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
2205: 2073: 2596: 2688:(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 1459:
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.
2661:) 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 1944: 3946:
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.
437:. 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 1951: 2470: 584:
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).
2477: 457:). 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 1162:
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,
3524:. 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). 3176: 1196:
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
528:| < 10. Though similar in concept, engineering notation is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their corresponding 3821: 2376: 1848: 570:. 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 3218: 4356: 3412:(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.) 3506:" which is technically incorrect, and the letter D to separate the "mantissa" from the decapower for typewritten numbers, as Jim also suggests. For example, 464:
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
3677: 2383: 1166:); these gained some currency in the programmable calculator user community. The letters "E" or "D" were used as a scientific-notation separator by 1430:
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
1755: 930:. While common in computer output, this abbreviated version of scientific notation is discouraged for published documents by some style guides. 2605:
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.
4296: 3997: 2936: 2882: 1472:, 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 2796:
I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since
3825: 3949:"The IAU 2009 system of astronomical constants: The report of the IAU working group on numerical standards for Fundamental Astronomy" 2931:(3rd ed.). Washington, DC : Oxford ; New York: American Chemical Society ; Oxford University Press. p. 210. 508:
Engineering notation (often named "ENG" on scientific calculators) differs from normalized scientific notation in that the exponent
2200:{\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}} 1220:
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:
1682: 1622: 4038: 4443: 4076: 3858: 3400: 2666: 2068:{\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}} 3108: 1371: 946: 27: 1398:. Using scientific notation, this value can be uniformly expressed to any desired precision, from the nearest tenth of a 3741: 2805: 3854: 3160: 1173:
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
2965: 307:. The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the 2992: 3772: 2281: 2221: 4160: 3883: 2770: 1103: 625:. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous. 20: 2591:{\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}} 66:
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
938: 3811:(Technica Report). WHOI Document Collection. Woods Hole, MA: Woods Hole Oceanographic Institution. WHOI-76-59 3651: 3606: 50:, since to do so would require writing out an inconveniently long string of digits. It may be referred to as 1151: 3695: 2849:– a Chinese numeral system formerly used in commerce, with order of magnitude written below the significand 2843:– an international standard which guides the use of physical quantities and units of measurement in science 3910: 3806:"A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB" 3780: 3296: 2681: 1745: 958: 513: 334: 71: 3805: 2899: 4254: 4141: 4018: 2613: 953:– use this "E" notation, which comes from Fortran and was present in the first version released for the 480: 67: 4398: 4393: 4388: 4281:
The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library
3747: 2662: 1114: 4448: 3960: 3902: 3259: 2823: 503: 465: 3915: 3843: 3565: 3301: 4229: 4088:(NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.) 3569: 3561: 3266: 2835: 1205: 974: 704: 567: 561: 438: 3862: 4419: 4310: 4179: 3928: 3892: 3314: 3212: 3049: 3030: 2961: 2341: 1488:
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
1000:. This presented a challenge for computer systems which did not provide such a character, so 4284: 4169: 3968: 3920: 3581: 3306: 3039: 1434:
reached 79.6 billion percent; the approximate value with three significant figures would be
1083: 970: 862: 442: 312: 3391: 3468: 3432: 3369: 3333: 2846: 2774: 2707: 1170: 1155: 308: 3151: 552:
would likely be read out as "one-point-two-five times ten-to-the-negative-eight metres".
3964: 3906: 3102: 1146:), or a pair of smaller and slightly raised digits were reserved for the exponent (e.g. 479:
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
2703: 1749: 1741: 1426: 700: 470: 412: 346: 324: 4403: 4046: 3527: 2973:(Preliminary report). New York: Programming Research Group, Applied Science Division, 2855:– a notation to specify resistor and capacitor values, with symbols for powers of 1000 4437: 3831: 3597: 3593: 3585: 3530: 3175:"6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter". 3092: 2840: 2809: 1009: 913: 449:
is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as
4425: 4314: 4183: 3053: 1939:{\displaystyle {\frac {x_{0}}{x_{1}}}={\frac {m_{0}}{m_{1}}}\times 10^{n_{0}-n_{1}}} 3932: 3318: 1523:
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
4364: 4288: 3973: 3948: 3832:"Bryn Mawr College: Survival Skills for Problem Solving – Scientific Notation" 3200: 2801: 1399: 1213: 1185: 1047: 966: 950: 858: 4408: 4140:, this package also supports calculations for binary, octal, and hexadecimal 2926: 2925:
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).
3044: 3025: 3000:. New York: Applied Science Division and Programming Research Department, 2706:
representation commonly used in computer arithmetic, and the usage of IEC
2657:(or shorter: 1.001E11) with the letter "E" now standing for "times two (10 1549:
would have its decimal separator shifted 6 digits to the right and become
4042: 3503: 3495: 3455: 3427: 3233: 2852: 2209: 1230: 1017: 1008:, and some Soviet Algol variants allowed the use of the Cyrillic letter " 290: 63: 31: 3370:"SIMULA standard as defined by the SIMULA Standards Group – 3.1 Numbers" 2797: 2789: 337:
is a computer arithmetic system closely related to scientific notation.
