976: 1964: 1939: 1926: 1921: 1906: 1896: 1890: 1879: 1869: 1863: 1861: 1838: 1825: 1820: 1807: 1797: 1784: 1774: 1768: 1732: 1727: 1714: 1701: 1695: 1672: 1667: 1654: 1641: 1635: 4405:Scientific Notation to Decimal Converter 4400:Decimal to Scientific Notation Converter 4294:(1 ed.). Salt Lake City: Springer. 2391:Next, add or subtract the significands: 725: 430:remains at least one but less than ten ( 331: 87: 4123:HP16C Emulator Library for the HP48S/SX 2876: 1235:Further examples of scientific notation 1061:text encoding (1964), and was added to 1057:" character was included in the Soviet 456:. In normalized notation, the exponent 3999:Various (2000). Lide, David R. (ed.). 3221: 2713:This is closely related to the base-2 330:, as in ordinary decimal notation. In 4432:Lessons In Electric Circuits Vol 1 DC 4264:The IEEE and The Open Group (2013) . 3106:, Compaq/Digital Visual Fortran, and 2799:conversion specifiers. Starting with 334:, the exponent is chosen so that the 7: 4410:Scientific Notation in Everyday Life 4135:(NB. This library also works on the 3354:(Working Group Document), L2/08-030R 3102:For instance, DEC FORTRAN 77 (f77), 980:as of 1961) also use "D" to signify 4165:Martin, Bruce Alan (October 1968). 1535: 1500: 1490: 1484: 1004: 41:. For the food additive codes, see 4290:Beebe, Nelson H. F. (2017-08-22). 4270:The Open Group Base Specifications 4050:"Zimbabwe inflation hits new high" 3782:Whitaker, Ronald O. (1962-06-15). 2776:family of functions following the 1592:places to the left (or right) and 1453: %, or more simply a rate of 1365:. In scientific notation, this is 25: 4090:. 1974. p. 7. 1304-389 Rev A 4001:Handbook of Chemistry and Physics 3141:Intel Fortran: Language Reference 2653:using binary numbers (or shorter 269:times ten raised to the power of 4147:. Beyond the feature set of the 1105:supports the shorthand notation 472:for all elements of the series. 342:is at least 1 but less than 10. 3815:Moller, Donald A. (June 1976). 3723:電言板5 PC-1490UII PROGRAM LIBRARY 3505:– In the January 1976 issue of 3343:Broukhis, Leonid (2008-01-22), 3251:. The Early Days of Hexadecimal 1136:calculator display showing the 4088:Texas Instruments Incorporated 4024:Kadzere, Martin (2008-10-09). 3474:(1). Santa Ana, CA: 4. V3N1P4. 3412:Texas Instruments Incorporated 3306:(1–3): 1–236. September 1973. 3112:"Double Precision, REAL**16". 2755:= 1.40H0 = 1.40h0, or 98000 = 2678:Brookhaven National Laboratory 2450: 2424: 2165: 2156: 1544:digits to the right (positive 535:| < 1000, rather than 1 ≤ | 1: 4420:Scientific Notation Converter 3734:電言板6 PC-U6000 PROGRAM LIBRARY 3685:. 1989. 9G1KS(TINSE1189ECZZ). 3280:, Computer Science Department 3120:Digital Equipment Corporation 3085:. Math.hawaii.edu. 2012-02-12 653:can properly be expressed as 338:(modulus) of the significand 4438:Lessons In Electric Circuits 4056:. 