Talk:Order of magnitude

"1 E* J" series and others...

Interested parties should see the List of energies in joules, which I just created before coming across this (these) page(s). (See also Talk:List of energies in joules.) I should have followed the "Orders of magnitude" link first! Anyway, the information there should probably be refactored into Orders of magnitude (energy). There are also collections of pages for length, area, volume, time, etc., as pointed out in earlier discussions. In my opinion, all of these should be redirected to the relevant "Order" pages to avoid future confusion and duplication of effort. - dcljr 09:02, 29 Aug 2004 (UTC)

I prefer the collections (or "chains") of pages 1 E6 m, 1 E7 m, etc. That is how this area of WP began originally. The "Orders of magnitude (foo)" pages began as either an overview or a botched attempt at simplifying the main "Orders of magnitude" page. I would suggest we look into restoring the "chain" pages, a number of which have been turned into redirects. -- Tarquin 12:06, 29 Aug 2004 (UTC)

Is it a question of one or the other? Some of these lists would be best split up chain-like, others might be a little too thin for this. Moreover I'd like to see these chains have larger links—thousands rather than tens would probably be better. In fact, some parts of a chain could be bigger, and other parts smaller (I'd suggest, 10, 1000 or 10⁶ⁿ for interger, n). Further, it would be nice if they could have titles written in English rather than some kind of computer code (see Talk:1 E-3 s#Title). Jɪmp 07:03, 22 November 2007 (UTC)

Contradictory section "Working Out the Orders of Magnitude"

This oddly worded section (which I boldly deleted) gave the order of magnitude of 340 as 3. This contradicts the earlier "take the log and truncate" method which would give trunc(2.53) or 2. Thoughts on this? Restore it if you liked it (and don't tell me please). Caltrop 01:19, 16 March 2007 (UTC)

Torque

Orders of magnitude of torque? I could use that. --Remi0o 09:25, 30 March 2007 (UTC)

Text taken from another source

It looks like some of the text in this article was taken from another source, which had chapters. There's an unchanged reference to "the first chapter" in the Non-decimal orders of magnitude section.

Radiation

How about the order of magnitude for radiation? Magniloquent 23:55, 6 August 2007 (UTC)

Fixed! (only 3 years late!) SteveBaker (talk) 19:10, 9 September 2010 (UTC)

Order of magnitude??

In Computer Science the order of magnitude often refers to powers of 2 or more commonly powers of n where n is any integer. I my humble opinion this entire article needs the help of someone who understands number theory. --209.216.184.118 (talk) 00:55, 9 February 2008 (UTC) Sorry, I wasn't logged in. --DRoll (talk) 00:57, 9 February 2008 (UTC)

Order of magnitude of zero

Such a dumb question but ...

$lim_{x\to 0}x=-\infty$

so it would seem to me that the order of magnitude of zero would generally be taken as undefined. Am I right? Is it considered to be −∞? Surely the order of magnitude of zero is not zero ... right? JIMp _talk·cont 23:40, 3 June 2008 (UTC)

You are correct. Orders of magnitude are associated with positive numbers. Xihr (talk) 03:40, 5 June 2008 (UTC)

So, like zero isn't a positive number? Is it negative? 88.151.26.71 (talk) 00:26, 23 September 2009 (UTC)

0 is neither positive nor negative. --Jhertel (talk) 08:47, 31 October 2016 (UTC)

You're wrong. $lim_{x\to 0}x\neq -\infty$. Actually $lim_{x\to 0}x=0.$CountMacula (talk) 19:04, 26 December 2013 (UTC)

He meant $lim_{x\to 0^{+}}Log(x)=-\infty$ — Preceding unsigned comment added by 200.121.65.4 (talk) 23:35, 5 March 2014 (UTC)

Between two stools

This page is terrible. It seems like it is trying to find a common ground between readers with little or no mathematical background and someone with a modicum of understanding of the language of mathematics. It needs to decide which class of reader it is aimed at. My preference would be someone who does not have a mathematical background. With that in mind the first two paragraphs could be much better summarised as something like: ``Most commonly, when two quantities are compared as having an order-of-magnitude difference, it is taken to mean that the two quantities involved differ by a factor of about ten. Logarithmic scales and questions of which base is most likely being invoked by the qualifier "order-of-magnitude" can be introduced, but the page should try to introduce such concepts in a logical way.