19:
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
4129: 3879:"CODATA recommended values of the fundamental physical constants: 2014" 3310: 1051: 1001: 962: 954: 934: 282: 267: 4255:"dprintf, fprintf, printf, snprintf, sprintf – print formatted output" 3061:(4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.) 2928:
The ACS style guide: effective communication of scientific information
26:"E notation" redirects here. For the series of preferred numbers, see 4137: 4125: 3822:"Cengage – the Leading Provider of Higher Education Course Materials" 2761: 1071: 978: 639: 3897: 3258:
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
942: 4306: 4230:"Rationale for International Standard – Programming Languages – C" 3499: 3448: 3435: 3072:"UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc" 2777: 2723: 2719: 2715: 2711: 1340: 1292: 1143: 1113: 985: 4203: 4110: 2646:
if binary context is obvious). In E notation, this is written as
532:, which facilitates reading and oral communication. For example, 475:– although the latter term is more general and also applies when 245:
In scientific notation, nonzero numbers are written in the form
2465:{\displaystyle x_{0}\pm x_{1}=(m_{0}\pm m_{1})\times 10^{n_{0}}} 1388: 1296: 3537:. Vol. 1, no. 6. Dayton, OH. November 1976. p. 1 2901:
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
468:, is desired. Normalized scientific notation is often called 3453:
Davidson, Jim (January 1976). Nelson, Richard J. (ed.). "".
1838:{\displaystyle x_{0}x_{1}=m_{0}m_{1}\times 10^{n_{0}+n_{1}}} 1070:
Some programming languages use other symbols. For instance,
981:
programming language supports the use of either "E" or "D".
3650:. 1987. pp. 105–108, 131–134, 370, 375. Archived from 3260:"ALGOL W – Notes For Introductory Computer Science Courses" 3120:
decimal digits This type of constant is only available on
2680:(or shorter: 1.001B11). For comparison, the same number in 2608:
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
3729:] (in Japanese). Vol. 6. University Co-op. 1993. 3718:] (in Japanese). Vol. 5. University Co-op. 1991. 3679:
SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung
3635:
SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung
3608:
SHARP Taschencomputer Modell PC-1280 Bedienungsanleitung
3438:
users, and Richard C. Vanderburgh promoted these in the
3393:
Texas Instruments electronic slide rule calculator SR-10
3334:"Revised proposal to encode the decimal exponent symbol" 315:. If the number is negative then a minus sign precedes 3287:"Revised Report on the Algorithmic Language Algol 68". 16:
Method of writing numbers with a large amount of digits
1020:
programming language provided a choice of characters:
4361:
Guides and Sample Code: Developer: Language Reference
3684:
SHARP Pocket Computer Model PC-E500S Operation Manual
2873:
Caliò, Franca; Alessandro, Lazzari (September 2017).
2480: 2386: 2344: 2284: 2224: 2081: 1954: 1851: 1758: 1685: 1625: 3668:
SHARP Pocket Computer Model PC-E500 Operation Manual
3640:
SHARP Pocket Computer Model PC-1475 Operation Manual
3613:
SHARP Pocket Computer Model PC-1280 Operation Manual
992:" character instead of the letter "E", for example: 4224: 4222: 3516:] which is displayed in scientific notation as 2875:
Elements of Mathematics with Numerical Applications
1163: 1099: 1095: 1087: 1079: 1075: 1033: 1029: 1025: 1021: 1013: 1004:(1966) replaced the symbol by a single quote, e.g. 965:in 1958. Later versions of Fortran (at least since 927: 923: 909: 905: 850: 834: 818: 802: 786: 770: 751: 735: 4015:"Zimbabwe: Inflation Soars to 231 Million Percent" 3623:. 1987. pp. 56–60. 7M 0.8-I(TINSG1123ECZZ)(3) 2826:can be viewed as a base-1000 scientific notation. 2590: 2464: 2370: 2330: 2270: 2199: 2067: 1938: 1837: 1731: 1671: 988:(1960) programming language uses a subscript ten " 4069:electronic hexadecimal calculator/converter SR-22 1748:are performed using the rules for operation with 691:. However it is still unclear whether the error ( 376:in many ways: for example, 350 can be written as 3026:"The SHARE 709 System: Input-Output Translation" 3024:DiGri, Vincent J.; King, Jane E. (April 1959) . 