View source for Talk:Scientific notation

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==Standard index notation==

The name I've always been taught is something like 'standard index notation'.   
:If you don't remember what it was then the teaching must have been rather ineffective.  Are you sure it wasn't "index standard anecdotal notation"?

'Scientific notation' seems a bit vague - aren't there many other scientific notations?
:It is a fairly commonly understood phrase. Yes there are many other scientific notations, but are there any that could be referred to without qualification? &ndash; [[User:Smyth|Smyth]] 15:34, 9 Oct 2004 (UTC)

==suggested paragraph==

Should the following paragraph (or parts of) from [[Floating point]] be put on this page?

: In other words, we could represent a number a by two numbers m and e, such that a = m × be. In any such system we pick a base b (called the base of numeration, also radix) and a precision p (how many digits to store). m (which is called the mantissa, also significand) is a p digit number of the form +-d.ddd...ddd (each digit being an integer between 0 and b-1 inclusive). If the leading digit of m is non-zero then the number is said to be normalised.

==breaking quantities==
If we follow a convention of writing
1.2E<sup>31</sup> instead we can avoid the problem of having a break in the quanity...1.2 x 

10<sup>31</sup>
[[User:Pizza Puzzle|Pizza Puzzle]]

: You can force quantities to break as one word with the "non-breaking space" (&amp;nbsp;):  1.2&nbsp;&times;&nbsp;10<sup>31</sup>. Besides, 1.2E31 is very ugly "calculator notation". I nearly cried when I saw someone use it on his math test paper. &ndash; [[User:Bou|Boudewijn]] 1 July 2005 12:12 (UTC)

:: 1.2E<sup>31</sup>  is incorrect, as stated on this page. [[User:Fresheneesz|Fresheneesz]] 04:13, 15 September 2006 (UTC)

:::Better still use {{tl|val}} ... don't use E notation if you're writing for humans. [[User:Jimp|J<small>IM</small>p]]<sub>&nbsp;[[User talk:Jimp|talk]]·[[Special:Contributions/Jimp|cont]]</sub> 07:55, 28 June 2009 (UTC)

== Cleaning Up ==

What needs cleaning up about this article? [[User:Lochok|Lochok]] 04:03, 14 November 2005 (UTC)

: It's not as bad as when the request was orginally made, but there are still a proliferation of one sentence paragraphs and I usually find a couple typos or redundancies everytime I look at it.  It is much better now.  The label can probably go soon. [[User:Jmeppley|Jmeppley]] 22:21, 14 November 2005 (UTC)

== parenthesis notation ==

Should also explain parenthesis notation indicating error, e.g., "1.345(67)" .


102.33
2536
=2253.00

== Fortran  ==

In Fortran, I recall that their exponential notation sometimes uses a 'd' instead of 'e'. For example, a number might be written as 1.234d-4 meaning the same thing as 1.234 * 10^-4 . I could have been incorrectly informed, but I think this would be a nice note on this page if someone can find a source for it (I looked quickly, but didn't find anything). [[User:Fresheneesz|Fresheneesz]] 04:10, 15 September 2006 (UTC)

: From the Nastran 77 Standard (http://www.fortran.com/F77_std/rjcnf-4.html#sh-4.5)

:: '''4.5.1 Double Precision Exponent.'''

::The form of a double precision exponent is the letter D followed by an optionally signed integer constant. A double precision exponent denotes a power of ten. Note that the form and interpretation of a double precision exponent are identical to those of a real exponent, except that the letter D is used instead of the letter E.

: Nastran uses the letter D to denote double precision instead of the single precision (or float) data type. Thus, this is an artifact of Nastran syntax. [[User:Jebix|Jebix]]

== Normalised form ==

Re the 3rd paragraph - i believe it should read as follows:
*In normalized form, b is chosen such that <math>1 \le \left | a \right \vert < 10</math>
rather than "''a'' is chosen". Given a number we wish to represent in normalised form, the |''a''| value is determined (mod a power of 10) - there is nothing to choose. We ''choose'' ''b'' so that ''a'' has the desired magnitude, not the other way round.

I changed this yesterday, but it was reverted by [[User:75.35.109.215|75.35.109.215]] with no comment. Before I put it back, would any one like to comment? [[User:JoeKearney|JoeKearney]] 21:17, 18 January 2007 (UTC)


Since there has been noting said here for ten days I've changed it back. Please discuss here if you think it's wrong rather than just re-editing it. [[User:JoeKearney|JoeKearney]] 01:09, 29 January 2007 (UTC)

== Standard form? ==

I thought that was the entire number, ie-

6,765

instead of

6.765*10^3

[[User:Lunakeet|DarkestMoonlight]] ([[User talk:Lunakeet|talk]]) 16:15, 17 March 2008 (UTC)

:Sorry, you thought wrong, for example: http://www.gcse.com/maths/standard_form.htm - [[Special:Contributions/81.138.169.201|81.138.169.201]] ([[User talk:81.138.169.201|talk]]) 15:49, 7 April 2008 (UTC)

