View source for Scientific notation

{{Short description|Method of writing numbers with a large amount of digits}}
{{Redir|E notation|the series of preferred numbers|E series of preferred numbers{{!}}E series|the food additive codes|E number}}
{{Use list-defined references|date=December 2022}}

'''Scientific notation''' is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as '''scientific form''' or '''standard index form''', or '''standard form''' in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators, it is usually known as "SCI" display mode.

{| class="wikitable" style="float:right; margin:5px;"
!Decimal notation
!Scientific notation
|-
|{{val|2}}
|{{val|2E0}}
|-
|{{val|300}}
|{{val|3E2}}
|-
|{{val|4321.768}}
|{{val|4.321768E3}}
|-
|{{val|−53000}}
|{{val|-5.3E4}}
|-
|{{val|6720000000}}
|{{val|6.72E9}}
|-
|{{val|0.2}}
|{{val|2E-1}}
|-
|{{val|987}}
|{{val|9.87E2}}
|- 
|{{val|0.00000000751}}
|{{val|7.51E-9}}
|}
In scientific notation, nonzero numbers are written in the form 
{{block indent | em = 1.5 | text = ''m'' × 10{{sup|''n''}}}}
or ''m'' times ten raised to the power of ''n'', where ''n'' is an [[Integer|integer]], and the [[Coefficient|coefficient]] ''m'' is a nonzero [[Real number|real number]] (usually between 1 and 10 in absolute value, and nearly always written as a [[Decimal|terminating decimal]]). The integer ''n'' is called the exponent and the real number ''m'' is called the ''[[Significand|significand]]'' or ''mantissa''.<ref name="Calio_2017"/> The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the [[Fractional part|fractional part]] of the [[Common logarithm|common logarithm]]. <!-- These are actually floating-point terms, not scientific notation. --> If the number is negative then a minus sign precedes ''m'', as in ordinary decimal notation. In normalized notation, the exponent is chosen so that the [[Absolute value|absolute value]] (modulus) of the significand ''m'' is at least 1 but less than 10.

[[Decimal floating point]] is a computer arithmetic system closely related to scientific notation.

== History ==

==Normalized notation==
{{main|Normalized number}}
Any real number can be written in the form {{gaps|''m''|e=''n''}} in many ways: for example, 350 can be written as {{val|3.5E2}} or {{val|35E1}} or {{val|350E0}}.<!-- "Any given real number" includes irrational numbers, which can't be represented exactly. It also includes rational numbers, sometimes requiring recurring decimal representation, e.g., 1/3 = 1.333333... -->

In ''normalized'' scientific notation (called "standard form" in the United Kingdom), the exponent ''n'' is chosen so that the [[Absolute value|absolute value]] of ''m'' remains at least one but less than ten ({{nowrap begin}}1 ≤ |''m''| < 10{{nowrap end}}). Thus 350 is written as {{val|3.5E2}}. 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 orders of magnitude separating the numbers.  It is also the form that is required when using tables of [[Common logarithm|common logarithm]]s. In normalized notation, the exponent ''n'' is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as {{val|5E-1}}). 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 ''m'' for all elements of the series.

Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such as [[Engineering:Engineering notation|engineering notation]], is desired. Normalized scientific notation is often called '''[[Exponentiation|exponential]] notation'''—although the latter term is more general and also applies when ''m'' is not restricted to the range 1 to 10 (as in engineering notation for instance) and to [[Base (exponentiation)|base]]s other than 10 (for example, {{gaps|3.15|base=2|e=20}}).

==Engineering notation==
{{Main|Engineering:Engineering notation}}
Engineering notation (often named "ENG" on scientific calculators) differs from normalized scientific notation in that the exponent ''n'' is restricted to [[Multiple (mathematics)|multiples]] of 3. Consequently, the absolute value of ''m'' is in the range 1 ≤ |''m''| < 1000, rather than 1 ≤ |''m''| < 10. Though similar in concept, engineering notation is rarely called scientific notation. Engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. For example, {{val|12.5E-9|u=m}} can be read as "twelve-point-five nanometres" and written as {{val|12.5|u=nm}}, while its scientific notation equivalent {{val|1.25E-8|u=m}} would likely be read out as "one-point-two-five times ten-to-the-negative-eight metres".

==Significant figures==
{{Main|Significant figures}}
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 [[Significant figures#Identifying significant digits|indicated to be significant]].
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 {{val|1230400}} 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.

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 {{val|1230400}} would become {{val|1.2304E6}} if it had five significant digits. If the number were known to six or seven significant figures, it would be shown as {{val|1.23040E6}} or {{val|1.230400E6}}. Thus, an additional advantage of scientific notation is that the number of significant figures is unambiguous.

===Estimated final digits===
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 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).

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 [[Physics:Proton|proton]] can properly be expressed as {{val|1.67262192369E-27|(51)|u=kg}}, which is shorthand for {{val|1.67262192369E-27|0.00000000051|u=kg}}. However it is still unclear whether the error ({{val|5.1E-37}} in this case) is the maximum possible error, [[Standard error|standard error]], or some other [[Confidence interval|confidence interval]].

==E notation==
<!-- Section title used as link target. -->
[[Image:Avogadro's number in e notation.jpg|thumb|upright|A Texas Instruments TI-84 Plus calculator display showing the Avogadro constant to three significant figures in E notation]]

Scientific notation allows simple low tech low digit displays, as used in calculators, to display numbers beyond the range of ordinary [[Decimal|decimal notation]]. However, the usual way to notate an exponent or the raising to a power like 10<sup>7</sup> in superscript cannot be displayed in the simplest [[Engineering:Display device|segmented or dot-matrix]] displays as in most calculators or in [[Plain text|plain text]] as used for [[Source code|source code]].

[[Mathematical notation]] commonly reduces operations to a single symbol. In '''E notation''', the letter '''E''' or '''e''' followed by the value of the exponent stands for "times ten raised to the power of." For any decimal number ''m'' and integer ''n'', ''m''E''n'' means the same as writing {{nowrap|''m'' × 10<sup>''n''</sup>}}. This is referred to as '''E notation''', rather than exponential notation.

{{code|6.022E23}} or {{code|6.022e23}} or {{code|6.022E+23}} equates to {{val|6.022E23}}, the [[Chemistry:Avogadro number|Avogadro number]].