2808:supports it as well. It is also required by the 1577:decimal separator in the significand is shifted 1212:may be represented by a normal width space or a 3802:Samples of usage of terminology and variants: 2907:. McLean, VA: Health Physics Society. p. 5 933:Most popular programming languages – including 4357:"The Swift Programming Language (Swift 3.0.1)" 4109:Schwartz, Jake; Grevelle, Rick (2003-10-20) . 3467:Vanderburgh, Richard C., ed. (November 1976). 2877:. Società Editrice Esculapio. pp. 30–32. 4235:. 5.10. April 2003. pp. 52, 153–154, 159 4202:Schwartz, Jake; Grevelle, Rick (2003-10-21). 3859:"INTOUCH 4GL a Guide to the INTOUCH Language" 3535:52-Notes – Newsletter of the SR-52 Users Club 3476:52-Notes – Newsletter of the SR-52 Users Club 1529:on the end, then shift the decimal separator 1158:calculator user Jim Davidson coined the term 699:in this case) is the maximum possible error, 347:Exponentiation § History of the notation 345:For the history of exponential notation, see 74:, it is usually known as "SCI" display mode. 8: 4197: 4195: 4193: 4104: 4102: 4100: 4098: 4096: 4094: 3716:Telephone board 5 PC-1490UII program library 3694:. 1995. 6J3KS(TINSG1223ECZZ). Archived from 2331:{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} 2271:{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}} 1732:{\displaystyle x_{1}=m_{1}\times 10^{n_{1}}} 1672:{\displaystyle x_{0}=m_{0}\times 10^{n_{0}}} 4156:"Letters to the editor: On binary notation" 3953:Celestial Mechanics and Dynamical Astronomy 3205:Report on the Algorithmic Language ALGOL 60 3140:. 2005 . pp. 3-7–3-8, 3–10. 253261-003 3002:International Business Machines Corporation 2975:International Business Machines Corporation 1362:. In engineering notation, this is written 1184:series of calculators (1996–present) use a 544:, while its scientific notation equivalent 363:Any real number can be written in the form 3727:Telephone board 6 PC-U6000 program library 3217:: CS1 maint: location missing publisher ( 3153:Compaq Visual Fortran – Language Reference 1619:Given two numbers in scientific notation, 1328:. In scientific notation, this is written 1274:. In scientific notation, this is written 1129:to three significant figures in E notation 516:of 3. Consequently, the absolute value of 4261:(Issue 7, IEEE Std 1003.1, 2013 ed.) 4173: 3972: 3914: 3896: 3425:and recommended the "D" separator in the 3300: 3043: 2579: 2557: 2535: 2513: 2491: 2479: 2454: 2449: 2433: 2420: 2404: 2391: 2385: 2362: 2349: 2343: 2320: 2315: 2302: 2289: 2283: 2260: 2255: 2242: 2229: 2223: 2191: 2172: 2138: 2113: 2095: 2082: 2080: 2056: 2034: 2006: 1987: 1965: 1953: 1928: 1915: 1910: 1895: 1885: 1879: 1868: 1858: 1852: 1850: 1827: 1814: 1809: 1796: 1786: 1773: 1763: 1757: 1721: 1716: 1703: 1690: 1684: 1661: 1656: 1643: 1630: 1624: 4394:Scientific Notation to Decimal Converter 4389:Decimal to Scientific Notation Converter 4283:(1 ed.). Salt Lake City: Springer. 2380:Next, add or subtract the significands: 714: 419:remains at least one but less than ten ( 320: 76: 4112:HP16C Emulator Library for the HP48S/SX 2865: 1224:Further examples of scientific notation 1050:text encoding (1964), and was added to 1046:" character was included in the Soviet 445:. In normalized notation, the exponent 3988:Various (2000). Lide, David R. (ed.). 3210: 2702:This is closely related to the base-2 319:, as in ordinary decimal notation. In 4421:Lessons In Electric Circuits Vol 1 DC 4253:The IEEE and The Open Group (2013) . 3095:, Compaq/Digital Visual Fortran, and 2788:conversion specifiers. Starting with 323:, the exponent is chosen so that the 7: 4399:Scientific Notation in Everyday Life 4124:(NB. This library also works on the 3343:(Working Group Document), L2/08-030R 3091:For instance, DEC FORTRAN 77 (f77), 969:as of 1961) also use "D" to signify 4154:Martin, Bruce Alan (October 1968). 1524: 1489: 1479: 1473: 993: 30:. For the food additive codes, see 4279:Beebe, Nelson H. F. (2017-08-22). 