In this same section, the exponents are not showing in my ie browser (but I don't know how to fix this on the page.  can someone else?
5.72×10^9 shows up as 5.72×10
−6.1×10^−9 shows up as −6.1×10  <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Mjvais|Mjvais]] ([[User talk:Mjvais|talk]] • [[Special:Contributions/Mjvais|contribs]]) 15:24, 22 April 2008 (UTC)</small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

== Isn't that backwards? ==

<blockquote>(Normalized) scientific notation is often called exponential notation...</blockquote>
AFAIK, "exponential notation" is generic, while "scientific notation" specifically refers to the one normalized so that the mantissa is in [1, 10), and "engineering notation" to the one normalized so that the mantissa is in [1, 1000) and the exponent is an integer multiple of three.
Is that correct? --[[User:Army1987|Army1987]] ([[User talk:Army1987|talk]]) 13:02, 9 June 2008 (UTC)

:: You are correct. The confusion arises because number notation is for many people the only place where they have to deal with exponents in any form or shape.  [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:42, 21 March 2021 (UTC)

Link Deletion  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/86.17.229.118|86.17.229.118]] ([[User talk:86.17.229.118|talk]]) 23:36, 6 November 2008 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

[[pt:Discussão:Notação científica]]

== programming languages ==

The list of programming languages seems idiosyncratic and/or obsolete.  The top languages are:
C
C++
Java
PHP
Visual Basic
Python

according to [http://langpop.com/]

I would add excel to that list.

[[User:Ccrrccrr|Ccrrccrr]] ([[User talk:Ccrrccrr|talk]]) 14:06, 6 March 2010 (UTC)

: The ones cited are those which many other later ones (including the ones that you cite) used as models for their notation, so are much more relevant than those which happen to be popular for a few years or decades now. [[User:Mfc|mfc]] ([[User talk:Mfc|talk]]) 17:10, 6 March 2010 (UTC)
::I'm glad to hear that it's a conscious choice, though I'm quite surprised.  The text doesn't present it as historical development..maybe I'll edit the text to say that.  The concern about "happen to be popular for a few years or decades now" doesn't seem like an issued to me, in that wikipedia gets updated much more frequently that that.[[User:Ccrrccrr|Ccrrccrr]] ([[User talk:Ccrrccrr|talk]]) 22:20, 7 March 2010 (UTC)

== Suggestion ==

I would personally be interested in seeing a History section for this page. It would be interesting to see where the idea of scientific notation originated, who invented it, and other things. If anyone is interested in researching/writing about that. [[User:Atallcostsky|<span style="color:purple;">atallcostsky</span>]] [[User talk:Atallcostsky|<span style="color:green;">talk</span>]]  20:02, 27 October 2011 (UTC)
:
:And also the approximate year. [[User:Gah4|Gah4]] ([[User talk:Gah4|talk]]) 20:40, 5 May 2025 (UTC)

== "form" vs. "notation"? ==

Shouldn't the article use the word "notation" instead of "form" in the case below?

"Normalized scientific '''form''' is the typical form of expression of large numbers for many fields [..]"<br>
"Normalized scientific '''notation''' is the typical form of expression of large numbers for many fields [..]" [[User:Tommy|Tommy]] ([[User talk:Tommy|talk]]) 03:28, 6 December 2011 (UTC)

== "&times;" vs. "&middot;"? ==

Shouldn't the article use this multiplication symbol "&middot;" instead of this "&times;"? The reason I'm asking is because I believe the "&times;" symbol looks confusingly alike the "x" character. So in one example in this article, it would be <math>a \cdot 10^b</math> instead of <math>a \times 10^b</math>, thus avoiding confusion with <math>ax10^b</math>. [[User:Tommy|Tommy]] ([[User talk:Tommy|talk]]) 03:28, 6 December 2011 (UTC)

: No, to the typographically untrained eye the multiplication cross is quite different from the lower-case x, even in Arial or Helvetica. The dot tends to be used between quantities in the abstract, usually denoted by letters in maths. Between numbers, it should really be the cross. As you advance in maths, you learn to drop the dot as well (and that quantities should not have multiple-letter designations) except when the inner product is meant. As you advance even further in algebra and functional analysis, even the dot product dot tends to be dropped. [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:38, 21 March 2021 (UTC)

== Explanation of difference between "standard form" and "alternative form" of scientific notation, missing. ==

There are two types of normalized scientific notation forms, namely the "standard form" and the "alternative form". But this Wikipedia article does not mention them. Can someone please add info about that to the article? I found an explanation here: http://www.education.com/study-help/article/trigonometry-help-power-10-notation/ . The web page explains the differences from a mathematical perspective, but does not elaborate on why the alternative form exists, what it's benefits are (if any) and exactly what countries it is that uses it. [[User:Tommy|Tommy]] ([[User talk:Tommy|talk]]) 05:23, 6 December 2011 (UTC)

== Digit grouping? ==

Numbers in the article seem to use different conventions (spaces or commas) for grouping digits. These conventions do vary from country to country (although I notice that a comma is not used for a decimal point here).  Is there a specific convention in scientific notation?  If not, should digits in this article's example numbers be grouped at all?

