Talk:Percentage

No history of % being used?

This is wikipedia, not a math textbook. Expand the article. --172.159.137.89 00:30, 26 January 2007 (UTC) what is the formula of; 3% of $61,110 —Preceding unsigned comment added by 65.160.213.25 (talk) 08:21, 17 March 2009 (UTC)

I thought this was very interesting, thank you for sharing this information. XxQueenBeeLoxx (talk) 00:12, 11 April 2018 (UTC)

Other

i like where this article is going. i'd like to see some examples how percentages can be misleading...how two opposite conclusions can be drawn from the same data...how politicians mislead the public. Kingturtle 07:11 Apr 13, 2003 (UTC)

in math when you ask what is 100% of 10 you get 10. in business when you say this $10 calculator increased by 100% you get $20. — Preceding unsigned comment added by 174.92.86.236 (talk) 17:13, 18 December 2015 (UTC)

about the "risen by 10%"

Percentages are always relative, because they are basically a type of fraction. Just because most people get it wrong, doesn't mean we should condone it. Financial reports always speak of "percent points" or just "points" or say what the rate changed to. -- Tarquin 16:33, 28 Aug 2003 (UTC)

%10 or 10% ?

Am I the only one that likes to use the percentage sign before the number? Is there a general usage of the percentage sign? I know in html, if you want to use a space character in a link you would use something like %20 which has totally different meaning in that context (hexadecimal for 32, the ascii number for space). But I've always liked using the percentage sign before the number. It gives the reader a warning.. "beware, the number you are about to look at represents a fraction multiplied by 100". Otherwise, I think I tend to ignore the sign (or reverse it in my head if I do notice). But now that I've actually seen the preview, 10% looks more correct. Hmmm. -- Root4(one) Section 2.1. 19:51:24, 1 Oct 2004 (UTC)

I've never seen that before (the prefix percent).  :-) - Omegatron 20:32, Oct 1, 2004 (UTC)

The article says

some examples on the Internet that have the symbol precede the number. This may have something to do either with a firm's typographic style, or perhaps an international standard relating to the metric system.

Where can I find examples like that (different from the above mentioned HTML usage), and which international standard is being referred to? AxelBoldt 21:08, 31 May 2005 (UTC)

The order "%10" is the standard one in Turkish. See for instance the exchange-rate banner labelled "PiyasaNet" on [1]. The writing order reflects the spoken order: "percent" is yüzde (literally: "on [one] hundred"), "ten" is on, and "ten percent" is yüzde on.  --Lambiam^Talk 22:00, 29 September 2006 (UTC)

Same in Basque. %6 matches spoken ehuneko sei ("hundred-of six").

Can we have sq. rt. (2)%, pi %, etc.?

Does it require all percentages to be rational numbers? That is to said, can we have sq rt (2)%, pi %, etc.?

As from its definition, it stated that "to express a proportion, a ratio or a fraction as a whole number ...".

Please advice, thank you.

Alan

In normal use the percent sign is preceded by a number written out in decimal form. Clearly, to actually do that requires that one use a finite decimal expansion, which always gives a rational number. However, it is often a rounded form. There is no reason to assume that this stands for an actually rational number. Take for instance the text: As early as the 19th century BC, Babylonian mathematicians were using π = 25/8, which is within 0.53% of the exact value. It is actually within X % of the actual value, where X = 100 × (1 − 25/(8π)) = 0.5281605675654.... This is an irrational amount. But to give an impression how good the approximation of the Babylonians was, we only need one or two decimals of the infinite expansion. It would be silly to write "100 × (1 − 25/(8π)) %", as this defeats the whole purpose of giving an impression, and is moreover more complicated than the equivalent expression "1 − 25/(8π)".  --Lambiam^Talk 22:43, 29 September 2006 (UTC)

Space or not?

Is there to be a space between the procentage, and the per cent sign? In this Wikipedia article, most English news articles, and The Chicago Manual of Style, there is not one, but according to ISO 31-0 (an NIST Special Publication 811 quotes it in secton 7.10.2), there should be a space. Which is the correct notation?