4259:The Open Group Base Specifications 4039:"Zimbabwe inflation hits new high" 3771:Whitaker, Ronald O. (1962-06-15). 2765:family of functions following the 1581:places to the left (or right) and 1442: %, or more simply a rate of 1354:. In scientific notation, this is 14: 4079:. 1974. p. 7. 1304-389 Rev A 3990:Handbook of Chemistry and Physics 3130:Intel Fortran: Language Reference 2642:using binary numbers (or shorter 258:times ten raised to the power of 4136:. Beyond the feature set of the 1094:supports the shorthand notation 461:for all elements of the series. 331:is at least 1 but less than 10. 3804:Moller, Donald A. (June 1976). 3712:電言板5 PC-1490UII PROGRAM LIBRARY 3494:– In the January 1976 issue of 3332:Broukhis, Leonid (2008-01-22), 3240:. The Early Days of Hexadecimal 1125:calculator display showing the 4077:Texas Instruments Incorporated 4013:Kadzere, Martin (2008-10-09). 3463:(1). Santa Ana, CA: 4. V3N1P4. 3401:Texas Instruments Incorporated 3295:(1–3): 1–236. September 1973. 3101:"Double Precision, REAL**16". 2744:= 1.40H0 = 1.40h0, or 98000 = 2667:Brookhaven National Laboratory 2439: 2413: 2154: 2145: 1533:digits to the right (positive 524:| < 1000, rather than 1 ≤ | 1: 4409:Scientific Notation Converter 3723:電言板6 PC-U6000 PROGRAM LIBRARY 3674:. 1989. 9G1KS(TINSE1189ECZZ). 3269:, Computer Science Department 3109:Digital Equipment Corporation 3074:. Math.hawaii.edu. 2012-02-12 642:can properly be expressed as 327:(modulus) of the significand 4427:Lessons In Electric Circuits 4045:. 2008-10-09. Archived from 3925:10.1103/RevModPhys.88.035009 3742:TI calculator character sets 3232:Savard, John J. G. (2018) . 483:other than 10 (for example, 62:in the United Kingdom. This 3161:Compaq Computer Corporation 2371:{\displaystyle n_{0}=n_{1}} 568:indicated to be significant 4470: 3748:"TI-83 Programmer's Guide" 3482:(6). Dayton, OH: 1. V1N6P1 2731:times 16 or 8 to the power 1484:. To represent the number 879:for a decimal significand 559: 501: 429:). Thus 350 is written as 356: 344: 25: 18: 4289:10.1007/978-3-319-64110-2 4161:Communications of the ACM 3974:10.1007/s10569-011-9352-4 3884:Reviews of Modern Physics 2780:standard, when using the 2771:Single Unix Specification 660:, which is shorthand for 21:Scientific pitch notation 4329:"floating point literal" 3722: 3711: 3178:The GNU Fortran Compiler 4075:(Revision A ed.). 3498:(V3N1p4) Jim Davidson ( 3389:Such as the TI SR-10. 2755:= 2.7732o5 = 2.7732C5. 1492:appended, resulting in 1065:DECIMAL EXPONENT SYMBOL 42:is a way of expressing 4142:floating-point numbers 3992:(81st ed.). CRC. 3348:"The Unicode Standard" 2898:Edwards, John (2009). 2682:decimal representation 2592: 2466: 2372: 2332: 2272: 2201: 2069: 1940: 1839: 1733: 1673: 1374:, this may be written 1130: 1104:mathematical constant 1098:(reserving the letter 959:SHARE Operating System 629:Estimated final digits 411:is chosen so that the 335:Decimal floating point 72:scientific calculators 4444:Mathematical notation 4175:10.1145/364096.364107 3844:"Scientific Notation" 3560:Specifically, models 3234:"Computer Arithmetic" 3104:DEC Fortran 77 Manual 3045:10.1145/320964.320969 2593: 2467: 2373: 2333: 2273: 2202: 2070: 1941: 1840: 1734: 1674: 1519:Scientific to decimal 1464:Decimal to scientific 1341:Earth's circumference 1117: 883:and integer exponent 520:is in the range 1 ≤ | 68:arithmetic operations 4017:. Harare, Zimbabwe: 3773:"Numerical Prefixes" 3520:will now be written 3421:Jim Davidson coined 3403:. 1973. 1304-739-266 2991:, ed. (1956-10-15). 2964:, ed. (1954-11-10). 2824:Engineering notation 2710:(e.g. 1B10 for 1×2 ( 2699:or shorter 1.001B3. 2478: 2384: 2342: 2282: 2222: 2079: 1952: 1849: 1756: 1683: 1623: 1537:) or left (negative 1016:. Subsequently, the 504:Engineering notation 498:Engineering notation 466:engineering notation 293:and the real number 83:Scientific notation 4415:Scientific Notation 4367:. Lexical Structure 4208:. 1.20 (1 ed.) 4115:. 1.20 (1 ed.) 3965:2011CeMDA.110..293L 3907:2016RvMP...88c5009M 3350:(v. 7.0.0 ed.) 3267:Stanford University 2962:Backus, John Warner 2836:Positional notation 2769:specification and ( 1948:Some examples are: 1193:for the separator. 