What about digit grouping in the exponent?  In an E-notation exponent?
[[User:Casu Marzu|Casu Marzu]] ([[User talk:Casu Marzu|talk]]) 15:12, 6 March 2012 (UTC)

==Scientific Notation vs Standard Form==

Whilst I can see that 'Scientific Notation' is apparently the established title and wording of this page, the fact that this article lacks many sources, not one of which give the subject of this article a title, I think that a debate could be had. Just a simple google search shows there to be 2,350,000 hits for scientific notation, 19,700,000 for Standard index form, and 429,000,000 for standard form. Thoughts?
[[User:Winnie412ii|Winnie412ii]] ([[User talk:Winnie412ii|talk]])  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|undated]] comment added 21:04, 2 September 2012 (UTC)</span><!--Template:Undated--> <!--Autosigned by SineBot-->
:I agree, standard index form is more applicable, since the definition of [[science]] is very wide, and something called ''scientific notation'' can have many different definitions, potentially. Standard index form makes more sense. Index actually means something specific.
:We don't use standard index form to ''"build and organize [[knowledge]] in the form of testable [[scientific theory|explanations]] and [[predictability|predictions]] about the [[universe]]"'' ([[science]] defined as such by Wikipedia). We use it to represent [[numbers]] in a more compact form using [[Exponent|indices]], something which has applications in not only science, but also [[economics]], [[statistics]], and anything else that involves very large numbers. --[[User:BurritoBazooka|BurritoBazooka]] ([[User talk:BurritoBazooka|talk]]) 23:04, 17 March 2013 (UTC)

== Use of Spaces ==
States - before and after 'x' and before 'e' yet in the examples, also uses it to seperate groups of 3 digits ?
[[User:Preroll|Preroll]] ([[User talk:Preroll|talk]]) 18:12, 13 November 2013 (UTC)

== Template "val" ==

A few months ago, {{t|val}} was inserted for much of the display.  However, it is not compatible with either [[WP:MOSNUM]] or common notation, in that most commas as digit separators were changed to spaces of some sort.  Comments?  — [[User:Arthur Rubin|Arthur Rubin]]  [[User talk:Arthur Rubin|(talk)]] 20:21, 26 June 2015 (UTC)

:I see very little change: in your revert there are still dominantly "spaces of some sort" anyway.  And [[WP:MOSNUM#Grouping of digits]] does suggest gaps for scientific articles ("This style is especially recommended for articles related to science, technology, engineering or mathematics."), so your revert has changed it from being consistent with the MoS to internally inconsistent.  If val is not consistent with the MoS, it should be changed so that it is.  —[[User_talk:Quondum|Quondum]] 20:56, 26 June 2015 (UTC)

== Edition at 11:17 on 21 May 2017 ==
... was accidentally anonymous (forgot that logged out) but done by MusJabłkowy. [[User:MusJabłkowy|MusJabłkowy]] ([[User talk:MusJabłkowy|talk]]) 11:57, 21 May 2017 (UTC)

== Edition on 27 November 2017 ==

This is a comment to an update at the end of „E-notation” section. I replaced the phrase „but it is not encouraged in publications”, which causes people to give up with this notation (Janice Sexton from The Astronomical Journal wrote to me, that I am the first person asking them about E-notation.). 
The deleted  reference [3] to Edwards, John (2009), Submission Guidelines for Authors: HPS 2010 Midyear Proceedings (PDF), McLean, Virginia: Health Physics Society is still in the Internet (however John Edwards no longer works in Health Physics Society and his email given there is out of date) and Health Physics Society still does not accept E-notation: http://edmgr.ovid.com/hpj/accounts/ifauth.htm  (search for “Use power of 10”), retrieved on June 11, 2017 (perhaps this would be good to alter the reference, because it is now not smart to reference the text dated 2009, which applies to a conference in 2010). I have sent the question "Do you accept E-notation? If not, please explain, why not." to over 40 journals. Only 10 journals answered: 4 would accept E-notation, 2 would not (because of the style of the journal and the tradition), and 4 would accept it in manuscript and convert it to classical (superscript) scientific notation. If Wikipedia editors want it, I can forward these e-mails or paste them here (on the Talk page) – please e-mail to me at ; please don't rely on my Talk page.
[[User:MusJabłkowy|MusJabłkowy]] ([[User talk:MusJabłkowy|talk]]) 11:34, 27 November 2017 (UTC)
: Unfortunately, this is unsourced and original research (see [[WP:OR]]). We either need public statements of these (and other) journals or a "meta" source discussing the issue, see [[WP:RS]]. I have therefore reverted your change (also, becaused it introduced some POV). --[[User:Matthiaspaul|Matthiaspaul]] ([[User talk:Matthiaspaul|talk]]) 20:30, 1 December 2017 (UTC)
: For privacy reasons I removed the email addresses in your comment above. --[[User:Matthiaspaul|Matthiaspaul]] ([[User talk:Matthiaspaul|talk]]) 20:34, 1 December 2017 (UTC)

: The OP has an agenda here "which causes people to give up with this notation" and OP clearly feels people should not give up, they should push E notation with all their might. Is the agenda one that Wikipedia should countenance? For: E notation eliminates the awkwardness of superscripts and the need to always explicitly write that base number, which is 10 and could clearly be understood without having to be written out every time. Against: if E notation becomes the standard, the visual link with where it comes from will be lost, and a few generations hence it will be a little bit harder for students to grasp what is actually going on, there will be more full professors who make egregious errors because they do not really know what they are doing, and the public image of scientists as high priests of arcane nonsense will be a bit more cemented. [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:49, 21 March 2021 (UTC)

== How is zero written in (normalized) scientific notation? ==

I can't find a mention of it in the article.