As it is this page has no cohesion, doesn't know who its _target audience is, and (to agree with another comment here) has sections that seem to be lifted verbatim from other sources without any consideration of the expository nature of this medium. If the author wishes merely to regurgitate what he has learned from other sources, he should at least make some effort to present that in a way that will be clear to those who do not have the appropriate textbooks to hand, and whose motivation in looking up this page is to expand their knowledge rather than merely read a poorly-constructed precis of someone's course notes. 88.151.26.71 (talk) 00:51, 23 September 2009 (UTC)

• Actually, I find it quite appropriate that it addresses the concept in simple terms in places for the broadest audience, and then fills in with a little more detail for those who remember their high school mathematics for others. -- Ithacagorges 22:45, 18 January 2011 (UTC)

• Wow, I'm reading this note a decade later and the 2009 comment is still *painfully* true. The introductory sentence is so bad I had to race to the talk page to see what poindexter orgy led to the birth of that monster. It's a nightmare labyrinth of prepositions ("of.. of.. of.. to.. of.. of.. of", in a single sentence!) gluing together a bunch of abstractions. This is not such a difficult concept in the way it is commonly used! There is no good reason why the first two sentences shouldn't be understandable on the first reading by a non-technical person who can then go on their way, and we can get as nerdy as we like with the rest of the article. Skip all references to logarithm in the first sentence; it should be short and use the language of laypeople like "ten times" (the suggestion from 2009 above would be a good enough start); then there should be a simple illustrative example. The next paragraph can then get into the broader and more rigorous mathematical definitions. Start simple and colloquial -- then get technical. DKEdwards (talk) 07:50, 7 May 2020 (UTC)

Here are a few examples of how normal earthlings introduce such a concept for laypeople:

• https://simple.wikipedia.org/wiki/Order_of_magnitude
• https://brians.wsu.edu/2016/05/19/orders-of-magnitude
• https://study.com/academy/lesson/order-of-magnitude-definition-examples.html
• https://mathworld.wolfram.com/OrderofMagnitude.html

Octillion, not "Gazillion"

I believe the correct number for 10^27 is octillion, not gazillion. I'll let someone else fill in the details. -- Ithacagorges 03:05, 6 January 2011 (UTC)

Yeah - we have someone trying to be funny here...we call them "vandals". SteveBaker (talk) 14:40, 19 January 2011 (UTC)

Redlinks

I have removed redlinks from the associated template Template:Orders of magnitude wide, listed here to encourage someone to start them:

• Orders of magnitude (angular frequency)
• Orders of magnitude (concentration)
• Orders of magnitude (current)
• Orders of magnitude (momentum)

This makes the template more consistent with its tall version, they can be re-added when the articles exist. -84user (talk) 19:04, 16 March 2011 (UTC)

New necessary links or articles!!!!

I propose the following orders of magnitude (I'm naming them after the measuring unit not after what they measure because I am not sure what they measure but if someone gives them their proper name these measurements should have links to them, indeed every measurement must have a link to the "orders of magnitude" link that corresponds to it) I would do these myself if I knew how to do them...

• Orders of magnitude (candela)
• Orders of magnitude (candela per square metre)
• Orders of magnitude (lux)
• Orders of magnitude (lux second)
• Orders of magnitude (lumen)
• Orders of magnitude (lumen second)
• Orders of magnitude (lumen second per metre cube)
• Orders of magnitude (lumen per watt)
• Orders of magnitude (watts)
• Orders of magnitude (hertz)
• Orders of magnitude (bits)
  • ¿Dont you agree?Undead Herle King (talk) 00:44, 19 April 2012 (UTC)

No, I don't agree...in fact, I disagree on every single one of those!

The trouble is that all of these light-related ones are going to have very similar content...the examples for lumens, lumen seconds and lumen second per meter cubed will all contain fireflies and stars and all of that stuff. People are already very confused by all of these distinctions in the measurement of light. If we're going to do anything, it should be to extend the existing "luminous flux" article by adding more tables to encompass the idea of continuous sources of energy versus pulsed or burst sources - and to distinguish directional sources (like lasers and pulsars) versus omnidirectional (like fireflies and stars). That would reduce the set of eight confusingly similar articles that you propose into three concise tables within a single article - where the distinctions between what is being measured may be explained.