975:quadruple precision 705:confidence interval 562:Significant figures 556:Significant figures 439:orders of magnitude 353:Normalized notation 321:normalized notation 283:terminating decimal 56:standard index form 40:Scientific notation 3311:10.1007/BF00265077 3031:Journal of the ACM 2588: 2462: 2368: 2328: 2268: 2197: 2065: 1936: 1835: 1729: 1669: 1455:Converting numbers 1381:40 megametres 1216:) that is allowed 1135:pocket calculators 1131: 887:means the same as 718:Explicit notation 4365:Apple Corporation 4298:978-3-319-64109-6 3999:978-0-8493-0481-1 3692:Sharp Corporation 3672:Sharp Corporation 3648:Sharp Corporation 3621:Sharp Corporation 3446:Texas Instruments 3138:Intel Corporation 2938:978-0-8412-3999-9 2722:), 1B40 for 1×2 ( 2718:), 1B30 for 1×2 ( 2714:), 1B20 for 1×2 ( 2663:Bruce Alan Martin 2123: 1901: 1874: 1432:Zimbabwean dollar 1343:is approximately 1233:'s mass is about 1191: 1175:Texas Instruments 1150:, as seen in the 1142:, as seen in the 1127:Avogadro constant 1120:Texas Instruments 863:computer programs 856: 855: 512:is restricted to 443:common logarithms 359:Normalized number 243: 242: 80:Decimal notation 4461: 4376: 4375: 4373: 4372: 4353: 4347: 4346: 4340: 4339: 4333:cppreference.com 4325: 4319: 4318: 4276: 4270: 4269: 4267: 4266: 4250: 4244: 4243: 4241: 4240: 4234: 4226: 4217: 4216: 4214: 4213: 4199: 4188: 4187: 4177: 4151: 4145: 4123: 4121: 4120: 4106: 4089: 4087: 4085: 4084: 4074: 4064: 4058: 4057: 4055: 4054: 4035: 4029: 4028: 4026: 4025: 4010: 4004: 4003: 3985: 3979: 3978: 3976: 3943: 3937: 3936: 3918: 3900: 3874: 3868: 3866: 3861:. Archived from 3853: 3851: 3850: 3841: 3839: 3838: 3829: 3824:. Archived from 3819: 3817: 3816: 3810: 3800: 3794: 3792: 3790: 3789: 3777: 3768: 3762: 3760: 3758: 3757: 3752: 3738: 3732: 3730: 3719: 3709: 3707: 3706: 3700: 3689: 3675: 3665: 3663: 3662: 3656: 3645: 3631: 3629: 3628: 3618: 3558: 3552: 3545: 3543: 3542: 3526: 3523: 3519: 3509: 3488: 3487: 3473: 3464: 3419: 3413: 3411: 3409: 3408: 3398: 3387: 3381: 3380: 3378: 3377: 3366: 3360: 3358: 3356: 3355: 3344: 3338: 3329: 3323: 3322: 3304: 3289:Acta Informatica 3284: 3278: 3277: 3275: 3274: 3264: 3255: 3249: 3248: 3246: 3245: 3229: 3223: 3222: 3216: 3208: 3197: 3191: 3189: 3187: 3186: 3171: 3169: 3168: 3158: 3148: 3146: 3145: 3135: 3126: 3116: 3115: 3089: 3083: 3082: 3080: 3079: 3068: 3062: 3060: 3047: 3021: 3015: 3012: 3010: 3009: 3004:. pp. 9, 27 2999: 2984: 2982: 2981: 2972: 2957: 2951: 2950: 2922: 2916: 2915: 2913: 2912: 2906: 2895: 2889: 2888: 2884:978-8-89385052-0 2870: 2819: 2754: 2743: 2698: 2687: 2679: 2656: 2645: 2641: 2630: 2620:) is written as 2597: 2595: 2594: 2589: 2587: 2586: 2565: 2564: 2543: 2542: 2521: 2520: 2499: 2498: 2471: 2469: 2468: 2463: 2461: 2460: 2459: 2458: 2438: 2437: 2425: 2424: 2409: 2408: 2396: 2395: 2377: 2375: 2374: 2369: 2367: 2366: 2354: 2353: 2337: 2335: 2334: 2329: 2327: 2326: 2325: 2324: 2307: 2306: 2294: 2293: 2277: 2275: 2274: 2269: 2267: 2266: 2265: 2264: 2247: 2246: 2234: 2233: 2206: 2204: 2203: 2198: 2196: 2195: 2177: 2176: 2158: 2157: 2124: 2122: 2121: 2120: 2101: 2100: 2099: 2083: 2074: 2072: 2071: 2066: 2064: 2063: 2042: 2041: 2020: 2019: 1992: 1991: 1973: 1972: 1945: 1943: 1942: 1937: 1935: 1934: 1933: 1932: 1920: 1919: 1902: 1900: 1899: 1890: 1889: 1880: 1875: 1873: 1872: 1863: 1862: 1853: 1844: 1842: 1841: 1836: 1834: 1833: 1832: 1831: 1819: 1818: 1801: 1800: 1791: 1790: 1778: 1777: 1768: 1767: 1738: 1736: 1735: 1730: 1728: 1727: 1726: 1725: 1708: 1707: 1695: 1694: 1678: 1676: 1675: 1670: 1668: 1667: 1666: 1665: 1648: 1647: 1635: 1634: 1615:Basic operations 1610: 1608: 1602: 1600: 1594: 1592: 1567: 1566: 1560: 1558: 1552: 1548: 1546: 1528: 1514: 1512: 1506: 1505: 1499: 1497: 1491: 1487: 1483: 1478:; to the right, 1477: 1449: 1447: 1441: 1439: 1422: 1420: 1417: 1408: 1406: 1397: 1382: 1377: 1372:SI writing style 1369: 1367: 1361: 1359: 1353: 1351: 1348: 1335: 1333: 1327: 1325: 1322: 1319: 1316: 1313: 1310: 1307: 1304: 1287: 1285: 1282: 1279: 1273: 