2008-10-09. Archived from 3936:10.1103/RevModPhys.88.035009 3753:TI calculator character sets 3243:Savard, John J. G. (2018) . 494:other than 10 (for example, 73:in the United Kingdom. This 3172:Compaq Computer Corporation 2382:{\displaystyle n_{0}=n_{1}} 579:indicated to be significant 4481: 3759:"TI-83 Programmer's Guide" 3493:(6). Dayton, OH: 1. V1N6P1 2742:times 16 or 8 to the power 1495:. To represent the number 890:for a decimal significand 570: 512: 440:). Thus 350 is written as 367: 355: 36: 29: 4300:10.1007/978-3-319-64110-2 4172:Communications of the ACM 3985:10.1007/s10569-011-9352-4 3895:Reviews of Modern Physics 2791:standard, when using the 2782:Single Unix Specification 671:, which is shorthand for 32:Scientific pitch notation 4340:"floating point literal" 3733: 3722: 3189:The GNU Fortran Compiler 4086:(Revision A ed.). 3509:(V3N1p4) Jim Davidson ( 3400:Such as the TI SR-10. 2766:= 2.7732o5 = 2.7732C5. 1503:appended, resulting in 1076:DECIMAL EXPONENT SYMBOL 53:is a way of expressing 4153:floating-point numbers 4003:(81st ed.). CRC. 3359:"The Unicode Standard" 2909:Edwards, John (2009). 2693:decimal representation 2603: 2477: 2383: 2343: 2283: 2212: 2080: 1951: 1850: 1744: 1684: 1385:, this may be written 1141: 1115:mathematical constant 1109:(reserving the letter 970:SHARE Operating System 640:Estimated final digits 422:is chosen so that the 346:Decimal floating point 83:scientific calculators 4455:Mathematical notation 4186:10.1145/364096.364107 3855:"Scientific Notation" 3571:Specifically, models 3245:"Computer Arithmetic" 3115:DEC Fortran 77 Manual 3056:10.1145/320964.320969 2604: 2478: 2384: 2344: 2284: 2213: 2081: 1952: 1851: 1745: 1685: 1530:Scientific to decimal 1475:Decimal to scientific 1352:Earth's circumference 1128: 894:and integer exponent 531:is in the range 1 ≤ | 79:arithmetic operations 4028:. Harare, Zimbabwe: 3784:"Numerical Prefixes" 3531:will now be written 3432:Jim Davidson coined 3414:. 1973. 1304-739-266 3002:, ed. (1956-10-15). 2975:, ed. (1954-11-10). 2835:Engineering notation 2721:(e.g. 1B10 for 1×2 ( 2710:or shorter 1.001B3. 2489: 2395: 2353: 2293: 2233: 2090: 1963: 1860: 1767: 1694: 1634: 1548:) or left (negative 1027:. Subsequently, the 515:Engineering notation 509:Engineering notation 477:engineering notation 304:and the real number 94:Scientific notation 4426:Scientific Notation 4378:. Lexical Structure 4219:. 1.20 (1 ed.) 4126:. 1.20 (1 ed.) 3976:2011CeMDA.110..293L 3918:2016RvMP...88c5009M 3361:(v. 7.0.0 ed.) 3278:Stanford University 2973:Backus, John Warner 2847:Positional notation 2780:specification and ( 1959:Some examples are: 1204:for the separator. 