We don't need Orders of magnitude (watts) (except perhaps as a redirect) because we already have Orders of magnitude (power). Also, Orders of magnitude (hertz) is just Orders of magnitude (frequency) and Orders of magnitude (bits) is just Orders of magnitude (data).

The point being that we don't make [[Orders of magnitude (<some SI unit>)]] - we have [[Orders of magnitude (<some physical property>)]]. You could argue for some redirects from the SI unit names to the property page - but I really don't want to have two different pages with (for example) Orders of magnitude (temperature) in Celsius and Fahrenheit - and we certainly don't want articles about weight for pounds, ounces, grains, short and long tons, tonnes, kilograms, grams and so forth! Maintaining all of those additional pages would be a nightmare.

So to keep it simple - we have one page per fundamental property (which we already have for every one of your examples) - and consider here the question of whether having redirects from similarly named pages with SI units would make sense. That is not the simple question you might think it would be because (for example) Orders of magnitude (hertz) could redirect to either Orders of magnitude (computing) or Orders of magnitude (frequency) or even Orders of magnitude (radiation) since all three can be measured in hertz. (the 'becquerel' is just 'hertz as applied to radiation particle counts')

Furthermore, with your proposal, wouldn't we also need articles for incomprehensible properties like Orders of magnitude (meters cubed per second per watt) - which I would call Orders of magnitude (pumping efficiency)? The units that are used to measure the property are not really what we're talking about here. Our articles are about the orders of magnitude of real-world phenomena - they are only incidentally related to particular units of measurement.

Hence, I strongly disagree with your proposal to create a bunch of new articles because none of them are needed. I'm nervous about creating redirects for them instead - although I could perhaps be persuaded.

SteveBaker (talk) 13:21, 19 April 2012 (UTC)

I found some suggestions by User:Mynameisnoted:

• capacitance - Added as of 2012-06-05
• current - Added as of 2012-06-11
• concentration
• probability (or is numbers good enough?)
• surface tension

Electron9 (talk) 00:17, 30 May 2012 (UTC)

I don't like "surface tension" - "surface energy density" might be a better choice - but it's pretty obscure. But the others look reasonable. SteveBaker (talk) 16:07, 30 May 2012 (UTC)

I added the new capacitance article into both of the orders-of-magnitude templates. SteveBaker (talk) 14:22, 5 June 2012 (UTC)

I agree, we need momentum; angular momentum; luminous intensity.--Solomonfromfinland (talk) 20:34, 14 August 2015 (UTC)

"of the order of" vs. "on the order of"

I've never heard "of the order of"; I've always heard "on the order of". Is this a regional or historical difference? (I'm in U.S.) A web search of "of the order of" returns mostly results like "...of the Order of Bath". Thrmlbrk (talk) 20:48, 27 June 2012 (UTC)

An order of magnitude is the magnitude

This article is a total mess. The very first sentence uses "magnitude" in the definition of "order of magnitude". I found where this article's definition came from, from Wiktionary which now lowers my estimation of Wiktionary by...uh...2 orders of magnitude".

Here is a great definition from the FreeDictionary.org/Wordnet [Note: its first def concerns order like *on the order of a kilometer*, see Thrmlbrk above] "a number assigned to the ratio of two quantities; two quantities are of the same order of magnitude if one is less than 10 times as large as the other; the number of magnitudes that the quantities differ is specified to within a power of 10" .... right! it's a comparative term.

All of the garbage that follows in this article is an attempt to place some kind of mathematical or technical meaning on a nebulous language concept "order of magnitude". It can't be done. Here's my go at it: An order of magnitude is 10X. Three orders of magnitude is 1000X. Since OoM is simply a phrase meaning "ten times" it has no positive or negative connotation therefore it must be succeeded by a comparative modifier such as bigger, smaller, longer, shorter, etc. Dangnad (talk) 19:59, 31 August 2013 (UTC)

I am adding to my criticism two years later. The original sentence using a word to define a word has been removed and replaced by a definition that is entirely wrong: "Orders of magnitude are written in powers of 10. For example, the order of magnitude of 1500 is 3, since 1500 may be written as 1.5 × 10^3." An OoM is NOT written as a power of ten and there is no such thing as an order of magnitude of 1500. The phrase "order of magnitude" is a comparative term thus it can't be written as a power of ten. OoMs are written as follows. "An order of magnitude [comparative term]", "two orders of magnitude [comparative term]", etc. If something is 10^2 times larger than something else it is written "something(2) is two orders of magnitude larger than something(1)". Likewise for 10^-2, "s(2) is two OsoM smaller than s(1)". The author of this article is trying to make a largely meaningless phrase into something it is not. "Order of magnitude" is a geek phrase. Dangnad (talk) 21:04, 30 August 2015 (UTC)