1271: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1244: 1241: 1238: 1192: 1189: 1171:pocket computers 1165: 1149: 1141: 1101: 1097: 1089: 1081: 1077: 1066: 1063: 1060: 1058: 1041: 1035: 1031: 1027: 1023: 1015: 1007: 999: 971:double precision 929: 925: 920: 918: 911: 907: 902: 900: 893: 878: 852: 847: 845: 836: 831: 829: 820: 815: 813: 804: 799: 797: 788: 783: 781: 772: 767: 765: 762: 753: 748: 746: 737: 732: 730: 715: 703:, or some other 698: 696: 690: 688: 684: 681: 678: 674: 671: 668: 665: 659: 657: 653: 650: 647: 624: 622: 619: 613: 611: 608: 602: 600: 594: 593: 590: 579: 578: 575: 551: 549: 543: 539: 537: 493: 492: 488: 456: 454: 436: 434: 428: 426: 399: 397: 391: 389: 383: 381: 375: 374: 370: 313:common logarithm 239: 237: 230: 229: 226: 223: 214: 212: 205: 198: 196: 189: 182: 180: 173: 172: 169: 166: 157: 155: 148: 147: 138: 136: 133: 126: 124: 115: 113: 106: 99: 97: 90: 77: 4469: 4468: 4464: 4463: 4462: 4460: 4459: 4458: 4454:Numeral systems 4434: 4433: 4424:free ebook and 4385: 4380: 4379: 4370: 4368: 4355: 4354: 4350: 4337: 4335: 4327: 4326: 4322: 4299: 4278: 4277: 4273: 4264: 4262: 4252: 4251: 4247: 4238: 4236: 4232: 4228: 4227: 4220: 4211: 4209: 4201: 4200: 4191: 4153: 4152: 4148: 4118: 4116: 4108: 4107: 4092: 4082: 4080: 4072: 4066: 4065: 4061: 4052: 4050: 4037: 4036: 4032: 4023: 4021: 4012: 4011: 4007: 4000: 3987: 3986: 3982: 3945: 3944: 3940: 3916:10.1.1.150.1225 3876: 3875: 3871: 3857: 3848: 3846: 3842: 3836: 3834: 3830: 3820: 3814: 3812: 3808: 3803: 3801: 3797: 3787: 3785: 3775: 3770: 3769: 3765: 3755: 3753: 3750: 3746: 3739: 3735: 3724: 3721: 3713: 3710: 3704: 3702: 3698: 3687: 3676: 3666: 3660: 3658: 3654: 3643: 3632: 3626: 3624: 3616: 3605: 3559: 3555: 3540: 3538: 3529: 3521: 3517: 3507: 3485: 3483: 3471: 3466: 3452: 3444:newsletter for 3433:Hewlett-Packard 3431:newsletter for 3420: 3416: 3406: 3404: 3396: 3390: 3388: 3384: 3375: 3373: 3368: 3367: 3363: 3353: 3351: 3346: 3336: 3331: 3330: 3326: 3302:10.1.1.219.3999 3286: 3285: 3281: 3272: 3270: 3262: 3257: 3256: 3252: 3243: 3241: 3231: 3230: 3226: 3209: 3199: 3198: 3194: 3184: 3182: 3174: 3166: 3164: 3156: 3150: 3143: 3141: 3133: 3127: 3113: 3111: 3100: 3090: 3086: 3077: 3075: 3070: 3069: 3065: 3023: 3022: 3018: 3013:(2+51+1 pages) 3007: 3005: 2997: 2987: 2979: 2977: 2970: 2960: 2958: 2954: 2939: 2924: 2923: 2919: 2910: 2908: 2904: 2897: 2896: 2892: 2885: 2872: 2871: 2867: 2862: 2847:Suzhou numerals 2832: 2817: 2813: 2775:IEEE Std 1003.1 2753: 2749: 2745: 2742: 2738: 2734: 2708:binary prefixes 2697: 2693: 2689: 2685: 2678: 2674: 2670: 2669:in 1968, as in 2660: 2655: 2651: 2647: 2643: 2640: 2636: 2632: 2629: 2625: 2621: 2619: 2611: 2603: 2575: 2553: 2531: 2509: 2487: 2476: 2475: 2450: 2445: 2429: 2416: 2400: 2387: 2382: 2381: 2378: 2358: 2345: 2340: 2339: 2316: 2311: 2298: 2285: 2280: 2279: 2256: 2251: 2238: 2225: 2220: 2219: 2187: 2168: 2134: 2109: 2102: 2091: 2084: 2077: 2076: 2052: 2030: 2002: 1983: 1961: 1950: 1949: 1924: 1911: 1906: 1891: 1881: 1864: 1854: 1847: 1846: 1823: 1810: 1805: 1792: 1782: 1769: 1759: 1754: 1753: 1717: 1712: 1699: 1686: 1681: 1680: 1657: 1652: 1639: 1626: 1621: 1620: 1617: 1612: 1606: 1604: 1598: 1596: 1590: 1588: 1574: 1564: 1562: 1556: 1554: 1550: 1544: 1542: 1521: 1510: 1508: 1503: 1501: 1495: 1493: 1485: 1466: 1457: 1445: 1443: 1437: 1435: 1418: 1415: 1413: 1409:to the nearest 1404: 1402: 1395: 1380: 1375: 1365: 1363: 1357: 1355: 1349: 1346: 1344: 1331: 1329: 1323: 1320: 1317: 1314: 1311: 1308: 1305: 1302: 1300: 1283: 1280: 1277: 1275: 1269: 1266: 1263: 1260: 1257: 1254: 1251: 1248: 1245: 1242: 1239: 1236: 1234: 1226: 1202: 1188: 1156:Hewlett-Packard 1152:Commodore PR100 1147: 1139: 1064: 1061: 1056: 1055: 1045: 1040: 1037: 1005: 997: 991: 916: 914: 898: 896: 888: 874: E  870: 843: 841: 827: 825: 811: 809: 795: 793: 779: 777: 763: 760: 758: 744: 742: 728: 726: 713: 694: 692: 686: 682: 679: 676: 672: 669: 666: 663: 661: 655: 651: 648: 645: 643: 631: 620: 617: 615: 609: 606: 604: 598: 596: 591: 588: 586: 576: 573: 571: 564: 558: 547: 545: 541: 535: 533: 506: 500: 490: 486: 484: 452: 450: 432: 430: 422: 420: 395: 393: 387: 385: 379: 377: 372: 368: 364: 361: 355: 350: 343: 309:fractional part 285:). The integer 252: 235: 233: 227: 224: 221: 219: 210: 208: 203: 194: 192: 187: 178: 176: 170: 167: 164: 162: 153: 151: 145: 143: 134: 131: 129: 122: 120: 111: 109: 104: 95: 93: 88: 52:scientific form 35: 24: 17: 12: 11: 5: 4467: 4465: 4457: 4456: 4451: 4446: 4436: 4435: 4432: 4431: 4411: 4406: 4401: 4396: 4391: 4384: 4383:External links 4381: 4378: 4377: 4348: 4320: 4297: 4271: 4245: 4218: 4189: 4146: 4090: 4059: 4030: 4005: 3998: 3980: 3959:(4): 293–304. 