986:quadruple precision 716:confidence interval 573:Significant figures 567:Significant figures 450:orders of magnitude 364:Normalized notation 332:normalized notation 294:terminating decimal 67:standard index form 51:Scientific notation 3322:10.1007/BF00265077 3042:Journal of the ACM 2599: 2473: 2379: 2339: 2279: 2208: 2076: 1947: 1846: 1740: 1680: 1466:Converting numbers 1392:40 megametres 1227:) that is allowed 1146:pocket calculators 1142: 898:means the same as 729:Explicit notation 4376:Apple Corporation 4309:978-3-319-64109-6 4010:978-0-8493-0481-1 3703:Sharp Corporation 3683:Sharp Corporation 3659:Sharp Corporation 3632:Sharp Corporation 3457:Texas Instruments 3149:Intel Corporation 2949:978-0-8412-3999-9 2733:), 1B40 for 1×2 ( 2729:), 1B30 for 1×2 ( 2725:), 1B20 for 1×2 ( 2674:Bruce Alan Martin 2134: 1912: 1885: 1443:Zimbabwean dollar 1354:is approximately 1244:'s mass is about 1202: 1186:Texas Instruments 1161:, as seen in the 1153:, as seen in the 1138:Avogadro constant 1131:Texas Instruments 874:computer programs 867: 866: 523:is restricted to 454:common logarithms 370:Normalized number 254: 253: 91:Decimal notation 16:(Redirected from 4472: 4387: 4386: 4384: 4383: 4364: 4358: 4357: 4351: 4350: 4344:cppreference.com 4336: 4330: 4329: 4287: 4281: 4280: 4278: 4277: 4261: 4255: 4254: 4252: 4251: 4245: 4237: 4228: 4227: 4225: 4224: 4210: 4199: 4198: 4188: 4162: 4156: 4134: 4132: 4131: 4117: 4100: 4098: 4096: 4095: 4085: 4075: 4069: 4068: 4066: 4065: 4046: 4040: 4039: 4037: 4036: 4021: 4015: 4014: 3996: 3990: 3989: 3987: 3954: 3948: 3947: 3929: 3911: 3885: 3879: 3877: 3872:. Archived from 3864: 3862: 3861: 3852: 3850: 3849: 3840: 3835:. Archived from 3830: 3828: 3827: 3821: 3811: 3805: 3803: 3801: 3800: 3788: 3779: 3773: 3771: 3769: 3768: 3763: 3749: 3743: 3741: 3730: 3720: 3718: 3717: 3711: 3700: 3686: 3676: 3674: 3673: 3667: 3656: 3642: 3640: 3639: 3629: 3569: 3563: 3556: 3554: 3553: 3537: 3534: 3530: 3520: 3499: 3498: 3484: 3475: 3430: 3424: 3422: 3420: 3419: 3409: 3398: 3392: 3391: 3389: 3388: 3377: 3371: 3369: 3367: 3366: 3355: 3349: 3340: 3334: 3333: 3315: 3300:Acta Informatica 3295: 3289: 3288: 3286: 3285: 3275: 3266: 3260: 3259: 3257: 3256: 3240: 3234: 3233: 3227: 3219: 3208: 3202: 3200: 3198: 3197: 3182: 3180: 3179: 3169: 3159: 3157: 3156: 3146: 3137: 3127: 3126: 3100: 3094: 3093: 3091: 3090: 3079: 3073: 3071: 3058: 3032: 3026: 3023: 3021: 3020: 3015:. pp. 9, 27 3010: 2995: 2993: 2992: 2983: 2968: 2962: 2961: 2933: 2927: 2926: 2924: 2923: 2917: 2906: 2900: 2899: 2895:978-8-89385052-0 2881: 2830: 2765: 2754: 2709: 2698: 2690: 2667: 2656: 2652: 2641: 2631:) is written as 2608: 2606: 2605: 2600: 2598: 2597: 2576: 2575: 2554: 2553: 2532: 2531: 2510: 2509: 2482: 2480: 2479: 2474: 2472: 2471: 2470: 2469: 2449: 2448: 2436: 2435: 2420: 2419: 2407: 2406: 2388: 2386: 2385: 