Inconsistent SI scale standard (IMPORTANT Reminder to SI double-standard)

Corrections:

Kilo [K], not kilo [k]. (e.g: Km = Kilometer)

Hecto [H], not hecto [h]. (e.g: Ha = Hectoare)

Deka/Deca [D], not deka/deca [da]. (e.g: Dg = Dekagram/Decagram)

You don't need such "ONLY ONE" inconsistent 2-letter symbol here ("da" for "Deka") while all other SI magnitude scale symbols use solely and only 1-letter symbols! Be consistent with your own standard, SI!

The SI was defined scale symbols above base reference (10^0 = 1) must be capitalized and below must be lower-cased, this measure was done to avoid misinterpretation between its own 1-letter scale symbols. We can see the traces for all MAJOR/UP scale symbols following the 'old' rule with capitalized letters such as [G]iga/[M]ega/[T]era/[P]eta, etc (very useful to differentiate with other MINOR/DOWN scale symbols that uses lowercased 1-letter symbols such as "[p]ico" from "[P]eta" for example). So, why on earth SI beginning to use lowercase-letter symbols for those three MAJOR magnitude scales that violates its own standard?

Si should define and prioritize the magnitude scale symbols FIRST, since this one uses 1-letter symbols and conflicts are greater in this scope/region. For example, how one can tell that "1 K" means "1 Kilo" instead of "1 Kelvin", if both have the same 1-letter symbol and capital case?

Proposal:

Kelvin as temperature unit can be symbol-defined with more than 1-letter symbol as: "Kn" (just like "Pa" for "Pascal" and "Wb" for "Weber" - so, why is it not also valid for Kelvin?), "Kelv", "Kvn"/"Klv", or simply reverting to old standard to prefix temperature unit with degree symbol (°K). Even I can propose to use lowercased "k" for Kelvin, I prefer to reserve it for future MINOR/DOWN magnitude scale of SI standard, just in case the magnitude scale order is widened/enlarged and necessary.

Other SI symbols conflicting with these 1-letter magnitude scale symbols should be replaced with non-conflicting ones, using more than 1-letter symbol is recommended if conflicts always exist when searching/using 1-letter symbols just like my Kelvin symbol replacement proposal here.

Prioritize your SI magnitude scale symbols FIRST, then other non-MagnitudeScale symbols - then you will be confused much less by your own double standards, since scale symbols can always be paired with other non-scale unit symbols that may added more confusion if the magnitude scale symbols group (that uses 1-letter symbols, as strictly as possible as an excellent magnitude scale standard) is not strictly predefined FIRST in the 1st place.

==> [Ois1974 @ 2013-12-21 Sat] 114.79.49.125 (talk) 07:38, 21 December 2013 (UTC)

For what it's worth: Since this user insisted on restoring this same message at Talk:International System of Units after it was removed, I've now attempted to communicate with this user at User talk:114.79.49.227. --Closeapple (talk) 20:10, 3 January 2014 (UTC)

Unit and prefix symbols are officially standardized. Prefix symbols less than or equal to 10³ (kilo-, k-) are lowercase, while bigger prefixes are capitalized (only the symbols, not the names; hence megawatt, gigawatt etc. are not capitalized). A number of unit symbols are the same as a prefix symbol; m can mean meter or milli-; G can mean gauss or giga-; T can mean tesla or tera-. However, prefix symbols are normally used only in combination with root unit names, so it is understood whether a unit or a prefix is meant. Capital K is sometimes used informally to mean thousand, but it is understood from context whether thousand or kelvin is meant.--Solomonfromfinland (talk) 20:45, 14 August 2015 (UTC)

Dubious quote

I cut this quote since the definition it provides is dubious:

We say two numbers have the same order of magnitude of a number if the big one divided by the little one is less than 10. For example, 23 and 82 have the same order of magnitude, but 23 and 820 do not.