The [[Planck length]] in metres, {{val|1.6E-35}}, is written {{code|1.6E-35}}

The plus sign in {{code|E+23}} is the [[Sign (mathematics)|sign]] and not [[Addition|addition]] and may be omitted. The character '''e''' is not related to other uses of '''e''', such as the [[E (mathematical constant)|mathematical constant ''e'']] and the [[Exponential function|exponential function]] ''e''<sup>''x''</sup>.

E notation provides brevity that may enhance readability and reduce keystrokes for scientific [[Data entry|data entry]]. E notation is meant for unformatted text, and formatted publications such as [[Scientific journal|journals]] do not encourage E notation.<ref name="Edwards_2009"/>

On scientific calculators, it is typically invoked by a key labelled {{button|EXP}} (for ''exponent''), {{button|EEX}} (for ''enter exponent''), {{button|EE}}, {{button|EX}}, {{button|E}}, or {{button|×10<sup>''x''</sup>}} depending on vendor and model.

{{anchor|Decapower|D notation|Q notation}}

Since its first version released for the IBM 704 in 1956, the [[Fortran]] language has used E&nbsp;notation for floating point numbers.<ref name="Sayre_1956"/> It was not part of the preliminary specification as of 1954.<ref name="Backus_1954"/>

The E&nbsp;notation was already used by the developers of [[Software:SHARE Operating System|SHARE Operating System]] (SOS) for the IBM 709 in 1958.<ref name="DiGri-King_1958"/><!-- Not necessarily the first use, but an early one. -->

E notation is used in most popular programming languages, e.g. [[Ada (programming language)|Ada]], [[Software:Analytica|Analytica]], [[C (programming language)|C]]/[[C++]], Fortran, [[Software:MATLAB|MATLAB]], [[Software:Scilab|Scilab]], [[Perl]], [[Java (programming language)|Java]],<ref name="Oracle_Java"/> [[Python (programming language)|Python]], [[Lua (programming language)|Lua]], [[JavaScript]], and many others.

After the introduction of the first pocket calculators supporting scientific notation in 1972 (HP-35, SR-10<ref name="TI_1973_SR-10"/>) the term ''decapower'' was sometimes used in the emerging user communities for the power-of-ten multiplier in order to better distinguish it from "normal" exponents. Likewise, the letter "D" was used in typewritten numbers. This notation was proposed by Jim Davidson and published in the January 1976 issue of Richard J. Nelson's [[Company:Hewlett-Packard|Hewlett-Packard]] newsletter ''65 Notes''<ref name="Davidson_1976"/> for HP-65 users, and it was adopted and carried over into the [[Company:Texas Instruments|Texas Instruments]] community by Richard C. Vanderburgh, the editor of the ''52-Notes'' newsletter for SR-52 users in November 1976.<ref name="Vanderburgh_1976"/>

The displays of LED pocket calculators did not display an "E" or "e". Instead, one or more digits were left blank between the significand and the exponent, e.g. <code>6.022 23</code>, such as in the Hewlett-Packard HP-25, or a pair of smaller and slightly raised digits reserved for the exponent was used, e.g. <code>6.022 <sup>23</sup></code>, such as in the [[Company:Commodore International|Commodore PR100]].

Fortran (at least since FORTRAN IV as of 1961<!-- Possibly also by some versions of FORTRAN II and III. -->) also uses "D" to signify double precision numbers in scientific notation.<ref name="UH-Manoa"/>

Similarly, a "D" was used by [[Company:Sharp Corporation|Sharp]] pocket computers 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 --> to indicate 20-digit double-precision numbers in scientific notation in <!-- RUN and PROG mode -->[[BASIC]] between 1987 and 1995.<ref name="Sharp_1987_PC-1280"/><ref name="Sharp_1987_PC-1475"/><ref name="Sharp_1989_PC-E500"/><ref name="Sharp_1995_PC-E500S"/><ref name="PC-1490UII"/><ref name="PC-U6000"/>

Some newer FORTRAN compilers like DEC FORTRAN 77 (f77),<ref name="DEC-FORTRAN77"/> Intel Fortran,<ref name="Intel_2005"/> Compaq/Digital Visual Fortran<ref name="Compaq_2001"/> or [[Software:GNU Fortran|GNU Fortran]] (gfortran) support "Q" to signify quadruple precision numbers in scientific notation.<ref name="gfortran"/>

[[Software:MATLAB|MATLAB]] supports both letters, "E" and "D", to indicate numbers in scientific notation.

The [[ALGOL|ALGOL 60]] (1960) programming language uses a subscript ten "<sub>10</sub>" character instead of the letter "E", for example: <code class=nowrap>6.022<sub>10</sub>23</code>.<ref name="Naur_1960"/><ref name="Savard_2005"/>

The use of the "<sub>10</sub>" in the various Algol standards provided a challenge on some computer systems that did not provide such a "<sub>10</sub>" character. As a consequence [[Organization:Stanford University|Stanford University]] Algol-W required the use of a single quote, e.g. <code>6.022'+23</code>,<ref name="Bauer-Becker-Graham_1968"/> and some Soviet Algol variants allowed the use of the Cyrillic character "ю" character, e.g. 6.022ю+23.

Subsequently, the [[ALGOL 68]] programming language provided the choice of 4 characters: {{kbd|E}}, {{kbd|e}}, {{kbd|\}}, or {{kbd|<sub>10</sub>}}. By examples: {{code|6.022E23}}, {{code|6.022e23}}, {{code|6.022\23}} or <code class=nowrap>6.022<sub>10</sub>23</code>.<ref name="Algol_1973"/>
{{SpecialChars |alt=Decimal Exponent Symbol |link=http://mailcom.com/unicode/DecimalExponent.ttf |special=Unicode "[https://www.unicode.org/charts/PDF/U2300.pdf Miscellaneous Technical]" characters |fix=Unicode#External_links |characters="<sub>10</sub>" ([http://mailcom.com/unicode/DecimalExponent.ttf Decimal Exponent Symbol U+23E8 TTF])}}

''Decimal Exponent Symbol'' is part of the Unicode Standard,<ref name="Unicode_2018"/> e.g. {{code|class=nowrap|6.022⏨23}}. It is included as {{unichar|23E8|DECIMAL EXPONENT SYMBOL}} to accommodate usage in the programming languages Algol 60 and Algol 68.