Mathworld has this to say about it: "The special case of 0 does not have a unique representation in scientific notation, i.e., 0=0×10^0=0×10^1=...." at http://mathworld.wolfram.com/ScientificNotation.html

[[User:Andopp|Andopp]] ([[User talk:Andopp|talk]]) 11:35, 17 January 2018 (UTC)

:By convention 0 is written 0 in scientific notation. There is no way to write it with a normalized mantissa.  <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/201.111.154.89|201.111.154.89]] ([[User talk:201.111.154.89#top|talk]]) 20:15, 1 March 2018 (UTC)</small> <!--Autosigned by SineBot-->

:: scientific notation was introduced to handle numbers that are awkward on the page in full form; zero is the diametrical opposite of a number that is too big too handle. [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:32, 21 March 2021 (UTC)

== Exponent versus "order of magnitude" as the term for N, the power of 10. ==

The article says that where 10^N is the power of 10 in the scientific notation representation of a number, N is called the "order of magnitude".  I think it is actually standard to call it "the exponent" and uncommon or almost nonexistent to call it the "order of magnitude".  The Google Books source cited is unavailable to my IP address. Is there a broader range of sources for establishing the standard usage?  ('''update:''' I was later able to obtain a copy of the source and it does not support the text in article. See comment below.) [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 09:36, 10 November 2020 (UTC)
: 'Exponent' is already used in the previous sentence. [[User:Praemonitus|Praemonitus]] ([[User talk:Praemonitus|talk]]) 18:01, 10 November 2020 (UTC)
:: The problem is in what article says are the names for the parts of a scientific notation expression M x 10^N.  It says, correctly, M is called "the mantissa", and incorrectly, that N is called "the order of magnitude".  It should be stated clearly that N is called "the exponent" of the expression, and the words "order of magnitude" removed. Unless references exist to support the usage claimed in the article as being standard.[[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 23:41, 10 November 2020 (UTC)
I've corrected the lead, which supported "order of magnitude" by citing a reference that in fact did not use that term and clearly described N as the "exponent".  I do not think there are any sources published in English that call N as the order of magnitude. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 00:05, 11 November 2020 (UTC)
:The use of "order of magnitude" for that quantity is in my experience universal. [[Exponent]] refers to any y in an expression x^y, whereas [[order of magnitude]] specifically refers to the power of 10 being factored out. The source in this instance is not a great one, as it is about computing, and so is really covering the analogous [[floating-point arithmetic]] (I expect because of lack of controversy over the terminology, an "any source will do" approach was taken!). I think it would be worth replacing this with "Elements of Mathematics with Numerical Applications" by Franca Caliò and Alessandro Lazzari, as that has a nice, clear explanation of exponential notations, separating scientific, floating point, and engineering notation, and including an explanation of the order of magnitude. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 15:30, 11 November 2020 (UTC)
:: "Order of magnitude" is usually used as a generalization of the notation. It's a rounding term, rather than specifically referring to the exponent. Anyway, I usually see "power" in that context. Probably all three are valid. [[User:Praemonitus|Praemonitus]] ([[User talk:Praemonitus|talk]]) 15:43, 11 November 2020 (UTC)
::: Quite possibly yes, it would come down to personal preference. In the source I mentioned order of magnitude is the term used. I'm happy to include any other terms also, but if there ends up being a large number of different terms it may get a bit ridiculous! [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 15:52, 11 November 2020 (UTC)
:: To be specific, you are saying there exists a textbook that uses sentences like "the current human population of Earth has order of magnitude 9"?  That would be a highly, highly unusual way of describing it.  The more standard phrasing would be that world population has "order of magnitude 10^9" or "is of order 10^9".
:: Likewise, to say that a number in scientific notation M x 10^N is "of the order", "of the same order of magnitude as", or "of order of magnitude" 10^N is a common turn of phrase but I have never encountered "order of magnitude N" for this.  In addition to being uncommon it means that a number has a different order of magnitude than its order of magnitude. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 07:26, 12 November 2020 (UTC)
::: The source I mentioned has a clear explanation of order of magnitude in the context of scientific notation. It's also clearly relevant to the topic, so I am minded to add it in shortly. It does not say the exact thing you just said as that would be quite an unusual wording, unless one were very specifically studying scientific notation at the time! An important thing not to confuse here is the use of the word "order" which has two contradictory uses throughout mathematics. The first is its substitution for exponent in many contexts. Just like leading digits, polynomials have a leading order (the degree of the polynomial), which is the largest exponent. In p-adic valuations, the order of some prime is the number of times it can divide into something - essentially it is the exponent in the prime factorisation of that number. Where some countries use PEMDAS to mean order of operations, many use BODMAS, with the E being changed to an O for suggestive reasons! While the term "order of magnitude" is really its own linguistic token, it can be understood in relation to these uses - "order" meaning exponent of some term and "magnitude" specifying the 10. The other main use of order is related to approximations. The order of a function, the order of convergence, or the entirety of big-O notation. Your nice example of "the population of the world is of order 10^9" I think would come under this second common usage. In that instance, "order of magnitude" would be the entirety of the exponential term - "order" meaning approximation and "magnitude" meaning the size. I'm happy to include this usage also, but have never come across it before - perhaps a cultural thing? Do you have a source? [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 08:42, 12 November 2020 (UTC)
:::: {{tq|It does not say the exact thing you just said}} (i.e., phrases in which 10^N "has order of magnitude N") {{tq|as that would be quite an unusual wording}}.  But a few lines above you said the use of "order of magnitude" for the N in 10^N is universal.  These seem to be completely opposite statements. To make this clear, what are examples of phrases that follow the usage you are calling universal? [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 09:40, 12 November 2020 (UTC)
::::: It does not say "the current human population of Earth has order of magnitude 9." It says, in the context of numbers written in the form m10^n, "The order of magnitude is the resulting exponent n (positive or negative)." It then includes a table of examples, the first being the number 0.05, where the exponential form is 5x10^-2 and the order of magnitude is -2. In my experience for this context, yes, order of magnitude is the universally used term for this quantity. If we can find a good source supporting other terms for this value, then it makes sense to note them in addition. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 10:17, 12 November 2020 (UTC)
:::::: First of all, that book is an obscure and probably unreliable source for English usage of mathematical terms.  Italian authors and publisher, book content based on teaching at an Italian university.  On Amazon it is listed as not in print and has no reviews. It is possible that "order of magnitude" is used in Italian, but that is not relevant to the article and the book is not widely used.