— John C. Baez

But e.g. 1 and 9 are not of the same order of magnitude. Baez has ignore the element of rounding. 9/1 = 9 which is of the order of magnitude of 10, not 1. So instead, I suggest the rule should be that the ratio should be < the square root of 10, i.e. 10^0.5. Elsewhere in the article it suggests the ratio should be between 0.5 and 5, but no citation is given and that seems to ignore the use of the log scale. Ben Finn (talk) 10:28, 30 January 2017 (UTC)

Yes, exactly. I see that comment which I just posted echoes yours. 174.199.11.51 (talk) 18:39, 9 March 2017 (UTC)

References

The quote by Baez is correct and superior to what is now in the article, which confuses order of magnitude assertions with particular schemes for rounding numbers to nearby powers of 10. The scheme advocated by @Bfinn: is probably the most logical one, but all rounding procedures are subject to discontinuities where virtually identical (extremely close) numbers, ones that "have the same order of magnitude" in any reasonable meaning of that term, are assigned different powers of 10.

This argument demonstrates that rounding to power of 10, and order-of-magnitude language, are related but distinct concepts, and the article should not treat them as the same thing. 73.89.25.252 (talk) 10:08, 24 November 2020 (UTC)

I don't know if I ever wrote that stuff - that's the main dubious thing about that quote. Anyway, according to that quote the numbers 51 and 10 are of the same order of magnitude, while someone editing this page made up a definition where they're not. I agree with this comment:

"It is founded on a definition that exists only on Wikipedia, a definition that was crafted by a Wikipedian editor/author but is not sourced."

But the quote attributed to me isn't sourced either.

Are A and B of the same order of magnitude iff

$-1\leq \log _{10}A/B\leq 1$,

or

$-1/2\leq \log _{10}A/B\leq 1/2$?

I don't think the concept of "order of magnitude" is precise enough to support arguments about which definition is right! It's not *supposed* to be so precise! I think the article should explain this somewhere. John Baez (talk) 01:18, 10 December 2020 (UTC)

I suspect that the ratio being between 0.1 and 10 has never been in dispute; Ben Finn was writing about the edit at (https://en.wikipedia.org/w/index.php?title=Order_of_magnitude&type=revision&diff=762720021&oldid=759437258 ) for which "ratio" is not the ratio A/B that determines the difference in order of magnitude between a pair of quantities A and B, but the ratio of a single number to a nearby power of 10 to which it is to be rounded (and the rounded thing designated as the number's "order of magnitude"). In other words, he is not talking about what is conventionally known as order of magnitude, but about schemes of rounding numbers to nearby powers of 10. I agree that rounding to the power of 10 with smallest log-ratio to the input is most logical (though not the easiest to read off from scientific notation) but methods of rounding to powers of 10 do not capture what people in STEM mean by "order of magnitude" language. 73.89.25.252 (talk) 06:24, 10 December 2020 (UTC)

Wikipedian invention

This article suffers from a problem that afflicts many minor articles on Wikipedia. It is founded on a definition that exists only on Wikipedia, a definition that was crafted by a Wikipedian editor/author but is not sourced --and therefore a break with the fundamental principle of Wikipedia. In particular, the article claims that we need to work out the order of magnitude of a number by expressing it as a*10^b and further that 0.5<a<=5. This does not represent common understanding of the concept. Rather it represents some editor's attempt to formalize a definition. It is also mathematically inconsistent. If an order of magnitude is accepted as being a power of ten, then half an order of magnitude is 10^0.5 (the square root of 10, roughly 3.16). In order of magnitude terms, 400 is closer to 10^3 than it is to 10^2 (since 400 is approximately 10^2.60). Hence this attempted definition, placing the dividing line for orders of magnitude at 0.5 or 5, is not just unsourced, it is also arguably mathematically incorrect. 174.199.11.51 (talk) 18:38, 9 March 2017 (UTC)

Unicode symbols

The “Unicode Symbols” column should be removed from the table. These symbols exist in Unicode for round-trip compatibility with previously existing Japanese character sets. They are not the preferred or recommended way of representing these units in normal Unicode text.

For example, if you want to write that something weighs 5 kg, you just write the two ASCII letters “k” and “g”; you would not use the compatibility symbol “㎏” unless you are writing in Japanese (kanji and kana) where these symbols are expected.