2380: 2378: 2377: 2365: 2364: 2348: 2346: 2345: 2340: 2338: 2337: 2336: 2335: 2318: 2317: 2305: 2304: 2288: 2286: 2285: 2280: 2278: 2277: 2276: 2275: 2258: 2257: 2245: 2244: 2217: 2215: 2214: 2209: 2207: 2206: 2188: 2187: 2169: 2168: 2135: 2133: 2132: 2131: 2112: 2111: 2110: 2094: 2085: 2083: 2082: 2077: 2075: 2074: 2053: 2052: 2031: 2030: 2003: 2002: 1984: 1983: 1956: 1954: 1953: 1948: 1946: 1945: 1944: 1943: 1931: 1930: 1913: 1911: 1910: 1901: 1900: 1891: 1886: 1884: 1883: 1874: 1873: 1864: 1855: 1853: 1852: 1847: 1845: 1844: 1843: 1842: 1830: 1829: 1812: 1811: 1802: 1801: 1789: 1788: 1779: 1778: 1749: 1747: 1746: 1741: 1739: 1738: 1737: 1736: 1719: 1718: 1706: 1705: 1689: 1687: 1686: 1681: 1679: 1678: 1677: 1676: 1659: 1658: 1646: 1645: 1626:Basic operations 1621: 1619: 1613: 1611: 1605: 1603: 1578: 1577: 1571: 1569: 1563: 1559: 1557: 1539: 1525: 1523: 1517: 1516: 1510: 1508: 1502: 1498: 1494: 1489:; to the right, 1488: 1460: 1458: 1452: 1450: 1433: 1431: 1428: 1419: 1417: 1408: 1393: 1388: 1383:SI writing style 1380: 1378: 1372: 1370: 1364: 1362: 1359: 1346: 1344: 1338: 1336: 1333: 1330: 1327: 1324: 1321: 1318: 1315: 1298: 1296: 1293: 1290: 1284: 1282: 1279: 1276: 1273: 1270: 1267: 1264: 1261: 1258: 1255: 1252: 1249: 1203: 1200: 1182:pocket computers 1176: 1160: 1152: 1112: 1108: 1100: 1092: 1088: 1077: 1074: 1071: 1069: 1052: 1046: 1042: 1038: 1034: 1026: 1018: 1010: 982:double precision 940: 936: 931: 929: 922: 918: 913: 911: 904: 889: 863: 858: 856: 847: 842: 840: 831: 826: 824: 815: 810: 808: 799: 794: 792: 783: 778: 776: 773: 764: 759: 757: 748: 743: 741: 726: 714:, or some other 709: 707: 701: 699: 695: 692: 689: 685: 682: 679: 676: 670: 668: 664: 661: 658: 635: 633: 630: 624: 622: 619: 613: 611: 605: 604: 601: 590: 589: 586: 562: 560: 554: 550: 548: 504: 503: 499: 467: 465: 447: 445: 439: 437: 410: 408: 402: 400: 394: 392: 386: 385: 381: 324:common logarithm 250: 248: 241: 240: 237: 234: 225: 223: 216: 209: 207: 200: 193: 191: 184: 183: 180: 177: 168: 166: 159: 158: 149: 147: 144: 137: 135: 126: 124: 117: 110: 108: 101: 88: 21: 4480: 4479: 4475: 4474: 4473: 4471: 4470: 4469: 4465:Numeral systems 4445: 4444: 4435:free ebook and 4396: 4391: 4390: 4381: 4379: 4366: 4365: 4361: 4348: 4346: 4338: 4337: 4333: 4310: 4289: 4288: 4284: 4275: 4273: 4263: 4262: 4258: 4249: 4247: 4243: 4239: 4238: 4231: 4222: 4220: 4212: 4211: 4202: 4164: 4163: 4159: 4129: 4127: 4119: 4118: 4103: 4093: 4091: 4083: 4077: 4076: 4072: 4063: 4061: 4048: 4047: 4043: 4034: 4032: 4023: 4022: 4018: 4011: 3998: 3997: 3993: 3956: 3955: 3951: 3927:10.1.1.150.1225 3887: 3886: 3882: 3868: 3859: 3857: 3853: 3847: 3845: 3841: 3831: 3825: 3823: 3819: 3814: 3812: 3808: 3798: 3796: 3786: 3781: 3780: 3776: 3766: 3764: 3761: 3757: 3750: 3746: 3735: 3732: 3724: 3721: 