Unfortunately, as discussed previously in the Manual of Style archives, there's an inconsistency between the overwhelmingly more common English practice of having no space, and that recommended by ISO 31-0.

Personally, I'm heavily in favour of having no space as I think it looks much better from a typographical perspective. In fact, until I found out about ISO 31-0, I wasn't even aware that it was an issue: as far as I knew, not using a space was simply the correct way to format percentages. I'll try to see if I can dig up any typographical advice on the subject.

One thing that should be noted is that if people decide to use a space between the number and the percent sign, it must be a non-breaking space, otherwise you'll get scenarios where the number appears at the end of a line of text, and the percent sign on the next line. Cmdrjameson 22:34, 31 July 2006 (UTC)

Thank you for dropping by and replying! Myself, I definitely prefer without space - it's easier to read, and it never breaks down to two lines, no matter how careless the writer is. The reason I noticed the issue when Cmdrjameson ran his bot was because I'm used to Microsoft Word (back when I still used that) constantly telling me to put a space inbetween, which I constantly refused to do. Perhaps we should just leave it to the style guide and pray this obscure international standard corrects itself in a future revision? Jobjörn (Talk ° contribs) 02:24, 1 August 2006 (UTC)

At first, we should figure out whether the "per( )cent" is a unit or not. Is it a unit or symbol? If it is a unit, there is a general rule: "Always use figures when a unit of measurement follows (e.g., 5 A)" [2]. Furthermore, it should follow the space rule given above. The famous TeX typography, which collects and establishes the best document formatting standards, enforces the space between value and unit see units pdf by producing nice thin spaces. The document shows that all units have a name and a symbol and the symbols are used for writing down quantities. A particular must have a strong excuse to violate a general, since adding exceptions complicates the rules. Arbitrariness in rules produces garbage, chaos -- the world without any order and everything is exception. So I suggest that the article or the rule telling "Most guides agree that they always be written with a numeral, as in '5 percent' and not 'five percent'" be corrected. I recommend to follow the simple general rule: textual 'Five percent' at the beginning of sentence and figural '5\,%' elsewhere. --Javalenok 12:14, 8 November 2006 (UTC)

Based on the discussion above, I've tried to clarify the subject. I've also moved the section from Percentage#Word_and_symbol to Percent_sign#Spacing and added a link from the former to the latter. After all the question of spacing is irrelevant to the concept it has to do with the symbol. --Alf 20:34, 5 January 2007 (UTC)

thanks for clarification; to me this seems to be an evantgelism in en-WP -- internationally seen the handling in en-WP with the percent sign and space reminds me a bit of this image. Greetings, -- 79.219.14.240 (talk) 09:54, 29 October 2008 (UTC)

Whole number only?

Re a comment made at the reference desk ([3]), the definition as it stands seems to imply that only whole number (i.e. non-negative integer) percentages are percentages. This contradicts most dictionary definitions I can find; should it be reworded, or am I missing something? Ziggurat 02:39, 29 June 2006 (UTC)

Not only should it be reworded, at least one example of a non-whole percent should be added. Currently the entire article suggests that only whole percentages are used, which is simply wrong. Melchoir 02:49, 29 June 2006 (UTC)

What's more, since percentages are so common in statistics, it is very common to show the accuracy of the number as trailing decimals, even when they are zero. (Just look at this: [4] ).

Or look at the percentages here: http://www.bulletinph.com/395-candidates-pass-prc-exam-for-architects.html :{ --Lambiam^Talk 18:54, 3 July 2006 (UTC)