3938: 3869: 3865:on 2015-05-03. 3828:on 2007-10-19. 3795: 3763: 3733: 3553: 3546:(NB. The term 3414: 3382: 3361: 3324: 3279: 3250: 3224: 3203:, ed. (1960). 3192: 3172:(1441 pages) 3084: 3063: 3038:(2): 141–144. 3016: 2952: 2937: 2917: 2890: 2883: 2864: 2863: 2861: 2858: 2857: 2856: 2850: 2844: 2838: 2831: 2828: 2815: 2751: 2747: 2740: 2736: 2704:floating-point 2695: 2691: 2676: 2672: 2658: 2653: 2649: 2638: 2634: 2627: 2623: 2617: 2609: 2602: 2599: 2585: 2582: 2578: 2574: 2571: 2568: 2563: 2560: 2556: 2552: 2549: 2546: 2541: 2538: 2534: 2530: 2527: 2524: 2519: 2516: 2512: 2508: 2505: 2502: 2497: 2494: 2490: 2486: 2483: 2457: 2453: 2448: 2444: 2441: 2436: 2432: 2428: 2423: 2419: 2415: 2412: 2407: 2403: 2399: 2394: 2390: 2365: 2361: 2357: 2352: 2348: 2323: 2319: 2314: 2310: 2305: 2301: 2297: 2292: 2288: 2263: 2259: 2254: 2250: 2245: 2241: 2237: 2232: 2228: 2218: 2194: 2190: 2186: 2183: 2180: 2175: 2171: 2167: 2164: 2161: 2156: 2153: 2150: 2147: 2144: 2141: 2137: 2133: 2130: 2127: 2119: 2116: 2112: 2108: 2105: 2098: 2094: 2090: 2087: 2062: 2059: 2055: 2051: 2048: 2045: 2040: 2037: 2033: 2029: 2026: 2023: 2018: 2015: 2012: 2009: 2005: 2001: 1998: 1995: 1990: 1986: 1982: 1979: 1976: 1971: 1968: 1964: 1960: 1957: 1931: 1927: 1923: 1918: 1914: 1909: 1905: 1898: 1894: 1888: 1884: 1878: 1871: 1867: 1861: 1857: 1830: 1826: 1822: 1817: 1813: 1808: 1804: 1799: 1795: 1789: 1785: 1781: 1776: 1772: 1766: 1762: 1750:exponentiation 1742:Multiplication 1724: 1720: 1715: 1711: 1706: 1702: 1698: 1693: 1689: 1664: 1660: 1655: 1651: 1646: 1642: 1638: 1633: 1629: 1616: 1613: 1587: 1573: 1570: 1541:). The number 1520: 1517: 1465: 1462: 1456: 1453: 1452: 1451: 1427:Hyperinflation 1424: 1391:is defined as 1385: 1337: 1289: 1225: 1222: 1201: 1198: 1054:5.2 (2009) as 1043: 1038: 995: 989: 961:(SOS) for the 922:is written as 904:is written as 894:. For example 854: 853: 848: 838: 837: 832: 822: 821: 816: 806: 805: 800: 790: 789: 784: 774: 773: 768: 755: 754: 749: 739: 738: 733: 723: 722: 719: 712: 709: 701:standard error 630: 627: 560:Main article: 557: 554: 502:Main article: 499: 496: 427:| < 10 413:absolute value 357:Main article: 354: 351: 342: 339: 325:absolute value 297:is called the 289:is called the 247: 241: 240: 231: 216: 215: 206: 200: 199: 190: 184: 183: 174: 159: 158: 149: 140: 139: 127: 117: 116: 107: 101: 100: 91: 85: 84: 81: 15: 13: 10: 9: 6: 4: 3: 2: 4466: 4455: 4452: 4450: 4447: 4445: 4442: 4441: 4439: 4429: 4428: 4423: 4422: 4418:chapter from 4417: 4416: 4412: 4410: 4407: 4405: 4402: 4400: 4397: 4395: 4392: 4390: 4387: 4386: 4382: 4366: 4362: 4358: 4352: 4349: 4345: 4334: 4330: 4324: 4321: 4316: 4312: 4308: 4304: 4300: 4294: 4290: 4286: 4282: 4275: 4272: 4260: 4256: 4249: 4246: 4231: 4225: 4223: 4219: 4207: 4206: 4198: 4196: 4194: 4190: 4185: 4181: 4176: 4171: 4167: 4163: 4162: 4157: 4150: 4147: 4143: 4139: 4135: 4131: 4127: 4114: 4113: 4105: 4103: 4101: 4099: 4097: 4095: 4091: 4078: 4071: 4070: 4063: 4060: 4049:on 2009-05-14 4048: 4044: 4040: 4034: 4031: 4020: 4016: 4009: 4006: 4001: 3995: 3991: 3984: 3981: 3975: 3970: 3966: 3962: 3958: 3954: 3950: 3942: 3939: 3934: 3930: 3926: 3922: 3917: 3912: 3908: 3904: 3899: 3894: 3891:(3): 035009. 3890: 3886: 3885: 3880: 3873: 3870: 3867: 3864: 3860: 3855: 3845: 3833: 3827: 3823: 3807: 3799: 3796: 3783: 3782: 3778:. Crosstalk. 3774: 3767: 3764: 3761: 3749: 3743: 3737: 3734: 3731: 3728: 3717: 3701:on 2017-02-24 3697: 3693: 3690:(in German). 3685: 3681: 3680: 3673: 3669: 3657:on 2017-02-25 3653: 3649: 3646:(in German). 3641: 3637: 3636: 3622: 3619:(in German). 