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&nbsp;×&nbsp;10<sup>3</sup> would be written as "6.022③".<ref name="Whitaker_1962"/>

The TI-83 series and TI-84 Plus series of calculators use a stylized '''<small>E</small>''' character to display ''decimal exponent'' and the <small>10</small> character to denote an equivalent ×10^ operator.<ref name="TI-83"/>

The [[Simula]] programming language requires the use of {{kbd|&}} (or {{kbd|&&}} for long), for example: {{code|class=nowrap|6.022&23}} or {{code|class=nowrap|6.022&&23}}.<ref name="SIMULA_1986"/>

The [[Wolfram Language]] utilized in [[Software:Mathematica|Mathematica]] allows a shorthand notation of {{code|class=nowrap|6.022*^23}}. Instead, {{code|E}} denotes the [[E (mathematical constant)|mathematical constant ''e'']].

==Use of spaces==
In normalized scientific notation, in E notation, and in engineering notation, the space (which in typesetting may be represented by a normal width space or a thin space) that is allowed ''only'' before and after "×" or in front of "E" is sometimes omitted, though it is less common to do so before the alphabetical character.<ref name="Samples"/>

==Further examples of scientific notation==
* An [[Physics:Electron|electron]]'s mass is about {{val|0.000000000000000000000000000000910938356|u=kg}}.<ref name="CODATA2014Full"/> In scientific notation, this is written {{val|9.10938356E-31|u=kg}} (in SI units).
* The [[Astronomy:Earth|Earth]]'s [[Physics:Mass|mass]] is about {{val|5972400000000000000000000|u=kg}}.<ref name="Luzum_2011"/> In scientific notation, this is written {{val|5.9724E24|u=kg}}.
* The [[Astronomy:Earth#Size and shape|Earth's circumference]] is approximately {{val|40000000|u=m}}.<ref name="Lide_2000"/> In scientific notation, this is {{val|4E7|u=m}}. In engineering notation, this is written {{val|40E6|u=m}}. In [[International System of Units|SI writing style]], this may be written {{val|40|u=Mm}} (''{{val|40|u=megametres}}'').
* An [[Inch|inch]] is defined as ''exactly'' {{val|25.4|u=mm}}. Quoting a value of {{val|25.400|u=mm}} shows that the value is correct to the nearest micrometre. An approximated value with only two significant digits would be {{val|2.5E1|u=mm}} instead. As there is no limit to the number of significant digits, the length of an inch could, if required, be written as (say) {{val|2.54000000000E1|u=mm}} instead.
* [[Finance:Hyperinflation|Hyperinflation]] is a problem that is caused when too much money is printed with regards to there being too few commodities, causing the inflation rate to rise by 50% or more in a single month; currencies tend to lose their intrinsic value over time. Some countries have had an inflation rate of 1 million percent or more in a single month, which usually results in the abandonment of the country's currency shortly afterwards. In November 2008, the monthly inflation rate of the Zimbabwean dollar reached 79.6 billion percent; the approximated value with three significant figures would be {{val|7.96E10}} %.<ref name="Kadzere_2008"/><ref name="BBC"/>

==Converting numbers==
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.

===Decimal to scientific===
First, move the decimal separator point sufficient places, ''n'', 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 <code class=nowrap>× 10''<sup>n</sup>''</code>; to the right, <code class=nowrap>× 10''<sup>−n</sup>''</code>. To represent the number {{val|1230400|fmt=commas}} in normalized scientific notation, the decimal separator would be moved 6 digits to the left and <code class=nowrap>× 10<sup>6</sup></code> appended, resulting in {{val|1.2304E6}}. The number {{val|-0.0040321}} would have its decimal separator shifted 3 digits to the right instead of the left and yield {{val|-4.0321E-3}} as a result.

===Scientific to decimal===
Converting a number from scientific notation to decimal notation, first remove the <code class=nowrap>× 10''<sup>n</sup>''</code> on the end, then shift the decimal separator ''n'' digits to the right (positive ''n'') or left (negative ''n''). The number {{val|1.2304E6}} would have its decimal separator shifted 6 digits to the right and become {{val|1230400|fmt=commas}}, while {{val|-4.0321E-3}} would have its decimal separator moved 3 digits to the left and be {{val|-0.0040321}}.

=== Exponential===
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 decimal separator in the significand is shifted ''x'' places to the left (or right) and ''x'' is added to (or subtracted from) the exponent, as shown below.

{{block indent | em = 1.5 | text = {{val|1.234E3}} = {{val|12.34E2}} = {{val|123.4E1}} = 1234}}

==Basic operations==
<!-- This section is linked from [[Addition]] -->
Given two numbers in scientific notation,

<math display="block">x_0=m_0\times10^{n_0}</math>
and
<math display="block">x_1=m_1\times10^{n_1}</math>

[[Multiplication]] and [[Division (mathematics)|division]] are performed using the rules for operation with [[Exponentiation|exponentiation]]:

<math display="block">x_0 x_1=m_0 m_1\times10^{n_0+n_1}</math>
and
<math display="block">\frac{x_0}{x_1}=\frac{m_0}{m_1}\times10^{n_0-n_1}</math>

Some examples are:
<math display="block">5.67\times10^{-5} \times 2.34\times10^2 \approx 13.3\times10^{-5+2} = 13.3\times10^{-3} = 1.33\times10^{-2}</math>
and
<math display="block">\frac{2.34\times10^2}{5.67\times10^{-5}}  \approx 0.413\times10^{2-(-5)} = 0.413\times10^{7} = 4.13\times10^6</math>

[[Addition]] and [[Subtraction|subtraction]] require the numbers to be represented using the same exponential part, so that the significand can be simply added or subtracted:
{{block indent | em = 1.5 | text = <math>x_0 = m_0 \times10^{n_0}</math> and <math>x_1 = m_1 \times10^{n_1}</math> with <math>n_0 = n_1</math>}}

Next, add or subtract the significands:
<math display="block">x_0 \pm x_1=(m_0\pm m_1)\times10^{n_0}</math>

An example:
<math display="block">2.34\times10^{-5} + 5.67\times10^{-6} = 2.34\times10^{-5} + 0.567\times10^{-5} = 2.907\times10^{-5}</math>

=={{anchor|B notation|H notation|O notation|C notation|P notation}}Other bases==
While base ten is normally used for scientific notation, powers of other bases can be used too,<ref name="TI_1974_SR-22"/> base 2 being the next most commonly used one.