I was often asked at work to use percentages with one decimal place, such as 54.6%, but I didn't like doing it. (I was preparing reports about the money contributed towards various fundraising goals.) The extra decimal place gave to the reports the appearance of greater accuracy, which my boss liked. However, I felt that the extra decimal place hurt the reports, because the percentages were more difficult to read. For example, 54.6% is not as easy to read and understand as 55%. The purpose of percentages, in my reports and in most cases, is to explain the import of a long number like $38,727.50 by giving its equivalent as a short number like 55%.
In other situations it might be appropriate to use a percentage with one decimal place. In effect, the increment of measurement would not be one percent, but instead would be one-tenth of one percent. The measurement would not be per hundred, but per thousand. There is an old symbol for "per thousand," which looks like the percent sign with another zero. (Perhaps */oo is the best imitation I can type.) However, current usage is to say 54.6 percent instead of 546 per thousand.----

The symbol is ‰ and is called permille.  --Lambiam 08:27, 27 November 2007 (UTC)

Percentage vs. percent sign

Should these be split up? I notice that an anon has added the punctuation infobox here, but aside from one paragraph the whole article is about the concept, not the symbol. Is there enough content for a separate percent sign article? Ziggurat 22:39, 17 July 2006 (UTC)

punctuation infobox?

IP 24.131.125.172 added the punctuation infobox, which I find not particularly useful for this article. I removed it once, but it was re-added. Comments? Paul August ☎ 22:47, 17 July 2006 (UTC)

See above. The solution would be to split up the article on percentage the mathematical concept and percent sign the sign used to represent it, and then add the infobox to the latter only. Ziggurat 22:54, 17 July 2006 (UTC)

I hadn't noticed the section above when I made this comment. Yes separating the article might be a good solution. If you want to do this, please do. I doubt anyone will object. Paul August ☎ 23:13, 17 July 2006 (UTC)

Doing so now... Ziggurat 23:36, 17 July 2006 (UTC)

Unicode?

As I noticed many other articles where the topic was a symbol, letter, or character stated the unicode value of that character, should that not also be listed in this article as well? -Aknorals 10:49, 17 August 2006 (UTC)

This article is about the concept of the percentage, not the symbol. For that, you'd be looking for percent sign, which does indeed have the unicode value. Ziggurat 10:57, 17 August 2006 (UTC)

Actually, I was redirected here from "percent".. I had somehow figured that sense the word "unicode" didn't appear on the page, that the article also included info on the sign, but not the unicode of it... -Aknorals 12:42, 17 August 2006 (UTC)

Oh my, perhaps I should have read the first line of text? Sense I browse wikipedia a lot, I sometimes ignore that line unless it's in italics (indicating a different article) -Aknorals 12:48, 17 August 2006 (UTC)

Section Changes is wrong! There is no such thing as different usages in percentage!

"Due to inconsistent usage, .... to many people, any other usage is incorrect. .... In the case of interest rates, however, it is a common practice to use the percent change differently"

This section is wrong. Percentage have only 1 usage: representing a value as a N/100 fraction of another value. There is no other magical usage of it. Interest Rates is no exception. Then it is said 50% rate increase, from 10% to 15%, It is referring to the rate value. Then it is said it has increased by 5% (and not 50%) it is referring to the interest, NOT the rate. There is no difference in saying "10% of interest" and "the interest rate is 10%", but there IS difference between saying "+5% of interest rate" and "the interest rate is +5%". There is NO magically different usage in percentage of percent. The confusion is about meaning (interest X interest rate) and NOT different usages!!! I am trying to fix it but people are continuing to revert it. --SSPecteR

Unfortunately this incorrect usage does exist: [5]•[6]•[7]•[8]•[9]•[10]•[11]•[12]•[13]•[14]•[15]  --Lambiam^Talk 04:54, 1 November 2006 (UTC)

Then someone should define this "usage" as wrong in the article. As it is it appear the 2 are equally right. And when it say "it is a common practice to use the percent change differently" it don't define what usage is the different use. --SSPecteR

Well, perhaps "confusing" is a better term than "wrong"; I meant to echo the viewpoint of some people that this is incorrect usage. In any case, this usage is at best ambiguous. The text of the article is perhaps not optimally clear, which is also the case for the rest of the article.  --Lambiam^Talk 08:26, 1 November 2006 (UTC)