3614: 3610: 3609: 3603: 3599: 3595: 3591: 3587: 3583: 3579: 3575: 3571: 3567: 3563: 3557: 3554: 3551: 3549: 3536: 3532: 3528: 3525: 3515: 3514: 3505: 3501: 3497: 3493: 3481: 3477: 3470: 3462: 3458: 3457: 3450: 3447: 3443: 3442: 3437: 3434: 3430: 3429: 3424: 3418: 3415: 3402: 3395: 3394: 3386: 3383: 3372:. August 1986 3371: 3365: 3362: 3359: 3349: 3342: 3335: 3328: 3325: 3320: 3316: 3312: 3308: 3303: 3298: 3294: 3290: 3283: 3280: 3268: 3261: 3254: 3251: 3239: 3235: 3228: 3225: 3220: 3214: 3207:. Copenhagen. 3206: 3202: 3196: 3193: 3190: 3180: 3179: 3163:. August 2001 3162: 3155: 3154: 3149:(858 pages) 3139: 3132: 3131: 3125: 3123: 3122:Alpha systems 3110: 3106: 3105: 3098: 3094: 3093:Intel Fortran 3088: 3085: 3073: 3067: 3064: 3059: 3055: 3051: 3046: 3041: 3037: 3033: 3032: 3027: 3020: 3017: 3014: 3003: 2996: 2995: 2990: 2976: 2969: 2968: 2963: 2956: 2953: 2948: 2944: 2940: 2934: 2930: 2929: 2921: 2918: 2903: 2902: 2894: 2891: 2886: 2880: 2876: 2869: 2866: 2859: 2854: 2851: 2848: 2845: 2842: 2841:ISO/IEC 80000 2839: 2837: 2834: 2833: 2829: 2827: 2825: 2821: 2811: 2810:IEEE 754-2008 2807: 2803: 2799: 2795: 2791: 2787: 2783: 2779: 2776: 2772: 2768: 2764: 2763: 2756: 2733:as in 1.25 = 2732: 2727: 2725: 2721: 2717: 2713: 2709: 2705: 2700: 2683: 2668: 2664: 2615: 2606: 2600: 2598: 2583: 2580: 2576: 2572: 2569: 2566: 2561: 2558: 2554: 2550: 2547: 2544: 2539: 2536: 2532: 2528: 2525: 2522: 2517: 2514: 2510: 2506: 2503: 2500: 2495: 2492: 2488: 2484: 2481: 2472: 2455: 2451: 2446: 2442: 2434: 2430: 2426: 2421: 2417: 2410: 2405: 2401: 2397: 2392: 2388: 2363: 2359: 2355: 2350: 2346: 2321: 2317: 2312: 2308: 2303: 2299: 2295: 2290: 2286: 2261: 2257: 2252: 2248: 2243: 2239: 2235: 2230: 2226: 2217: 2215: 2211: 2207: 2192: 2188: 2184: 2181: 2178: 2173: 2169: 2165: 2162: 2159: 2151: 2148: 2142: 2139: 2135: 2131: 2128: 2125: 2117: 2114: 2110: 2106: 2103: 2096: 2092: 2088: 2085: 2060: 2057: 2053: 2049: 2046: 2043: 2038: 2035: 2031: 2027: 2024: 2021: 2016: 2013: 2010: 2007: 2003: 1999: 1996: 1993: 1988: 1984: 1980: 1977: 1974: 1969: 1966: 1962: 1958: 1955: 1946: 1929: 1925: 1921: 1916: 1912: 1907: 1903: 1896: 1892: 1886: 1882: 1876: 1869: 1865: 1859: 1855: 1828: 1824: 1820: 1815: 1811: 1806: 1802: 1797: 1793: 1787: 1783: 1779: 1774: 1770: 1764: 1760: 1751: 1747: 1743: 1739: 1722: 1718: 1713: 1709: 1704: 1700: 1696: 1691: 1687: 1662: 1658: 1653: 1649: 1644: 1640: 1636: 1631: 1627: 1614: 1586: 1584: 1580: 1571: 1569: 1540: 1536: 1532: 1527: 1518: 1516: 1515:as a result. 1500:. The number 1482: 1476: 1471: 1463: 1461: 1454: 1433: 1428: 1425: 1412: 1401: 1394: 1390: 1386: 1383: 1373: 1342: 1338: 1298: 1294: 1290: 1232: 1228: 1227: 1223: 1221: 1219: 1215: 1211: 1207: 1200:Use of spaces 1199: 1197: 1194: 1187: 1186:small capital 1183: 1179: 1176: 1172: 1169: 1161: 1157: 1153: 1145: 1136: 1128: 1124: 1121: 1116: 1112: 1110: 1108: 1107: 1093: 1085: 1073: 1068: 1053: 1049: 1042:. The ALGOL " 1019: 1011: 1003: 987: 982: 980: 976: 972: 968: 964: 960: 956: 952: 948: 944: 940: 936: 931: 921: 903: 891: 886: 882: 877: 873: 868: 864: 860: 849: 840: 839: 833: 824: 823: 817: 808: 807: 801: 792: 791: 785: 776: 775: 769: 757: 756: 750: 741: 740: 734: 725: 724: 720: 717: 716: 710: 708: 706: 702: 641: 635: 628: 626: 595:would become 582: 569: 563: 555: 553: 531: 527: 523: 519: 515: 511: 505: 497: 495: 482: 478: 474: 472: 467: 462: 460: 448: 444: 440: 425: 418: 414: 410: 406: 401: 367: 360: 352: 348: 340: 338: 336: 332: 330: 326: 322: 318: 314: 310: 306: 302: 301: 296: 292: 288: 284: 280: 277:is a nonzero 276: 273: 269: 265: 261: 257: 250: 246: 232: 218: 217: 207: 202: 201: 191: 186: 185: 175: 161: 160: 150: 142: 141: 128: 119: 118: 108: 103: 102: 92: 87: 86: 82: 79: 78: 75: 73: 69: 65: 61: 60:standard form 57: 53: 49: 45: 41: 37: 33: 29: 22: 4426: 4420: 4414: 4369:. Retrieved 4360: 4351: 4344:description. 4342: 4336:. Retrieved 4332: 4323: 4280: 4274: 4263:. 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Index

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
SI prefixes

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