:::::: Second, from Google book searches (I can see only the search hits, not page previews) it appears their discussion of ''scientific notation'' calls ''n'' the "exponent" (p.30) while their "order of magnitude" (p.32) is '''unequal''' to the ''n'' in scientific notation.  If you can post the full paragraph or two from page 30 on scientific notation that should clarify whether this book supports what you are claiming about OOM. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 08:16, 20 November 2020 (UTC)

::::::: Yes, the word exponent is used on page 30, because in any expression x^y, the value y is the exponent. In the case of scientific notation, the exponent is specifically called the order of magnitude, which is explained in the book. See also "Basic Math and Pre-Algebra for Dummies" page 213 - "the order of magnitude is its exponent in scientific notation. For example 703=7.03*10^2 (order of magnitude is 2)." This is getting fairly ridiculous, as you have attempted to undermine basic mathematics on a few articles now. Changes to the status quo need to be backed up by sources. If you have any good reason why the article should change, then present a source for this and try to build consensus. Edit warring is not the answer. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 13:35, 20 November 2020 (UTC)
:::::::: Was there something unclear about the word "'''unequal'''"?  The language you pushed into the article with the Italian textbook as source, says that e.g. Avogadro's number 6.023x10^23 has order of magnitude 23, but according to the definition in that book (p.32) the OoM of that number would be 24.  Moreover, that book never links this definition of OoM to the components of scientific notation, which are defined two pages earlier.  The book is defining OoM as its own concept, separate from scientific notation, using a representation with different exponents from scientific notation, that is not a real notation in actual use, but is introduced only for that one sentence of that one book as a peculiar way of stating their definition of OoM.  So the article (after your edit) totally misrepresents what is in the source.  Unless you have some detailed disagreement with this statement of the facts, it is clear that your edit should be removed, without waiting for any consensus to form on the more general issue.  Doing so would revert that portion of the lead to its stable state from 2004 to late 2019 while we await the outcome of this Talk section.
:::::::: The "Math for Dummies" book is not WP:RS for these matters, for reasons that should be obvious, and we can discuss if necessary but would be more polite and BLP compliant to not get into.  That you can only find sketchy sources despite the powers of the Google search engine is further evidence that the usage you call universal is a neologism that is somewhere between nonexistent and highly nonstandard (in English-speaking STEM). [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 11:50, 22 November 2020 (UTC)
:::::::::If you want to change the definition used in the article, then you need to present sources supporting this change. I have given two sources supporting the pre-existing version, both of which are clearly reliable and relevant. If you want to change the article, then propose a change, support your proposal with sources, and editors will quite possibly agree with you. If there are good sources supporting "exponent" then I'm happy adding in this term to the article. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 12:32, 22 November 2020 (UTC)
:::::::::: Your first source contradicts your edit.  23 is unequal to 24.  Please address that, because it looks like you are ignoring arithmetic violations and selectively omitting text to misquote that source as supporting your edit.  Where the source plainly  and objectively does not support the edit, it is your reversions forcing that erroneous edit to stay in place that need to be justified, not my restoration of what had been the stable content of the lead for 15 years.
:::::::::: Your second source is clearly not WP:RS, ie., expert secondary source and it contradicts virtually all usage of "order of magnitude", including hundreds of examples on Wikipedia itself ( https://en.wikipedia.org/w/index.php?title=Special:Search&limit=1500&offset=0&ns0=1&search=%22order+of+magnitude%22&advancedSearch-current={} and the tables in https://en.wikipedia.org/wiki/Category:Orders_of_magnitude  ).  You will need better sources to establish that there is any significant use of the term "order of magnitude" rather than "exponent" for the ''n'' of scientific notation. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 02:41, 23 November 2020 (UTC)
::::::::::: It is quite clear that both sources support the usage of "order of magnitude" in the article. That is, the exponent seen in scientific notation. I don't see an issue with the 23/24 thing, because different values will obviously appear here based on how we restrict the significand during normalisation (common restrictions of 1/x <= m < x will produce differing significands and so differing orders of magnitude). I don't need to keep producing more and more sources to maintain the article's current wording. If you want to make a change, then say the change you want to make, and produce good sources supporting it. I am not opposed in principle to adding "exponent" or "power" as alternative terms for this value. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 08:40, 23 November 2020 (UTC)