Symbol

The article states that the symbol is an abbreviation of the Italian "per cento". How so? As a backwards P and a closed-up c? I have always thought that it was a rearrangment of the numerals 1, 0 and 0 (forming "100"). Perhaps someone can give a reference here. — Paul G 12:21, 1 November 2006 (UTC)

See the article Percent sign, which is referred to by a wikilink in that sentence (although it is not clear to me that the further reference provided there entirely supports the iconic evolution as sketched).  --Lambiam^Talk 14:01, 1 November 2006 (UTC)

I think that article is wrong. See my arguments in the discussion there. sspecter 1 Novemver 2006

110%

I'm often hearing of the term 110% in various places (at work and on television). Is this strange mathematical phenomenon mentioned anywhere in Wikipedia? --Rebroad 21:29, 11 November 2006 (UTC)

This is not necessarily strange. If something grows by 10%, then afterwards it is 110% of the old value (100% + 10% = 110%). It can also refer to a difference: Suppose your snark hunting licence used to be ₤6,200 for a season, but they raise the price to ₤13,020. Then you can complain about this scandalous and ridiculous price raise by ₤6,820 (₤13,020 − ₤6,200), by saying that the price more than doubled. If you want to be precise, you can say it increased by a whopping 110%. The way you arrive at this number is that 6820/6200 = 1.10, which is 110 times 1/100, or 110%.  --Lambiam^Talk 12:55, 12 November 2006 (UTC)

I realized you probably were referring to people saying things like: "She is giving it 110 percent." I told them a million times not to exaggerate, but they won't listen. If I hear this one more time I will literally explode. It's called hyperbole, although I think there is a semantic aspect of "beyond the call of duty": where others would be done, she gives it an extra effort.  --Lambiam^Talk 13:25, 12 November 2006 (UTC)

Problematic text

I have moved the following text here from the article:

The number 100 is chosen as an arbitrary standard. It is unclear to even some scientists that 100 is not a factor or coefficient, but a notation. That is to say, percentages are calculated, for example, like this:

success-% = successes / trials, e.g. 15% = 0.15 = 150/1000

and not

success-% = 100 × successes / trials, e.g. 15% = 0.15 is not 100 × 150/1000 = 15 (1500%)

The latter would actually multiply the result with 100, rather than denote it as a percentage.

I have various problems with this text. First, it was placed (and after I deleted it, re-placed) in the section entitled "Word and symbol", but it is neither about the word (that is, percent), nor about the symbol (%). My main problem, however, is that even after multiple readings I cannot figure out what the text is attempting to say. Of course the choice of the number 100 is not "arbitrary". Clearly, 67 would have been a terrible choice, and we'd never have heard of (and certainly not had an article about) persexagintaseptemage. The point of using 100 is that you just shift the decimal point, and don't have to do any difficult multiplications and divisions. Why not 10 or 1000? One of the points of using percentages instead of fractions is that in many cases you can round the percentage to a whole number and not lose too much precision. The multiplier 10 is too small for that, while higher powers of 10 give too many digits. Usually 100 is just right. So it is not arbitrary. It was also not chosen "as a standard"; any standardization took place centuries after percentages became firmly entrenched.

The use of "some" in "some scientists" is a weasel word. Does the author have a bone to pick with a scientist? If this is something notable, we need a reference. Now it may indeed be unclear to some scientists that 100 is not "a factor or coefficient", and guess what: here is one! I just don't know what it is supposed to mean that 100 is or is not "a factor or coefficient, but a notation". Of course "100" is a notation, but it is not just a notation: it is a notation for a number. Whether it is a factor depends on a possible formula in which it occurs. Stating in isolation, without reference to a specific formula, that it is not a factor, is simply meaningless. It is explained in the article that percentages are a way of expressing numbers as fractions of 100. You can explain % as standing for "per 100", or more symbolically "/100", so 15% = 15/100. And that is of course where the name comes from: per cento is Italian for "per 100". In the formula 15/100, clearly 100 is not a factor, and one would be hard-pressed to find "some scientists" who claim otherwise.