Furthermore, the inclusion of these symbols adds nothing to the general discussion of order-of-magnitude. If they belong anywhere, it would be in the article on metric prefixes (in which case the base units and the non-metric symbols like “㏋” and “㏙” don't belong). And in any event, someone has added the pure-ASCII symbols “TB” and “PB” which completely defeat the purpose of having a column of special, beyond-ASCII symbols. Doug Ewell (talk) 17:52, 17 July 2017 (UTC)

Scale of Everything

Could we add a section presenting the scale of everything (e.g. elemtary particles, species, galaxies) that goes into more detail than the current image and its caption? — Preceding unsigned comment added by AHumanEditor (talk • contribs) 00:55, 7 October 2017 (UTC)

Article is misleading and trying to introduce a new usage for the term.

The article is trying to cleverly formalize a slightly informal linguistic usage as coming from a mathematical function that assigns to every positive (rational or real) number an integer called its "order of magnitude".

Nobody talks or writes this way. Not in precise scientific, quantitative or mathematical contexts and not in informal usage.

People talk about order of magnitude only in the relative sense, differences in order of magnitude. When they do, it's not usually in the precise sense of the article, nearest integer on the log_10 scale, but more like "number of decimal digits minus one" (before the decimal point) and sometimes not subtracting one, or saying "4 to 5 orders of magnitude", etc. The fuzziness is simply because the real concept is the logarithm of the ratio between two numbers, and for that all the ambiguities go away, but it's easier to speak of an integer. Regardless of how the integerization is done, nobody says things like "his annual income is of the fifth order of magnitude" that refer to a single quantity in isolation as having an order of magnitude.

If one were trying to find a precise integer valued function underpinning the common usage, the one given here would be the closest fit, but it's not possible to reproduce the actual use of the term by pointing to this newfangled "order of magnitude" construct.

Notice that most of the assertions in the article on this are unsourced. It is OR by someone well-intentioned but pushing their own ideas, or nonstandard ideas. 73.89.25.252 (talk) 22:40, 9 November 2020 (UTC)

I see that @Dangnad: and an IP editor have raised very similar objections above on this page and that the problem has existed for years. 73.89.25.252 (talk) 22:47, 9 November 2020 (UTC)

See scientific notation for the context of experts. For the fuzzy concept, usually the phrases are "a four-figure income", or "a five-figure income", or even a "six-figure income". — Rgdboer (talk) 02:09, 10 November 2020 (UTC)

There's plenty of informal language, more informal and fuzzy than orders of magnitude, about n-"figure" and n-"digit" integers, and the (often implicit or hypothetical) number of trailing "zeros" on numbers, especially financial numbers. This is certainly a related idea that should be mentioned in the article, and also the article on base 10 logarithms. But it doesn't support the neologism that this article is pushing, that order-of-magnitude references a standalone integer-valued function of rational or real numbers (ie, ratios). People don't say Pi or 22/7 are 1-figure numbers or that the inverse of the fine structure constant (about 137) is a 3-figure number. 73.89.25.252 (talk) 03:06, 10 November 2020 (UTC)

Looks like the John Baez explanation of order of magnitude quoted above also discusses it only as a comparison of two numbers, not a single-variable function. I have heard "order of magnitude" used hundreds of times but never any variation in this respect, it is always comparative. 73.89.25.252 (talk) 03:15, 10 November 2020 (UTC)

Another problem with the formulation in the article. It is commonplace to say things like a quantity known to be between 580 and 617 being "of order 600" or "on the order of 600" or "O(600)". This kind of phrase never means that the quantity is approximately a 600- or 601-digit integer, i.e., "order of magnitude 600" in the proposed language of this article. 73.89.25.252 (talk) 06:23, 10 November 2020 (UTC)

@73.89.25.252 I agree that this article is trying to formalize a very fuzzy and loosely used term and there aren't any sources associated with the definition presented here. I could take a stab at editing it to remove the unsourced OR and replace it with explanations that have reputable sources. Diskqualified (talk) 01:10, 4 February 2024 (UTC)

As mentioned above, please see the article on scientific notation as orders of magnitude come under that umbrella. With regards 613=O(600) this is confusing the order of magnitude (3 in this case) with the order, as in big O notation. These concepts are called confusingly similar things, but they are distinct. Awoma (talk) 06:54, 10 November 2020 (UTC)

People can and do write O(specific number) as an abbreviation of "on the order of (that number)". It's more standard and less confusing than saying 600 has OOM equal to 3.