:::::::::::: The dictionary definition shows that "order of magnitude" is intended as an approximation. Exponent is less ambiguous. [[User:Praemonitus|Praemonitus]] ([[User talk:Praemonitus|talk]]) 16:13, 23 November 2020 (UTC)
::::::::::::: Exponent is definitely less ambiguous, though also less specific, referring to any value y in an expression x^y. I am happy adding exponent as an alternative terminology, if there are sources supporting this. [[User:Awoma|Awoma]] ([[User talk:Awoma|talk]]) 17:54, 23 November 2020 (UTC)
:::::::::::::: In the meantime another editor has replaced your edit with one that removed OoM and restored "exponent", so this might be moot, but ''exponent'' is not an alternative term, it is the overwhelmingly dominant term to the point of practically being the only term in English-speaking STEM. It's possible there is some other community (such as high school education or something) in which people use OOM, and that could be indicated if true.  The reason the sourcing for "order of magnitude" has been so weak is that it does not get much use and as a result it is hard to find examples. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 08:27, 11 December 2020 (UTC) 
:::::::::::: That is a perfect, almost Platonic example of WP:SYNTH.  You are saying that if only the first section of the Italian source were rewritten using material from its second section then we would have a reference to what you want.  But that is not what the source ''actually says'', it is your production of what it might have said if it were to have supported the text added to this article.  You could edit-war by reinstating the same text citing the other source, Math For Dummies, but that is not an expert secondary source which is what's needed for science articles.  And if it were an expert source, it is so vastly outnumbered by other more-expert sources that use "exponent", that at best it would be an alternative language in need of qualification as such. I think it is simply a misunderstanding by the author. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 08:17, 11 December 2020 (UTC)

== Order as a scale, not a number ==

By referring to the Category:Orders of magnitude one can see that the sense of order in mathematics refers to a relation. The common use of the term in scientific notation refers to a particular number. By force of an early habit the exponent of ten became the order of magnitude, for instance in physics exercises. In building the encyclopedia silos have developed such as Category:Logarithmic scales of measurement and Category:Orders of magnitude. A dialogue in this Talk reflects an encounter where each wants the best designation of the exponent in scientific notation. A reference "for Dummies" exposes the naive answer in a debased context. Adjusting to diverse readership is implicit in  the  encyclopedic undertaking, and such adjustment is called for now. An edit on 21 December 2018 was a mistaken venture into the vernacular. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 04:07, 24 November 2020 (UTC)
::  {{tq|By force of an early habit the exponent of ten became the order of magnitude, for instance in physics exercises.}} It's not uncommon to hear the power of 10, ''10^n'' (not the exponent ''n'' itself) referred to as of the same order of magnitude or even "the" order of magnitude of the quantity.  Referring to the exponent ''n'' as the OOM would be rather strange in a physics context where one wants to make order of magnitude estimates of dimensionful quantities, not the (dimensionally meaningless) logarithm thereof.  It's easy to produce authoritative physics references, e.g., people at the top of the profession, stating the traditional use of order-of-magnitude terminology that excludes the exponent ''n''.  If you think the opposite convention is catching on that needs citations and, if it exists, a survey of usage to establish what is common and what is minority, fringe or upstart usage that should be either ignored or distinguished from the standard, default terminology. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 07:47, 29 November 2020 (UTC)

:: saying that logs of dimensionful quantities is meaningless is putting it nicely. As far as the actual numerical expression that is obtained when one logs something dimensionful, the unit that happened to be chosen is coming along for an awkward ride as an additive constant. The problem is resolved when this number is added to something with the awkward term in the negative, as the two then cancel. Yes, you say, they should have logged the dimensionless ratio in the first place. Agreed, only dimensionless quantities should ever be logged. The problem is that experimental scientists just continue to do this and any explanation goes whoosh. Try telling chemists or biologists they cannot have they pH and see what happens! [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:30, 21 March 2021 (UTC)