The next formula, with the typographically and linguistically horrible "success-%" is hard to follow; if this is supposed to be an example, it does not explain how the variables in the formula are related to the numbers in the example. In any case, if S is the number of successes on a run of T trials, and someone has the task to find the number P such that the percentage of successes is P%, then they should calculate P = (S/T) × 100. For example, if S = 150 and T = 1000, P = (150/1000) × 100 = 15, so then the answer is 15%. There is nothing wrong with this, and the number 100 is clearly a factor in the formula for P. There is nothing wrong with this, and if someone has learned it this way long time ago and wants to brush up by reading our article, the suggestion produced by the second "and not" formula that there is something terribly wrong with this is only confusing.

In the last example it is of course true that 15% is not the same as 15; however, isn't that a strawman?  --Lambiam^Talk 00:18, 5 January 2007 (UTC)

A rather convoluted commentary, but the point is rather simple. Often we see texts with formulas like "conversion = 100 × output/input". This would imply that conversion is 100 times the proportion, rendering formulas like "output = conversion × input" invalid. 100 is not a special number; it is chosen to represent fraction, not actually modify their value. Per cent means "/100", therefore 15% is 15/100 or 0.15. You cannot say that 100 × 15/100 = 15% — the correct formula is 15/100 = 15%. That is to say, converting to percentage doesn't involve a multiplication by a mathematical coefficient of 100. --Vuo 16:36, 5 January 2007 (UTC)

But isn't X = (X×100)%? Suppose that, instead of the arbitrary number 100, they had chosen 67 a long time ago, and we were stuck with it. Using $ as the symbol for persexagintaseptem, we have that 1 = 67$. Now suppose the task at hand is to express the value 0.597 as a persexagintaseptemage. How should one go about doing that?  --Lambiam^Talk 20:44, 5 January 2007 (UTC)

You are correct that X = X × 100%. It is correct to write 100% × 15/100 = 15%. Since X × 100% = X × 1 = X, the operator × 100% does not modify the value. It is incorrect to write X = 100 × X. --Vuo 19:09, 6 January 2007 (UTC)

History of per cent

Anyone know the history of per cent? When was it first used?--Drgs100 (talk) 09:30, 19 November 2008 (UTC)

• I saw a usage note on an online dictionary that said it started out as per centum and entered into English in the 16th century. This raises another issue, the history section in this article claims per centum is a pseudo-Latin phrase, yet Wiktionary and several non-wiki online dictionaries seem to claim otherwise. Where does the information on per centum in the article come from?Scotty Zebulon (talk) 22:48, 22 November 2008 (UTC)

Comment removed from page

to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%). —Preceding unsigned comment added by 220.237.149.57 (talk) 03:19, 20 February 2009 (UTC) . Percent is also used to talk about goods scores and points

100%

100% is the total and it is always wrong to express a percentage greater than this or to use a calculation that will yield greater than 1(00%). Per Cent means per 100 and anything greater is wrong, it is a mathematical term for a ratio calculation where the largest value is always the total (100%).

"Percentages larger than 100 can be meant literally (such as "a family must earn at least 125% over the poverty line to sponsor a spouse visa")."

is exactly the kind of statement that is quite wrong and also utterly misleading, what does this mean - poverty line + 25% or poverty line + 125% (which is what it actually states)?

If you invest 100 dollars, euros, or whatever and get 200 back then the growth is 50% (100 / 200) since of the new total 200 half (i.e. 100) was your original investment and not part of the growth. If a company has 100 dollars / euros turnover and some years later this has risen to 1,000 then the growth is 90% (900/1000). You could also say ten fold growth but percentage should never exceed 100 by definition. DesmondW (talk) 16:50, 19 March 2010 (UTC)

The section "comment removed from page" above answers your question. "Percentage should never exceed 100" is wrong, both in common usage (which you can argue), and in mathematical usage (which you should not). — Arthur Rubin (talk) 13:50, 21 March 2010 (UTC)

And I've removed the example you're referring to as misleading. — Arthur Rubin (talk) 13:57, 21 March 2010 (UTC)