Please give a reference other than this unsourced article for the term "order of magnitude" used as a function from rationals or reals to integers. 73.89.25.252 (talk) 08:43, 10 November 2020 (UTC)

The scientific notation article contradicts this article. It states that the exponent in the power of ten is the "order of magnitude", which is probably false as a statement about usage (I have only seen it called the "exponent", as confirmed by the capital E version of the notation as in 5.7 E 3 for 5700) and is incompatible with the definition given in this article using square root of 10. You just wrote that 600 has OOM equal to 3, as prescribed in order of magnitude, but the scientific notation article says its OOM is 2! Again, please point to a better source than Wikipedia articles to justify the content of Wikipedia articles. The people writing these articles are well intentioned but either using nonstandard sources or making it up themselves as WP:OR.73.89.25.252 (talk) 08:49, 10 November 2020 (UTC)

Further evidence on the usage can be found by searching internet for the exact phrase "order of magnitude equal to" and "order of magnitude is". They don't occur much and when found in scientific papers they appear to be non-native users of English writing something that would be natively expressed as "magnitude of order ...", equivalent to "O(that magnitude)". I did not see any technical article using those phrases to mean OOM as exponent of 10, number of digits or log-ratio. 73.89.25.252 (talk) 09:20, 10 November 2020 (UTC)

Terrible article, even worse illustration, stupid POV

This article falls far short of even the wiki standards for mediocre article. It is wrong, and poorly written. Moreover, the illustration is completely misleading, as it pretends that each level to level transition is the same zoom level which should ideally be 10 or at least around 30 as is in the picture but even that is not consistent. So, it is a complete mess. The article is written from idiozs POV.

Logarithm

Pervasive use of the word 'logarithm' dramatically increases the education required to understand the summary. I think this could be re-worded to make this topic more easily understood by folks with less education. 75.191.193.134 (talk) 15:14, 18 August 2022 (UTC)

Mathematics

Round of to the nearest 10 — Preceding unsigned comment added by 41.114.240.19 (talk) 18:20, 16 February 2023 (UTC)

This page should be Moved / Renamed to "Order of Magnitude Comparison"

Many issues raised in this talk page (lack of citations, inconsistency, new usage introduction) stem from the problem that the concept of "Order of Magnitude" is not well-defined at all. However, the concept of Comparison of Order of Magnitude is much better agreed on.

As others have mentioned, order of magnitude is a comparative tool to assess the similarity or difference between two numbers in a multiplicative, or geometric, sense. We have an intuitive idea that 1.001 and 1.002 are similar, and that 1001 and 1002 are similar in the same way (regardless of their absolute difference being much larger). Order of Magnitude Comparison formalizes this intuition.

This article should be focused more on Order of Magnitude as a comparative tool between two numbers, with the "assignment" of an integer order of magnitude to each real number minimized and contained to sub-sections on rules of thumb and estimation. Perhaps after these changes the article can be appropriately renamed to minimize this issue in the future.

Further, the closest thing to an academic citation on this article is the second paragraph here, which clearly indicates that the higher mathematics definition is about comparison, rather than assignment.

Ronoth (talk) 16:53, 30 August 2024 (UTC)

This article is key to a category containing

• Orders of magnitude (acceleration), Orders of magnitude (area), Orders of magnitude (bit rate), Orders of magnitude (current), Orders of magnitude (data), Orders of magnitude (energy), Orders of magnitude (force), Orders of magnitude (frequency), Orders of magnitude (illuminance), Orders of magnitude (length), Orders of magnitude (mass), Orders of magnitude (numbers), Orders of magnitude (power), Orders of magnitude (pressure), Orders of magnitude (radiation), Orders of magnitude (speed), Orders of magnitude (temperature), Orders of magnitude (time), Orders of magnitude (voltage), Orders of magnitude (volume).

True that comparison frequently describes the use of these orders, however, the large variety of contexts of use calls for a simple description of what order means throughout. — Rgdboer (talk) 22:06, 30 August 2024 (UTC)

After reading through more references, I agree. Usage on what "order" refers to seems to vary between a relative range, the action of multiplication or division by a set factor, or a specific range set by multiplication and division by 10. The page title does not need changing to capture these topics. Ronoth (talk) 16:40, 31 August 2024 (UTC)