3715: 3713: 3709: 3698: 3687: 3677: 3671: 3669: 3665: 3654: 3643: 3637: 3635: 3627: 3616: 3570: 3566: 3551: 3549: 3540: 3532: 3528: 3518: 3496: 3494: 3482: 3477: 3463: 3455:newsletter for 3444:Hewlett-Packard 3442:newsletter for 3431: 3427: 3417: 3415: 3407: 3401: 3399: 3395: 3386: 3384: 3379: 3378: 3374: 3364: 3362: 3357: 3347: 3342: 3341: 3337: 3313:10.1.1.219.3999 3297: 3296: 3292: 3283: 3281: 3273: 3268: 3267: 3263: 3254: 3252: 3242: 3241: 3237: 3220: 3210: 3209: 3205: 3195: 3193: 3185: 3177: 3175: 3167: 3161: 3154: 3152: 3144: 3138: 3124: 3122: 3111: 3101: 3097: 3088: 3086: 3081: 3080: 3076: 3034: 3033: 3029: 3024:(2+51+1 pages) 3018: 3016: 3008: 2998: 2990: 2988: 2981: 2971: 2969: 2965: 2950: 2935: 2934: 2930: 2921: 2919: 2915: 2908: 2907: 2903: 2896: 2883: 2882: 2878: 2873: 2858:Suzhou numerals 2843: 2828: 2824: 2786:IEEE Std 1003.1 2764: 2760: 2756: 2753: 2749: 2745: 2719:binary prefixes 2708: 2704: 2700: 2696: 2689: 2685: 2681: 2680:in 1968, as in 2671: 2666: 2662: 2658: 2654: 2651: 2647: 2643: 2640: 2636: 2632: 2630: 2622: 2614: 2586: 2564: 2542: 2520: 2498: 2487: 2486: 2461: 2456: 2440: 2427: 2411: 2398: 2393: 2392: 2389: 2369: 2356: 2351: 2350: 2327: 2322: 2309: 2296: 2291: 2290: 2267: 2262: 2249: 2236: 2231: 2230: 2198: 2179: 2145: 2120: 2113: 2102: 2095: 2088: 2087: 2063: 2041: 2013: 1994: 1972: 1961: 1960: 1935: 1922: 1917: 1902: 1892: 1875: 1865: 1858: 1857: 1834: 1821: 1816: 1803: 1793: 1780: 1770: 1765: 1764: 1728: 1723: 1710: 1697: 1692: 1691: 1668: 1663: 1650: 1637: 1632: 1631: 1628: 1623: 1617: 1615: 1609: 1607: 1601: 1599: 1585: 1575: 1573: 1567: 1565: 1561: 1555: 1553: 1532: 1521: 1519: 1514: 1512: 1506: 1504: 1496: 1477: 1468: 1456: 1454: 1448: 1446: 1429: 1426: 1424: 1420:to the nearest 1415: 1413: 1406: 1391: 1386: 1376: 1374: 1368: 1366: 1360: 1357: 1355: 1342: 1340: 1334: 1331: 1328: 1325: 1322: 1319: 1316: 1313: 1311: 1294: 1291: 1288: 1286: 1280: 1277: 1274: 1271: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1245: 1237: 1213: 1199: 1167:Hewlett-Packard 1163:Commodore PR100 1158: 1150: 1075: 1072: 1067: 1066: 1056: 1051: 1048: 1016: 1008: 1002: 927: 925: 909: 907: 899: 885: E  881: 854: 852: 838: 836: 822: 820: 806: 804: 790: 788: 774: 771: 769: 755: 753: 739: 737: 724: 705: 703: 697: 693: 690: 687: 683: 680: 677: 674: 672: 666: 662: 659: 656: 654: 642: 631: 628: 626: 620: 617: 615: 609: 607: 602: 599: 597: 587: 584: 582: 575: 569: 558: 556: 552: 546: 544: 517: 511: 501: 497: 495: 463: 461: 443: 441: 433: 431: 406: 404: 398: 396: 390: 388: 383: 379: 375: 372: 366: 361: 354: 320:fractional part 296:). The integer 263: 246: 244: 238: 235: 232: 230: 221: 219: 214: 205: 203: 198: 189: 187: 181: 178: 175: 173: 164: 162: 156: 154: 145: 142: 140: 133: 131: 122: 120: 115: 106: 104: 99: 63:scientific form 46: 35: 28: 23: 22: 15: 12: 11: 5: 4478: 4476: 4468: 4467: 4462: 4457: 4447: 4446: 4443: 4442: 4422: 4417: 4412: 4407: 4402: 4395: 4394:External links 4392: 4389: 4388: 4359: 4331: 4308: 4282: 4256: 4229: 4200: 4157: 4101: 4070: 4041: 4016: 4009: 3991: 3970:(4): 293–304. 