Proportion

The anon may not have had a good reason for deleting the section, but I do. The example "125% over the poverty line" is just wrong, even in common usage; it would be "125% of the poverty line". "125% over the poverty line" means "225% of the poverty line". The remaining valid sentence might be moved to the lede, but it doesn't deserve it's own section. — Arthur Rubin (talk) 13:56, 21 March 2010 (UTC)

100% (2)

An overzealous wiki administrator improperly removed my previous talk submission and I hope that he will have the courtesy to leave this one.
In standard ratio calculations 100% always represents the total and so no percentile should ever be properly expressed as greater than 100%
Taking the simpler case of reducing values, a value that reduces from 1,000 to 500 would be expressed as 50% reduction (1,000 - 500)/1,000 = .5 (50%). If the value reduces to zero then the calculation is (1,000 - 0)/1,000 = 1 (100%). This is common sense and surely beyond dispute.
Since no reduction can properly be expressed as greater than 100% it follows that no increase should ever be properly expressed as greater than 100%.
To complete a previous example, a value that reduces from 1,000 to 100 has reduced by 90% (1,000 - 100)/1,000 and if this value returns to 1,000 the percentile growth logically must be the same i.e. (1,000 - 100)/1,000 = .9 (90%)
Common usage of percentiles use growth calculations based on the lower total to give a larger apparent value, such as 100 increasing to 150 being described as "50% increase" but properly this is (150 - 100)/150 = .333 (33 1/3%) increase. The article should discuss both types of calculation and differentiate between true percentiles and common usage.
Common usage will often state "125%" or similar and the meaning may be understood but the article should differentiate between this and proper calculation.
When talking abount increasing values it is both better and correct to avoid percentiles completely and talk about "x fold growth" as appropriate.DesmondW ([[User talk
Oh, and by the way, these are not just random ideas. I am a computer programmer and business consultant to multinational companies and I teach them how to calculate precentiles.DesmondW|talk]]) 16:12, 21 March 2010 (UTC)

I restored your rant and replied, above. It might be preferable if things were done the way you specified, but that's not how it is done, either in common usage, or in mathematics. — Arthur Rubin (talk) 16:20, 21 March 2010 (UTC)

Perhaps you accurately describe what you recommend to the companies you consult for, but not in the real world or in real mathematics. — Arthur Rubin (talk) 06:25, 22 March 2010 (UTC)

See this article for more information on gross percentiles http://en.wikipedia.org/wiki/Gross_margin DesmondW (talk) 11:45, 24 March 2010 (UTC)

So, they're both percentages. It's just that the margin percentage and the markup percentage are not the same. — Arthur Rubin (talk) 16:25, 24 March 2010 (UTC)

OK, now we progress. Let me give a very simple example. If I buy three white cups today I have a collection of three cups or 100%. Tomorrow I buy three blue cups and have a collection of three white and three blue cups, 100% which is the total collection
What is the percentage of blue cups? Obviously 3/6 = 50% and surely nobody could disagree with this deliberately simple example.
What is the percentage of growth from day 1 to day 2? The blue cups are the new growth and we have already established their percentage of 50%; simple logical and common sense. Any other answer is misleading at best.DesmondW (talk) 12:40, 4 April 2010 (UTC)

Absolutely wrong. The increase is 100% of the amount before the increase, so the growth is 100%. Any other answer is misleading, at best. — Arthur Rubin (talk) 15:20, 4 April 2010 (UTC)

Nonsense! Once again:
Day 1: 3 new white cups
- Collection 3 cups = 100%
- Growth from start (3 cups) = 100%
Day 2: 3 white cups from day 1 + 3 new blue cups
- Collection 6 cups = 100%
- Growth from start (6 cups) = 100%
- Growth from day 1 (3 blue cups) = 50%
It's common sense!!!!!!!!!!DesmondW (talk) 16:02, 4 April 2010 (UTC)

Nope. Even if it were common sense (which I dispute), it's not useful mathematically. In your notation, the formula for percentage gain is

${\frac {new-old}{new}},$

while the formuls for a percentage loss is

${\frac {old-new}{old}}.$

Those don't combine easily. — Arthur Rubin (talk) 18:26, 4 April 2010 (UTC)

With standard notation, a x% gain and a y% loss combine as:

$z=(1+x\%)(1-y\%)-1$, converted to percentage, as a gain or loss. With your notation, the formulas are different for a gain or loss. With your notation, one would calculate

$R={\frac {1-y\%}{1-x\%}},$

If a gain (R > 1), the gain is:

$1-{\frac {1}{R}}.$ converted to a percentage.