For example, in base-2 scientific notation, the number 1001<sub>b</sub> in binary (=9<sub>d</sub>) is written as 
{{nowrap|1.001<sub>b</sub> × 2<sub>d</sub><sup>11<sub>b</sub></sup>}} or {{nowrap|1.001<sub>b</sub> × 10<sub>b</sub><sup>11<sub>b</sub></sup>}} using binary numbers (or shorter {{nowrap|1.001 × 10<sup>11</sup>}} if binary context is obvious). In E notation, this is written as {{nowrap|1.001<sub>b</sub>E11<sub>b</sub>}} (or shorter: 1.001E11) with the letter "E" now standing for "times two (10<sub>b</sub>) 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",<ref name="HP16C-Lib"/> a shorthand notation originally proposed by Bruce Alan Martin of [[Organization:Brookhaven National Laboratory|Brookhaven National Laboratory]] in 1968,<ref name="Martin_1968"/> as in {{nowrap|1.001<sub>b</sub>B11<sub>b</sub>}} (or shorter: 1.001B11). For comparison, the same number in [[Decimal representation|decimal representation]]: {{nowrap|1.125 × 2<sup>3</sup>}} (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 {{nowrap|1.001<sub>b</sub> × 10<sub>b</sub><sup>3<sub>d</sub></sup>}} or shorter 1.001B3.<ref name="HP16C-Lib"/>

This is closely related to the base-2 floating-point representation commonly used in computer arithmetic, and the usage of IEC binary prefixes (e.g. 1B10 for 1×2<sup>10</sup> (kibi), 1B20 for 1×2<sup>20</sup> (mebi), 1B30 for 1×2<sup>30</sup> (gibi), 1B40 for 1×2<sup>40</sup> (tebi)).

Similar to "B" (or "b"<ref name="HP16C-Add"/>), the letters "H"<ref name="HP16C-Lib"/> (or "h"<ref name="HP16C-Add"/>) and "O"<ref name="HP16C-Lib"/> (or "o",<ref name="HP16C-Add"/> or "C"<ref name="HP16C-Lib"/>) are sometimes also used to indicate ''times 16 or 8 to the power'' as in 1.25 = {{nowrap|1.40<sub>h</sub> × 10<sub>h</sub><sup>0<sub>h</sub></sup>}} = 1.40H0 = 1.40h0, or 98000 = {{nowrap|2.7732<sub>o</sub> × 10<sub>o</sub><sup>5<sub>o</sub></sup>}} = 2.7732o5 = 2.7732C5.<ref name="HP16C-Lib"/>

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.<ref name="Rationale_2003_C"/> This notation can be produced by implementations of the ''[[Printf|printf]]'' family of functions following the [[C99]] specification and (Single Unix Specification) IEEE Std 1003.1 [[POSIX]] standard, when using the ''%a'' or ''%A'' conversion specifiers.<ref name="Rationale_2003_C"/><ref name="printf_2013"/><ref name="Beebe_2017_Hex"/> Starting with [[C++11]], [[C++]] I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since [[C++17]].<ref name="C++17"/> [[Company:Apple Inc.|Apple]]'s [[Swift (programming language)|Swift]] supports it as well.<ref name="Swift_2017"/> It is also required by the [[IEEE 754-2008]] binary floating-point standard. Example: 1.3DEp42 represents {{nowrap|1.3DE<sub>h</sub> × 2<sup>42</sup>}}.

[[Engineering:Engineering notation|Engineering notation]] can be viewed as a base-1000 scientific notation.

==See also==
* [[Exponentiation]] (exponential notation)
* [[Binary prefix]]
* [[Positional notation]]
* Variable scientific notation
* [[Engineering:Engineering notation|Engineering notation]]
* [[Floating-point arithmetic]]
* ISO 31-0
* [[ISO 31-11]]
* Significant figure
* [[Suzhou numerals]] are written with order of magnitude and unit of measurement below the significand
* [[RKM code]]
* International scientific vocabulary