3949: 3880: 3876:on 2015-05-03. 3839:on 2007-10-19. 3806: 3774: 3744: 3564: 3557:(NB. The term 3425: 3393: 3372: 3335: 3290: 3261: 3235: 3214:, ed. (1960). 3203: 3183:(1441 pages) 3095: 3074: 3049:(2): 141–144. 3027: 2963: 2948: 2928: 2901: 2894: 2875: 2874: 2872: 2869: 2868: 2867: 2861: 2855: 2849: 2842: 2839: 2826: 2762: 2758: 2751: 2747: 2715:floating-point 2706: 2702: 2687: 2683: 2669: 2664: 2660: 2649: 2645: 2638: 2634: 2628: 2620: 2613: 2610: 2596: 2593: 2589: 2585: 2582: 2579: 2574: 2571: 2567: 2563: 2560: 2557: 2552: 2549: 2545: 2541: 2538: 2535: 2530: 2527: 2523: 2519: 2516: 2513: 2508: 2505: 2501: 2497: 2494: 2468: 2464: 2459: 2455: 2452: 2447: 2443: 2439: 2434: 2430: 2426: 2423: 2418: 2414: 2410: 2405: 2401: 2376: 2372: 2368: 2363: 2359: 2334: 2330: 2325: 2321: 2316: 2312: 2308: 2303: 2299: 2274: 2270: 2265: 2261: 2256: 2252: 2248: 2243: 2239: 2229: 2205: 2201: 2197: 2194: 2191: 2186: 2182: 2178: 2175: 2172: 2167: 2164: 2161: 2158: 2155: 2152: 2148: 2144: 2141: 2138: 2130: 2127: 2123: 2119: 2116: 2109: 2105: 2101: 2098: 2073: 2070: 2066: 2062: 2059: 2056: 2051: 2048: 2044: 2040: 2037: 2034: 2029: 2026: 2023: 2020: 2016: 2012: 2009: 2006: 2001: 1997: 1993: 1990: 1987: 1982: 1979: 1975: 1971: 1968: 1942: 1938: 1934: 1929: 1925: 1920: 1916: 1909: 1905: 1899: 1895: 1889: 1882: 1878: 1872: 1868: 1841: 1837: 1833: 1828: 1824: 1819: 1815: 1810: 1806: 1800: 1796: 1792: 1787: 1783: 1777: 1773: 1761:exponentiation 1753:Multiplication 1735: 1731: 1726: 1722: 1717: 1713: 1709: 1704: 1700: 1675: 1671: 1666: 1662: 1657: 1653: 1649: 1644: 1640: 1627: 1624: 1598: 1584: 1581: 1552:). The number 1531: 1528: 1476: 1473: 1467: 1464: 1463: 1462: 1438:Hyperinflation 1435: 1402:is defined as 1396: 1348: 1300: 1236: 1233: 1212: 1209: 1065:5.2 (2009) as 1054: 1049: 1006: 1000: 972:(SOS) for the 933:is written as 915:is written as 905:. For example 865: 864: 859: 849: 848: 843: 833: 832: 827: 817: 816: 811: 801: 800: 795: 785: 784: 779: 766: 765: 760: 750: 749: 744: 734: 733: 730: 723: 720: 712:standard error 641: 638: 571:Main article: 568: 565: 513:Main article: 510: 507: 438:| < 10 424:absolute value 368:Main article: 365: 362: 353: 350: 336:absolute value 308:is called the 300:is called the 258: 252: 251: 242: 227: 226: 217: 211: 210: 201: 195: 194: 185: 170: 169: 160: 151: 150: 138: 128: 127: 118: 112: 111: 102: 96: 95: 92: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4477: 4466: 4463: 4461: 4458: 4456: 4453: 4452: 4450: 4440: 4439: 4434: 4433: 4429:chapter from 