If a loss (R < 1), the loss is:

$1-R\,,$ converted to a percentage.

— Arthur Rubin (talk) 18:32, 4 April 2010 (UTC)

Relevant references, and relevant use of percentage

A student of mine had an experimental report with a table that illustrated different changes in temperatures, and in the rightmost column he expressed the change in percent relatively to an initial temperature. I asked him to change units from °C (Celsius) to K (Kelvin), on reference and table, then he also altered his conclusions; the temperature changes went from being "incredible" to "insignificant" :) —Preceding unsigned comment added by 194.132.104.253 (talk) 15:28, 9 June 2010 (UTC)

As a former math teacher I have a major comment about this article and much of the discussion. That is: a number followed by (or preceded by, as in some cultures) the % is a "percent", not a "percentage". The use of "percentage" in place of "percent" is a pervasive error, committed by some professional mathematicians and by many (probably most) laymen.

The word "percent" means "parts out of 100". The operation of calculating a percent allows us to compare two numbers as though we started with 100 objects.

A specific example: I had 50 oranges to sell. 40 of them were sold. What percent of my original stock was sold?

There are a couple of ways to determine the answer.

Since we are considering an equivalence of 100 items as our starting value, we can multiply the 50 by 2 to obtain 100, and since we have multiplied the 50 by 2, the 40 must be multiplied by 2 also, giving us 80. So our answer is an equivalence of 80 out of 100, or 80%.

But if we began with 153 oranges, determining and using the multiplier (0.0065 rounded) becomes a little more involved (I know, with a calculator it is as easy as pi). So we will use a different approach to determine the percent: dividing the number of oranges sold, 40, by the original number of oranges, 50. 40/50 = 0.8. A conversion to percent is made by multiplying the 0.8 by 100, which results in 80, to which we append the %. So we have sold 80% of the oranges, the same value as in the first solution.

The value that is the basis of the comparison, 50, is called the "base" and the value being compared to the base, 40, is labeled "percentage". The base and the percentage always have the same units of measure and the percent is a dimensionless, or pure, number.

Depending on the specific situation, percent values may be positive or negative and less than or greater than 100.

For some situations 100% is the maximum value. Sometimes a bit of hyperbole is used, for example when a coach, commenting on the output of one of the players, says "That boy gave 120% today." It is impossible to give more than is available, or 100%. The player gave more today than he has given before, because he was dogging it in prior days and the coach told him “Produce or you are off the team.”

It is possible to have percent values greater than 100. When I began teaching, in 1955, my annual salary was $2850. As I continued teaching my salary increased. Somewhere along the way it became $5700. The increase was $5700 - $2850 = 2850, or 100%, and the new salary to the old salary was $5700/$2850 = 2, converted to % = 200%. Let's suppose that my salary a number of years later was $28500. My new salary was 10 times as great as my old salary. The percent of my new salary, compared to my original, was 1000%.

Negatives percents have occurred quite frequently of late. A couple of years ago my house had a value, according to Zillow, of $160,000. It is down to $120,000. It has lost $40,000 of value, which is 25% of the earlier value. That is a loss, so it is a negative change of value, making the change -25%.

One additional comment about %. Most of the time we encounter % values that are given in integer form. But a % may have a decimal component or be a decimal. Consider the 153 oranges of earlier. Suppose only 1 orange was sold. The % sold was 1/153(100) = 0.0065(100) = 0.65%. That looks like the APR for my savings account.