==References==
{{Reflist|refs=
<ref name="Calio_2017">{{cite book |author-last1=Caliò |author-first1=Franca |author-first2=Lazzari |author-last2=Alessandro |title=Elements of Mathematics with Numerical Applications |publisher=Società Editrice Esculapio |pages=30–32 |date=September 2017 |isbn=978-8-89385052-0}}</ref>
<ref name="Edwards_2009">{{cite book |author-last=Edwards |author-first=John |date=2009 |title=Submission Guidelines for Authors: HPS 2010 Midyear Proceedings |publisher=Health Physics Society |location=McLean, Virginia |page=5 |url=http://hps.org/documents/2010_midyear_author-submission-guidelines.pdf |access-date=2013-03-30 |url-status=live |archive-url=https://web.archive.org/web/20130515112227/http://hps.org/documents/2010_midyear_author-submission-guidelines.pdf |archive-date=2013-05-15}}</ref>
<ref name="Backus_1954">{{cite book |title=Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN |type=Preliminary report |author-first1=John Warner |author-last1=Backus |author-first2=Harlan L. |author-last2=Herrick |author-first3=Robert A. |author-last3=Nelson |author-first4=Irving |author-last4=Ziller |editor-first=John Warner |editor-last=Backus |publisher=Programming Research Group, Applied Science Division, International Business Machines Corporation |location=New York, USA |date=1954-11-10 |url=https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf |access-date=2022-07-04 |url-status=live |archive-url=https://web.archive.org/web/20220329234459/https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf |archive-date=2022-03-29}} (29 pages)</ref>
<ref name="Sayre_1956">{{cite book |title=The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual |publisher=Applied Science Division and Programming Research Department, International Business Machines Corporation |location=New York, USA |date=1956-10-15 |editor-first=David |editor-last=Sayre |author-first1=John Warner |author-last1=Backus |author-first2=Robert J. |author-last2=Beeber |author-first3=Sheldon F. |author-last3=Best |author-first4=Richard |author-last4=Goldberg |author-link4=Richard Goldberg |author-first5=Harlan L. |author-last5=Herrick |author-first6=Robert A. |author-last6=Hughes |author-first7=Lois B. |author-last7=Mitchell (Haibt) |author-link7=Lois B. Mitchell |author-first8=Robert A. |author-last8=Nelson |author-first9=Roy |author-last9=Nutt |author-link9=Roy Nutt |author-first10=David |author-last10=Sayre |author-link10=David Sayre |author-first11=Peter B. |author-last11=Sheridan |author-first12=Harold |author-last12=Stern |author-first13=Irving |author-last13=Ziller |pages=9, 27 |url=http://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf |access-date=2022-07-04 |url-status=live |archive-url=https://web.archive.org/web/20220704193549/http://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf |archive-date=2022-07-04}} (2+51+1 pages)</ref>
<ref name="DiGri-King_1958">{{cite journal |title=The SHARE 709 System: Input-Output Translation |author-first1=Vincent J. |author-last1=DiGri |author-first2=Jane E. |author-last2=King |journal=[[Journal of the ACM]] |volume=6 |issue=2 |date=April 1959 |orig-date=1958-06-11 |doi=10.1145/320964.320969 |s2cid=19660148 |pages=141–144 |quote=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.|doi-access=free }} (4 pages) (NB. This was presented at the ACM meeting 11–13 June 1958.)</ref>
<ref name="Oracle_Java">{{cite web |url=http://download.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html |title=Primitive Data Types (The Java Tutorials > Learning the Java Language > Language Basics) |publisher=[[Company:Oracle Corporation|Oracle Corporation]] |access-date=2012-03-06 |url-status=live |archive-url=https://web.archive.org/web/20111117041930/http://download.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html |archive-date=2011-11-17}}</ref>
<ref name="Davidson_1976">{{cite journal |title=unknown |author-first=Jim |author-last=Davidson |editor-first=Richard J. |editor-last=Nelson |journal=65 Notes |publication-place=Santa Ana, California, USA |date=January 1976 |volume=3 |number=1 |page=4 |id=V3N1P4}}</ref>
<ref name="Vanderburgh_1976">{{cite journal |editor-first=Richard C. |editor-last=Vanderburgh |title=Decapower |journal=52-Notes - Newsletter of the SR-52 Users Club |volume=1 |number=6 |page=1 |date=November 1976 |id=V1N6P1 |publication-place=Dayton, Ohio, USA |url=http://www.claudiolarini.altervista.org/pdf/52NOTES.pdf |access-date=2017-05-28 |url-status=live |archive-url=https://web.archive.org/web/20170528031508/http://www.claudiolarini.altervista.org/pdf/52NOTES.pdf |archive-date=2017-05-28 |quote=''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, {{sic|<code>123|<sup>−45</sup></code>|expected=<code>123×10<sup>−45</sup></code>}} which is displayed in scientific notation as <code>1.23 -43</code> will now be written <code>1.23D-43</code>. Perhaps, as this notation gets more and more usage, the calculator manufacturers will change their keyboard abbreviations. HP's {{button|EEX}} and TI's {{button|EE}} could be changed to {{button|ED}} (for enter decapower).}} [https://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html<!-- https://web.archive.org/web/20170528122342/https://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html -->] {{Cite news |title=Decapower |volume=1 |number=6 |page=1 |date=November 1976 |newspaper=52-Notes - Newsletter of the SR-52 Users Club |location=Dayton, Ohio, USA |url=http://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html |access-date=2018-05-07 |url-status=live |archive-url=https://web.archive.org/web/20140803040138/http://www.rskey.org/DOCUMENTS/52NOTES/52v1n6.html |archive-date=2014-08-03}} (NB. The term ''decapower'' was frequently used in subsequent issues of this newsletter up to at least 1978.)</ref>
<ref name="UH-Manoa">{{cite web |url=http://www.math.hawaii.edu/lab/197/fortran/fort3.htm#double |title=UH Mānoa Mathematics » Fortran lesson 3: Format, Write, etc. |publisher=Math.hawaii.edu |date=2012-02-12 |access-date=2012-03-06 |url-status=live |archive-url=https://web.archive.org/web/20111208180836/http://www.math.hawaii.edu/lab/197/fortran/fort3.htm#double |archive-date=2011-12-08}}</ref>