4428: 4427: 4423: 4421: 4418: 4416: 4413: 4411: 4408: 4406: 4403: 4401: 4398: 4397: 4393: 4377: 4373: 4369: 4363: 4360: 4356: 4345: 4341: 4335: 4332: 4327: 4323: 4319: 4315: 4311: 4305: 4301: 4297: 4293: 4286: 4283: 4271: 4267: 4260: 4257: 4242: 4236: 4234: 4230: 4218: 4217: 4209: 4207: 4205: 4201: 4196: 4192: 4187: 4182: 4178: 4174: 4173: 4168: 4161: 4158: 4154: 4150: 4146: 4142: 4138: 4125: 4124: 4116: 4114: 4112: 4110: 4108: 4106: 4102: 4089: 4082: 4081: 4074: 4071: 4060:on 2009-05-14 4059: 4055: 4051: 4045: 4042: 4031: 4027: 4020: 4017: 4012: 4006: 4002: 3995: 3992: 3986: 3981: 3977: 3973: 3969: 3965: 3961: 3953: 3950: 3945: 3941: 3937: 3933: 3928: 3923: 3919: 3915: 3910: 3905: 3902:(3): 035009. 3901: 3897: 3896: 3891: 3884: 3881: 3878: 3875: 3871: 3866: 3856: 3844: 3838: 3834: 3818: 3810: 3807: 3794: 3793: 3789:. Crosstalk. 3785: 3778: 3775: 3772: 3760: 3754: 3748: 3745: 3742: 3739: 3728: 3712:on 2017-02-24 3708: 3704: 3701:(in German). 3696: 3692: 3691: 3684: 3680: 3668:on 2017-02-25 3664: 3660: 3657:(in German). 3652: 3648: 3647: 3633: 3630:(in German). 3625: 3621: 3620: 3614: 3610: 3606: 3602: 3598: 3594: 3590: 3586: 3582: 3578: 3574: 3568: 3565: 3562: 3560: 3547: 3543: 3539: 3536: 3526: 3525: 3516: 3512: 3508: 3504: 3492: 3488: 3481: 3473: 3469: 3468: 3461: 3458: 3454: 3453: 3448: 3445: 3441: 3440: 3435: 3429: 3426: 3413: 3406: 3405: 3397: 3394: 3383:. August 1986 3382: 3376: 3373: 3370: 3360: 3353: 3346: 3339: 3336: 3331: 3327: 3323: 3319: 3314: 3309: 3305: 3301: 3294: 3291: 3279: 3272: 3265: 3262: 3250: 3246: 3239: 3236: 3231: 3225: 3218:. Copenhagen. 3217: 3213: 3207: 3204: 3201: 3191: 3190: 3174:. August 2001 3173: 3166: 3165: 3160:(858 pages) 3150: 3143: 3142: 3136: 3134: 3133:Alpha systems 3121: 3117: 3116: 3109: 3105: 3104:Intel Fortran 3099: 3096: 3084: 3078: 3075: 3070: 3066: 3062: 3057: 3052: 3048: 3044: 3043: 3038: 3031: 3028: 3025: 3014: 3007: 3006: 3001: 2987: 2980: 2979: 2974: 2967: 2964: 2959: 2955: 2951: 2945: 2941: 2940: 2932: 2929: 2914: 2913: 2905: 2902: 2897: 2891: 2887: 2880: 2877: 2870: 2865: 2862: 2859: 2856: 2853: 2852:ISO/IEC 80000 2850: 2848: 2845: 2844: 2840: 2838: 2836: 2832: 2822: 2821:IEEE 754-2008 2818: 2814: 2810: 2806: 2802: 2798: 2794: 2790: 2787: 2783: 2779: 2775: 2774: 2767: 2744:as in 1.25 = 2743: 2738: 2736: 2732: 2728: 2724: 2720: 2716: 2711: 2694: 2679: 2675: 2626: 2617: 2611: 2609: 2594: 2591: 2587: 2583: 2580: 2577: 2572: 2569: 2565: 2561: 2558: 2555: 2550: 2547: 2543: 2539: 2536: 2533: 2528: 2525: 2521: 2517: 2514: 2511: 2506: 2503: 2499: 2495: 2492: 2483: 2466: 2462: 2457: 2453: 2445: 2441: 2437: 2432: 2428: 2421: 2416: 2412: 2408: 2403: 2399: 2374: 2370: 2366: 2361: 2357: 2332: 2328: 2323: 2319: 2314: 2310: 2306: 2301: 2297: 2272: 2268: 2263: 2259: 2254: 2250: 2246: 2241: 2237: 