: Right.  There is the logic of the situation, and the traditional or "professional" usage (both of which unequivocally treat OOM as describing ''relations'' between ''pairs'' of numbers, e.g., "same order of magnitude", "within K orders of magnitude", "differ by K orders of magnitude") ---- and then some well-intentioned revisionism that attempts to simplify that and [[retcon]] it, maybe for teaching students, by reducing the binary relation to a unary function (so x and y have same order of magnitude when OOM(x)=OOM(y) for some specified rounding function OOM()).  The simplifications run into a series of technical and linguistic problems which is why expressions like "Earth's population has order of magnitude equal to 9" are not observed in the wild, and certainly not in mathematics dictionaries, encyclopedias and handbooks that try to codify usage.

:It is surely possible to explain this (probably in the [[order of magnitude]] article) in a basic and accessible way that reconciles the difficulties without inverting reality and pretending that the retconned usage is the standard. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 06:10, 24 November 2020 (UTC)

Since the real numbers form a [[total order]], the idea of order of magnitude is inherited from this particular kind of [[homogeneous relation]]. Then the particular exponent in a given instance located in the order is an [[ordinal number]]. But "ordinal of magnitude" is not in use. The suggestion to rephrase [[Orders of magnitude]], main article for Category:Orders of magnitude, is right on. Note that in [[levels of measurement]], the [[ratio scale]] of real or rational numbers implies there is an included ordinal scale, which is the object of this discussion. Consider also the fact that frequently scientific notation uses negative exponents, requiring [[ordinal number#Negative ordinals|negative ordinals]]. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 19:32, 26 November 2020 (UTC)

[[Decade (log scale)]] offers a precise alternative to  "exponent" or "order of magnitude" as a name for ''N'' in 10<sup>N</sup>. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 03:39, 27 November 2020 (UTC)
: It's base 10 specific, and seems to be the same as [[characteristic]] which was formerly put into the article for the same purpose, but the same issues arise: relative or absolute measurement  (binary relation or unary function), and whether the term is really used.  I made some comments at the talk page of Decade about the recent edits to that article. [[Special:Contributions/73.89.25.252|73.89.25.252]] ([[User talk:73.89.25.252|talk]]) 07:51, 11 December 2020 (UTC)

:: Order of magnitude is used by many experimental scientists as equivalent, more or less, to "how many zeroes" or "how many decimal places" - obviously it annoys the heck out of proper mathematicians, who use this phrase to stand for a much more dignified and deeper idea. [[Special:Contributions/2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7]] ([[User talk:2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7|talk]]) 09:23, 21 March 2021 (UTC)

== Can "Scientific notation" use a base other than 10? ==

The article is currently somewhat inconsistent on this question.

The lede defines scientific notation as numbers of the form ''m''&nbsp;&times;&nbsp;10<sup>''n''</sup>.
The first section says that the alternative term 'exponential notation' can be used for "bases other than 10", rather strongly suggesting that 'scientific notation' is restricted to base 10.

But then the "Other bases" section says that "other bases can be used too", and explicitly refers to "base-2 scientific notation".

I honestly don't know whether it's correct to say things like "base-2 scientific notation".
(I suspect there's no definitive answer, and that usages differ.)
—[[User:scs|scs]] ([[User talk:scs|talk]]) 01:11, 14 June 2022 (UTC)

:Someone could obviously write a number like {{tmath|123_5 \times 5^{6} }} with a base-5 significand and 5 raised to some integer exponent, if they wanted to, but such use is going to be extremely uncommon by comparison with the decimal version. I think it's fine to say that "scientific notation" is decimal. However, the intended meaning of a phrase like "base-2 scientific notation" is clear enough. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 20:00, 25 March 2024 (UTC)

:: I agree that the words "scientific notation" quite strongly (or perhaps absolutely) imply base 10.  If you're talking about some other base, like 2, a much better term is "exponential notation".

:: The problem is that we don't have an article on [[exponential notation]]; it links back here. —[[User:scs|scs]] ([[User talk:scs|talk]]) 16:03, 27 September 2024 (UTC)
:::
:::''Scientific notation'' is commonly used for writing. Floating point is commonly used for computer (and calculator) computation. Calculators commonly do arithmetic in decimal, and computers most often in binary. Handwritten notation in bases other than 10 is rare enough to special case. Anyone needing to do it, can supply their own notation. As the article notes, there is notation for computer input and output. [[User:Gah4|Gah4]] ([[User talk:Gah4|talk]]) 20:46, 5 May 2025 (UTC)

== Do Not Confuse with Euler's Number (e) ==

Would like to add a Do Not Confuse to avoid conflation between E in scientific notation and ''e'' the numerical constant. [[User:MarsInSVG|MarsInSVG]] ([[User talk:MarsInSVG|talk]]) 15:03, 6 February 2023 (UTC)
:There is no place in this article where this confusion is possible. &#32;<span style="font-variant:small-caps; whitespace:nowrap;">[[User:Headbomb|Headbomb]] {[[User talk:Headbomb|t]] · [[Special:Contributions/Headbomb|c]] · [[WP:PHYS|p]] · [[WP:WBOOKS|b]]}</span> 16:09, 6 February 2023 (UTC)