<ref name="Sharp_1987_PC-1280">{{cite book |title=SHARP Taschencomputer Modell PC-1280 Bedienungsanleitung |language=de |trans-title=SHARP Pocket Computer Model PC-1280 Operation Manual |date=1987 |publisher=[[Company:Sharp Corporation|Sharp Corporation]] |id=7M 0.8-I(TINSG1123ECZZ)(3) |pages=56–60 |url=http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1280-de.pdf |access-date=2017-03-06 |url-status=live |archive-url=https://web.archive.org/web/20170306145930/http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1280-de.pdf |archive-date=2017-03-06}}</ref>
<ref name="Sharp_1987_PC-1475">{{cite book |title=SHARP Taschencomputer Modell PC-1475 Bedienungsanleitung |language=de |trans-title=SHARP Pocket Computer Model PC-1475 Operation Manual |pages=105–108, 131–134, 370, 375 |date=1987 |publisher=[[Company:Sharp Corporation|Sharp Corporation]] |url=http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf |access-date=2017-02-25 |archive-url=https://web.archive.org/web/20170225090805/http://www.instructionsmanuals.com/u2/pdf/calculadoras/Sharp-PC1475-de.pdf |archive-date=2017-02-25}}</ref>
<ref name="Sharp_1989_PC-E500">{{cite book |title=SHARP Pocket Computer Model PC-E500 Operation Manual |publisher=[[Company:Sharp Corporation|Sharp Corporation]] |date=1989 |id=9G1KS(TINSE1189ECZZ) <!-- |url=http://basic.hopto.org/basic/manual/Sharp%20PC-E500.pdf |access-date=2017-02-24 -->}}</ref>
<ref name="Sharp_1995_PC-E500S">{{cite book |title=SHARP Taschencomputer Modell PC-E500S Bedienungsanleitung |language=de |trans-title=SHARP Pocket Computer Model PC-E500S Operation Manual |publisher=[[Company:Sharp Corporation|Sharp Corporation]] |date=1995 |id=6J3KS(TINSG1223ECZZ) |url=http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf |access-date=2017-02-24 |url-status=live |archive-url=https://web.archive.org/web/20170224235944/http://vininc.de/Literatur/Sharp%20Bedienungsanleitungen/PC-E500S-DE.pdf |archive-date=2017-02-24}}</ref>
<ref name="PC-1490UII">{{cite book |script-title=ja:電言板5 PC-1490UII PROGRAM LIBRARY |trans-title=Telephone board 5 PC-1490UII program library |publisher=University Co-op |language=ja |date=1991 |volume=5}} (NB. {{cite web |title=University Co-operative |url=http://www.univcoop.or.jp/en/index.html |archive-url=https://web.archive.org/web/20170727143822/http://www.univcoop.or.jp/en/index.html |archive-date=2017-07-27}}.)</ref>
<ref name="PC-U6000">{{cite book |script-title=ja:電言板6 PC-U6000 PROGRAM LIBRARY |trans-title=Telephone board 6 PC-U6000 program library |publisher=University Co-op |language=ja |date=1993 |volume=6}} (NB. {{cite web |title=University Co-operative |url=http://www.univcoop.or.jp/en/index.html |archive-url=https://web.archive.org/web/20170727143822/http://www.univcoop.or.jp/en/index.html |archive-date=2017-07-27}}.)<!-- https://ja.wikipedia.org/w/index.php?title=%E3%83%8E%E3%83%BC%E3%83%88%3A%E3%83%9D%E3%82%B1%E3%83%83%E3%83%88%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF%E3%81%AE%E8%A3%BD%E5%93%81%E4%B8%80%E8%A6%A7&type=revision&diff=64766669&oldid=64653791 --></ref>
<ref name="DEC-FORTRAN77">{{cite book |title=DEC Fortran 77 Manual |chapter=Double Precision, REAL**16 |publisher=[[Company:Digital Equipment Corporation|Digital Equipment Corporation]] |date= |url=https://wwwth.mpp.mpg.de/members/hahn/decfortman.html |access-date=2022-12-21 |url-status=live |archive-url=https://web.archive.org/web/20191118152256/http://wwwth.mpp.mpg.de/members/hahn/decfortman.html |archive-date=2019-11-18 |quote=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 [[DEC Alpha|Alpha system]]s.}}</ref>
<ref name="Intel_2005">{{cite book |title=Intel Fortran: Language Reference |date=2005 |orig-date=2003 |publisher=Intel Corporation |id=253261-003 |pages=3-7–3-8, 3-10 |url=https://www.ehu.eus/sgi/ARCHIVOS/lang_for.pdf |access-date=2022-12-22 |url-status=live |archive-url=https://web.archive.org/web/20221222003153/https://www.ehu.eus/sgi/ARCHIVOS/lang_for.pdf |archive-date=2022-12-22}} (858 pages)</ref>
<ref name="Compaq_2001">{{cite book |title=Compaq Visual Fortran - Language Reference |date=August 2001 |publisher=[[Company:Compaq Computer Corporation|Compaq Computer Corporation]] |publication-place=Houston, Texas, USA |url=https://jp.xlsoft.com/documents/intel/cvf/cvf_lref.pdf |access-date=2022-12-22 |url-status=live |archive-url=https://web.archive.org/web/20041213023030/http://jp.xlsoft.com/documents/intel/cvf/cvf_lref.pdf |archive-date=2004-12-13}} (1441 pages)</ref>
<ref name="gfortran">{{cite book |title=The GNU Fortran Compiler |chapter=6. Extensions: 6.1 Extensions implemented in GNU Fortran: 6.1.8 Q exponent-letter |date=2014-06-12 |url=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 |access-date=2022-12-21 |url-status=live |archive-url=https://web.archive.org/web/20221221180840/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 |archive-date=2022-12-21}}</ref>
<ref name="Naur_1960">{{cite book |title=Report on the Algorithmic Language ALGOL 60 |editor-first=Peter |editor-last=Naur |location=Copenhagen |date=1960}}</ref>
<ref name="Savard_2005">{{cite web |title=Computer Arithmetic |at=The Early Days of Hexadecimal |author-first=John J. G. |author-last=Savard |date=2018 |orig-date=2005 |work=quadibloc |url=http://www.quadibloc.com/comp/cp02.htm |access-date=2018-07-16 |url-status=live |archive-url=https://web.archive.org/web/20180716102439/http://www.quadibloc.com/comp/cp02.htm |archive-date=2018-07-16}}</ref>
<ref name="Bauer-Becker-Graham_1968">{{cite web |title=ALGOL W - Notes For Introductory Computer Science Courses |author-first1=Henry R. |author-last1=Bauer |author-first2=Sheldon |author-last2=Becker |author-first3=Susan L. |author-last3=Graham |date=January 1968 |publisher=[[Organization:Stanford University|Stanford University]], Computer Science Department |url=http://i.stanford.edu/pub/cstr/reports/cs/tr/68/86/CS-TR-68-86.pdf |access-date=2017-04-08 |url-status=live |archive-url=https://web.archive.org/web/20150909195915/http://i.stanford.edu/pub/cstr/reports/cs/tr/68/86/CS-TR-68-86.pdf |archive-date=2015-09-09}}</ref>