2228: 2226: 2222: 2218: 2203: 2199: 2195: 2192: 2189: 2184: 2180: 2176: 2173: 2170: 2162: 2159: 2153: 2150: 2146: 2142: 2139: 2136: 2128: 2125: 2121: 2117: 2114: 2107: 2103: 2099: 2096: 2071: 2068: 2064: 2060: 2057: 2054: 2049: 2046: 2042: 2038: 2035: 2032: 2027: 2024: 2021: 2018: 2014: 2010: 2007: 2004: 1999: 1995: 1991: 1988: 1985: 1980: 1977: 1973: 1969: 1966: 1957: 1940: 1936: 1932: 1927: 1923: 1918: 1914: 1907: 1903: 1897: 1893: 1887: 1880: 1876: 1870: 1866: 1839: 1835: 1831: 1826: 1822: 1817: 1813: 1808: 1804: 1798: 1794: 1790: 1785: 1781: 1775: 1771: 1762: 1758: 1754: 1750: 1733: 1729: 1724: 1720: 1715: 1711: 1707: 1702: 1698: 1673: 1669: 1664: 1660: 1655: 1651: 1647: 1642: 1638: 1625: 1597: 1595: 1591: 1582: 1580: 1551: 1547: 1543: 1538: 1529: 1527: 1526:as a result. 1511:. The number 1493: 1487: 1482: 1474: 1472: 1465: 1444: 1439: 1436: 1423: 1412: 1405: 1401: 1397: 1394: 1384: 1353: 1349: 1309: 1305: 1301: 1243: 1239: 1238: 1234: 1232: 1230: 1226: 1222: 1218: 1211:Use of spaces 1210: 1208: 1205: 1198: 1197:small capital 1194: 1190: 1187: 1183: 1180: 1172: 1168: 1164: 1156: 1147: 1139: 1135: 1132: 1127: 1123: 1121: 1119: 1118: 1104: 1096: 1084: 1079: 1064: 1060: 1053:. The ALGOL " 1030: 1022: 1014: 998: 993: 991: 987: 983: 979: 975: 971: 967: 963: 959: 955: 951: 947: 942: 932: 914: 902: 897: 893: 888: 884: 879: 875: 871: 860: 851: 850: 844: 835: 834: 828: 819: 818: 812: 803: 802: 796: 787: 786: 780: 768: 767: 761: 752: 751: 745: 736: 735: 731: 728: 727: 721: 719: 717: 713: 652: 646: 639: 637: 606:would become 593: 580: 574: 566: 564: 542: 538: 534: 530: 526: 522: 516: 508: 506: 493: 489: 485: 483: 478: 473: 471: 459: 455: 451: 436: 429: 425: 421: 417: 412: 378: 371: 363: 359: 351: 349: 347: 343: 341: 337: 333: 329: 325: 321: 317: 313: 312: 307: 303: 299: 295: 291: 288:is a nonzero 287: 284: 280: 276: 272: 268: 261: 257: 243: 229: 228: 218: 213: 212: 202: 197: 196: 186: 172: 171: 161: 153: 152: 139: 130: 129: 119: 114: 113: 103: 98: 97: 93: 90: 89: 86: 84: 80: 76: 72: 71:standard form 68: 64: 60: 56: 52: 48: 44: 40: 33: 19: 4437: 4431: 4425: 4380:. Retrieved 4371: 4362: 4355:description. 4353: 4347:. Retrieved 4343: 4334: 4291: 4285: 4274:. 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Index

E notation
Scientific pitch notation
E series
E number
numbers
decimal form
base ten
arithmetic operations
scientific calculators
integer
coefficient
real number
terminating decimal
exponent
significand
fractional part
common logarithm
normalized notation
absolute value
Decimal floating point
Exponentiation § History of the notation
Normalized number
absolute value
orders of magnitude
common logarithms
engineering notation
exponential
bases
Engineering notation
multiples

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