== How about some history? ==

Conspicuously absent from this article is any discussion of who first thought of doing this, when and in what circumstances the idea emerged and what it was first applied to. That's what I wanted to know when I looked up the term. [[User:Jalinker59|Jalinker59]] ([[User talk:Jalinker59|talk]]) 13:37, 15 July 2023 (UTC)

:Apparently [[Archimedes#The_Sand_Reckoner|Archimedes invented the idea]]. [[User:Dondervogel 2|Dondervogel 2]] ([[User talk:Dondervogel 2|talk]]) 16:01, 15 July 2023 (UTC)

== E notation section is a mess ==

@[[User:Matthiaspaul|Matthiaspaul]] just did a revert of some changes to the section {{alink|E notation}} made by @[[User:Erudecorp|Erudecorp]] a couple of months ago. I'm not entirely sold on the edited version, but the restored version, with the long miscellaneous bullet list of vaguely narrative sentences, is a mess. In my opinion it is unhelpful for this article to try to list every variant ever used in any obscure calculator or document for representing floating point decimal numbers. We should explain the purpose and context of a compressed calculator notation (something @[[User:Erudecorp|Erudecorp]] was trying to do), and then describe the most influential few variants with clear paragraphs of prose (not a bullet list). The long tail of trivia should be chopped as out of scope and irrelevant. Cf. [[WP:INDISCRIMINATE]]. (And we should get rid of the little button symbols, {{button|EXP}} etc., in running prose. Plain text "EXP" or perhaps {{code|EXP}} is less distracting and conveys the same information.) –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 19:37, 25 March 2024 (UTC)
: I'm afraid, I disagree with you here. I consider the chronological list of examples to be historically, encyclopedically, and educationally highly relevant for the article, as readers can thereby follow the interesting development of expression and notation over the decades and in the context of the available technology. I find this list fascinating to read and this kind of information is exactly the detail level I expect to find when turning to Wikipedia in order to learn more about a topic than what can be found elsewhere. While I have no principal objections in regard to turning this list into prose eventually, it would thereby become much longer and more difficult to parse. At the present state I consider it easier accessible as a bulleted list. --[[User:Matthiaspaul|Matthiaspaul]] ([[User talk:Matthiaspaul|talk]]) 20:33, 25 March 2024 (UTC)
::Many people find fascination in piles of trivia, but that doesn't (by itself) make them encyclopedic. Fascinating or not, this section is a confusing and largely illegible mess which must be cleaned up to meet basic Wikipedia standards for writing style. One useful approach might be to keep material which can be supported by [[WP:RS|"reliable"]] [[WP:SECONDARY|secondary sources]], and drop the rest. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 20:38, 25 March 2024 (UTC)
::Okay, I rewrote the section as paragraphs without taking out any of the details. It would be good to find secondary sources discussing this though. I feel like we're straying a bit toward original research in this section. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 23:12, 25 March 2024 (UTC)
::@[[User:Matthiaspaul|Matthiaspaul]] – Does that reformatting seem okay to you? I'm not trying to step on toes here / undermine anyone's hard work. (And sorry if my wording yesterday seemed sharp.) I tried to organize the paragraphs based on each separate notational variant, instead of the roughly chronological bullet points which I felt made for a confusing and disjointed narrative. But the organization and writing could probably still be improved. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 19:56, 26 March 2024 (UTC)

== History section should probably be added ==

It links to a '20th century' section in the [[Exponentiation]] article, but said section no longer exists, so a proper history section should probably be added. [[User:ThrowawayEpic1000|ThrowawayEpic1000]] ([[User talk:ThrowawayEpic1000|talk]]) 21:01, 26 April 2025 (UTC)
:The subsection '20th century' in Exponentiation has been restored. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 23:02, 5 May 2025 (UTC)
::A proper history section should still be added here. The linked section doesn't really do a good job at summarizing the history of scientific notation, nor would we expect it to as it would be off topic / out of scope in that context. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 00:05, 6 May 2025 (UTC)

== E, D, and Q ==

As well as I know, E notation goes back to Fortran I, and D (for double precision) to Fortran II. The IBM 360/85 supports quad precision (S/360 format) hexadecimal notation, with the REAL*16 data type and Q constants and format descriptor. With VAX, DEC supported (but rare in hardware) H-float, as a 128 bit floating point type, using IBM's REAL*16 and Q constants and format descriptor. [[User:Gah4|Gah4]] ([[User talk:Gah4|talk]]) 20:50, 5 May 2025 (UTC)

:Are you asking for a change to the article? If so, please be specific about what you think should be changed and present [[WP:RS|"reliable sources"]] attesting to whatever change you want to see. (Feel free to directly make changes to the article, if you have reliable sources supporting them.) –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 00:08, 6 May 2025 (UTC)