<ref name="Algol_1973">{{cite journal |title=Revised Report on the Algorithmic Language Algol 68 |journal=Acta Informatica |volume=5 |pages=1–236 |date=September 1973 |issue=1–3 |doi=10.1007/BF00265077 |citeseerx=10.1.1.219.3999 |s2cid=2490556}}</ref>
<ref name="Unicode_2018">{{cite web |url=https://www.unicode.org/versions/Unicode7.0.0/ |title=The Unicode Standard |access-date=2018-03-23 |archive-url=https://web.archive.org/web/20180505125703/http://www.unicode.org/versions/Unicode7.0.0/ |archive-date=2018-05-05 |url-status=live}}</ref> <ref name="Whitaker_1962">{{cite magazine |title=Numerical Prefixes |author-first=Ronald O. |author-last=Whitaker |location=Indianapolis, Indiana, USA |date=1962-06-15 |magazine=[[Engineering:Electronics (magazine)|Electronics]] |department=Crosstalk |publisher=McGraw-Hill Publishing Co., Inc. |publication-place=New York, USA |page=4 |url=http://www.bitsavers.org/magazines/Electronics/Electronics_V35_N24_19620615.pdf |access-date=2022-12-24 |url-status=live |archive-url=https://web.archive.org/web/20221205211744/http://www.bitsavers.org/magazines/Electronics/Electronics_V35_N24_19620615.pdf |archive-date=2022-12-05}} (1 page)</ref>
<ref name="TI-83">{{cite web |url=http://education.ti.com/downloads/guidebooks/sdk/83p/sdk83pguide.pdf |title=TI-83 Programmer's Guide<!-- exact title to be checked --> |access-date=2010-03-09 |url-status=live |archive-url=https://web.archive.org/web/20100214195930/http://education.ti.com/downloads/guidebooks/sdk/83p/sdk83pguide.pdf |archive-date=2010-02-14}}</ref>
<ref name="SIMULA_1986">{{cite web |title=SIMULA standard as defined by the SIMULA Standards Group - 3.1 Numbers |url=http://prosjekt.ring.hibu.no/simula/Standard/chap_1.htm |access-date=2009-10-06 |date=August 1986 |url-status=live |archive-url=https://web.archive.org/web/20110724175858/http://prosjekt.ring.hibu.no/simula/Standard/chap_1.htm |archive-date=2011-07-24}}</ref>
<ref name="Samples">Samples of usage of terminology and variants: {{cite web |title=A Computer Program For The Design And Static Analysis Of Single-Point Sub-Surface Mooring Systems: NOYFB |series=WHOI Document Collection |author-first=Donald A. |author-last=Moller |date=June 1976 |type=Technica Report |publisher=Woods Hole Oceanographic Institution |id=WHOI-76-59 |location=Woods Hole, Massachusetts, USA |url=http://darchive.mblwhoilibrary.org/bitstream/1912/665/1/WHOI-76-59.pdf |access-date=2015-08-19 |url-status=live |archive-url=https://web.archive.org/web/20081217135249/https://darchive.mblwhoilibrary.org/bitstream/1912/665/1/WHOI-76-59.pdf |archive-date=2008-12-17 |postscript=none}}, {{cite web |url=http://www.brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html |archive-url=https://web.archive.org/web/20071019061437/http://brookscole.com/physics_d/templates/student_resources/003026961X_serway/review/expnot.html |archive-date=2007-10-19 |title=Cengage - the Leading Provider of Higher Education Course Materials |postscript=none}}, {{cite web |url=http://www.brynmawr.edu/nsf/tutorial/ss/ssnot.html |access-date=2007-04-07 |url-status=live |archive-url=https://web.archive.org/web/20070404125922/http://www.brynmawr.edu/nsf/tutorial/ss/ssnot.html |archive-date=2007-04-04 |title=Bryn Mawr College: Survival Skills for Problem Solving--Scientific Notation |postscript=none}}, {{cite web |url=http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html |access-date=2007-04-07 |url-status=live |archive-url=https://web.archive.org/web/20070225085247/http://www.lasalle.edu/~smithsc/Astronomy/Units/sci_notation.html |archive-date=2007-02-25 |title=Scientific Notation |postscript=none}}, [https://web.archive.org/web/20061029195358/http://www.gnsphysics.com/mathreview.pdf], {{cite web |url=http://www.ttinet.com/doc/language_v44_003.html#heading_3.2.4.2 |archive-url=https://web.archive.org/web/20150503005623/http://www.ttinet.com/doc/language_v44_003.html |archive-date=2015-05-03 |title=INTOUCH 4GL a Guide to the INTOUCH Language}}</ref>
<ref name="CODATA2014Full">{{cite journal |author-last1=Mohr |author-first1=Peter J. |author-last2=Newell |author-first2=David B. |author-last3=Taylor |author-first3=Barry N. |date=July–September 2016 |title=CODATA recommended values of the fundamental physical constants: 2014 |url=http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=920687 |journal=[[Physics:Reviews of Modern Physics|Reviews of Modern Physics]] |volume=88 |issue=3 |page=035009 |doi=10.1103/RevModPhys.88.035009 |arxiv=1507.07956 |url-status=live |archive-url=http://archive.wikiwix.com/cache/20170123205803/http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=920687 |archive-date=2017-01-23 |bibcode=2016RvMP...88c5009M |citeseerx=10.1.1.150.1225 |s2cid=1115862}}</ref>
<ref name="Luzum_2011">{{cite journal |author-last1=Luzum |first1=Brian |author-last2=Capitaine |author-first2=Nicole |author-last3=Fienga |author-first3=Agnès |author-last4=Folkner |author-first4=William |author-last5=Fukushima |author-first5=Toshio |author-last6=Hilton |author-first6=James |author-last7=Hohenkerk |author-first7=Catherine |author-last8=Krasinsky |author-first8=George |author-last9=Petit |author-first9=Gérard |author-last10=Pitjeva |author-first10=Elena |author-last11=Soffel |author-first11=Michael |author-last12=Wallace |author-first12=Patrick |title=The IAU 2009 system of astronomical constants: The report of the IAU working group on numerical standards for Fundamental Astronomy |journal=Celestial Mechanics and Dynamical Astronomy |volume=110 |issue=4 |date=August 2011 |pages=293–304 |bibcode=2011CeMDA.110..293L |doi=10.1007/s10569-011-9352-4 |doi-access=free}}</ref>
<ref name="Lide_2000">{{cite book |author=Various |editor-first=David R. |editor-last=Lide |date=2000 |title=Handbook of Chemistry and Physics |edition=81st |publisher=CRC |isbn=978-0-8493-0481-1}}</ref>
<ref name="Kadzere_2008">{{cite web |url=http://allafrica.com/stories/200810090256.html |title=Zimbabwe: Inflation Soars to 231 Million Percent |publisher=The Herald |publication-place=Harare, Zimbabwe |author-first=Martin |author-last=Kadzere |date=2008-10-09 |access-date=2008-10-10 |archive-url=https://web.archive.org/web/20081012214518/http://allafrica.com/stories/200810090256.html |archive-date=2008-10-12 |url-status=live}}</ref>
<ref name="BBC">{{cite web |url=http://news.bbc.co.uk/1/hi/world/africa/7660569.stm |title=Zimbabwe inflation hits new high |archive-url=https://web.archive.org/web/20090514123525/http://news.bbc.co.uk/1/hi/world/africa/7660569.stm |archive-date=2009-05-14 |publisher=BBC News |access-date=2009-10-09}}</ref>
<ref name="TI_1974_SR-22">{{cite book |title=electronic hexadecimal calculator/converter SR-22 |publisher=Texas Instruments Incorporated |date=1974 |page=7 |edition=Revision A |id=1304-389 Rev A |url=http://www.datamath.net/Manuals/SR-22_US.pdf |access-date=2017-03-20 |url-status=live |archive-url=https://web.archive.org/web/20170320001329/http://www.datamath.net/Manuals/SR-22_US.pdf |archive-date=2017-03-20}} (NB. This calculator supports floating point numbers in scientific notation in bases 8, 10 and 16.)</ref>
<ref name="Martin_1968">{{cite journal |title=Letters to the editor: On binary notation |author-first=Bruce Alan |author-last=Martin |journal=[[Communications of the ACM]] |volume=11 |issue=10 |date=October 1968 |page=658 |doi=10.1145/364096.364107 |s2cid=28248410|doi-access=free }}</ref>
<ref name="HP16C-Lib">{{cite book |title=HP16C Emulator Library for the HP48S/SX |author-first1=Jake |author-last1=Schwartz |author-first2=Rick |author-last2=Grevelle |date=2003-10-20 |orig-date=April 1993 |edition=1 |version=1.20 |url=http://www.pahhc.org/mul8r.htm |access-date=2015-08-15 |url-status=live |archive-url=https://web.archive.org/web/20160621211708/http://www.pahhc.org/mul8r.htm |archive-date=2016-06-21}} (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.)</ref>
<ref name="HP16C-Add">{{cite book |title=HP16C Emulator Library for the HP48 - Addendum to the Operator's Manual |author-first1=Jake |author-last1=Schwartz |author-first2=Rick |author-last2=Grevelle |date=2003-10-21 |edition=1 |version=1.20 |url=http://www.pahhc.org/mul8r.htm |access-date=2015-08-15 |url-status=live |archive-url=https://web.archive.org/web/20160621211708/http://www.pahhc.org/mul8r.htm |archive-date=2016-06-21}}</ref>
<ref name="Rationale_2003_C">{{cite web |title=Rationale for International Standard - Programming Languages - C |version=5.10 |date=April 2003 |pages=52, 153–154, 159 |url=http://www.open-std.org/jtc1/sc22/wg14/www/C99RationaleV5.10.pdf |access-date=2010-10-17 |url-status=live |archive-url=https://web.archive.org/web/20160606072228/http://www.open-std.org/jtc1/sc22/wg14/www/C99RationaleV5.10.pdf |archive-date=2016-06-06}}</ref> <ref name="printf_2013">{{cite web |title=dprintf, fprintf, printf, snprintf, sprintf - print formatted output |work=The Open Group Base Specifications |edition=Issue 7, IEEE Std 1003.1, 2013 |date=2013 |orig-date=2001 |author=The IEEE and The Open Group |url=http://pubs.opengroup.org/onlinepubs/9699919799/functions/printf.html |access-date=2016-06-21 |url-status=live |archive-url=https://web.archive.org/web/20160621211105/http://pubs.opengroup.org/onlinepubs/9699919799/functions/printf.html |archive-date=2016-06-21}}</ref>
<ref name="Beebe_2017_Hex">{{cite book |author-first=Nelson H. F. |author-last=Beebe |title=The Mathematical-Function Computation Handbook - Programming Using the MathCW Portable Software Library |date=2017-08-22 |location=Salt Lake City, UT, USA |publisher=Springer International Publishing AG |edition=1 |lccn=2017947446 |isbn=978-3-319-64109-6 |doi=10.1007/978-3-319-64110-2 |s2cid=30244721}}</ref>
<ref name="C++17">{{cite web |work=cppreference.com |title=floating point literal |url=http://en.cppreference.com/w/cpp/language/floating_literal |access-date=2017-03-11 |url-status=live |archive-url=https://web.archive.org/web/20170429201447/http://en.cppreference.com/w/cpp/language/floating_literal |archive-date=2017-04-29 |quote=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.}}</ref>
<ref name="Swift_2017">{{cite web |title=The Swift Programming Language (Swift 3.0.1) |at=Lexical Structure |work=Guides and Sample Code: Developer: Language Reference |publisher=[[Company:Apple Inc.|Apple Corporation]] |url=https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/LexicalStructure.html |access-date=2017-03-11 |url-status=live |archive-url=https://web.archive.org/web/20170311124440/https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/LexicalStructure.html |archive-date=2017-03-11}}</ref>
<ref name="TI_1973_SR-10">{{cite book |title=Texas Instruments electronic slide rule calculator SR-10 |date=1973 |publisher=Texas Instruments Incorporated |publication-place=Dallas, Texas, USA |id=1304-739-266 |url=https://www.sliderulemuseum.com/Calculators/SR-10_US.pdf |access-date=2023-01-01 |url-status=live |archive-url=https://web.archive.org/web/20220417012300/https://www.sliderulemuseum.com/Calculators/SR-10_US.pdf |archive-date=2022-04-17}} (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.)</ref>
}}

==External links==
* [http://www.miniwebtool.com/decimal-to-scientific-notation-converter/ Decimal to Scientific Notation Converter]
* [http://www.miniwebtool.com/scientific-notation-to-decimal-converter/ Scientific Notation to Decimal Converter]
* [http://www.math.toronto.edu/mathnet/plain/questionCorner/scinot.html Scientific Notation in Everyday Life]
* [http://science.widener.edu/svb/tutorial/scinot.html An exercise in converting to and from scientific notation]
* [http://www.scientificnotationconverter.com Scientific Notation Converter]
* [http://www.ibiblio.org/kuphaldt/electricCircuits/DC/DC_4.html ''Scientific Notation''] chapter from [http://www.ibiblio.org/kuphaldt/electricCircuits/DC/index.html ''Lessons In Electric Circuits Vol 1 DC''] free ebook and [http://www.ibiblio.org/kuphaldt/electricCircuits/ ''Lessons In Electric Circuits''] series.

{{DEFAULTSORT:Scientific Notation}}
[[Category:Mathematical notation]]
[[Category:Measurement]]
[[Category:Numeral systems]]

{{Sourceattribution|Scientific notation}}