Percentile is a type of percent operation that differe from a general percent. It indicates the position rank of an object, A, such as the score a person has on a test, or the height or weight of a plant, etc. Informally, it shows what percent of the objects are below the position of object A. Therefore, a %ile value is always < 100.

As I stated at the beginning, the error is pervasive, and I have not been able to determine how it came to be. I suspect it was due to people not understanding the distinction between the words “percent” and “percentage” and it was like Topsy, who "just growed".

Most of the sites I have visited trying to get documentation simply repeat the error. One site I found that does not repeat the error is http://www.math.com/school/subject1/lessons/S1U1L7GL.html#sm4. I will continue to look, and if I find more I will post the information here. 66.177.36.107 (talk) 01:15, 10 July 2010 (UTC)

Thanks

I just want to say who ever wrote this article good job it was very helpful and well thought out I appreciate it very much thanks urName (talk) 06:02, 21 August 2010 (UTC)

Inconsistent usage of percentage system

For clarification reasons, I think it might be worth giving an example of the inconsistent usage of percentage addition by common calculators.

• Google, or Excel:

50 + 10% = 50 + (10/100) = 50.1

• Soulver (Mac), or Microsoft Calculator (Win7):

50 + 10% = 50 + (50*10/100) = 55

Interestingly, unlike the others, Microsoft calculator does this for multiplication:
50 * 10% = 50 * (50*10/100) = 250

The other calcs result in 5. Enough to drive a logician crazy ;) I think the only long-term solution for mankind would be to define new operators to suit all occasions (or at least get everyone away from percentages and learn that adding 10% is like multiplying by 1.1) --Skytopia (talk) 23:45, 2 July 2011 (UTC)

Expressing Steepness in Percent

The article mentions that steepness is expressed in percent on road signs. (begin of quote) As "percent" it is used to describe the steepness of the slope of a road or railway. Where 100% is a 90 degree angle straight up and down. 5-15% can be found on some mountain range roads with over 20% being very steep. (end of quote) Well, this is not the case here in germany: 100% is a 45 degree angle. The rule is: the number given in percent expresses how many meters of height difference are made for every 100 meters horizontally (ewm...you got what I mean, right?). So maybe this is either handled differently in the english speaking world or an error in the text. As I don't know it I leave this one for a native speaker to solve. Thanks. 81.173.207.140 (talk) 13:01, 23 January 2012 (UTC)

Yes, grade (slope) is measured that way in American English that I know. Our linked article says that and adds that percent(age) is the most common unit of grade:Grade (slope)#Expression nomenclature, points 2 and 4 and the following paragraph. [There we specify "percentage grade" but I understand "percent grade" to be the common unit.]

Evidently this has been corrected here but it's the last paragraph in the article, oddly combined with a sporting ;-) mis-use of "percentage" in the section "Other uses", where it follows a list of cross-references to grade among other articles. The combination, heading, and placement are all questionable.

I would use and expect "grade" rather than "slope" regarding train, car, carrige, bike, or walking trail; or terrain without any trail. --but "slope of grain" rather than alliterative "grade of grain" in a piece of wood. --P64 (talk) 15:34, 12 June 2012 (UTC)

Our Lumber#Grades and standards neither links nor defines terms and merely lists "slope of grain" among qualities that bear on grade of lumber (grade in a different sense). It says nothing quantitative about any slope and any grade --such as "high grade is less than 5% slope". --P64 (talk) 15:40, 12 June 2012 (UTC)

10 is to 100 as 5 is to ????? — Preceding unsigned comment added by 203.118.167.239 (talk) 13:09, 31 August 2012 (UTC)

Percentages

Since it doesn't say anything in the article about this question, here is as follows. When talkng about % one could say; There is a town in Engand, there are 4000 people unemployed. This represents almost a quarter of the total working population. If the qustion was asked, is 5% jobless, could one say yes? As 5% falls in the 25% (quarter) that is described. This question was on an official exam in my country and currently everyone disagrees with each other if its a correct answer or not (it was a foreign language (english) exam).

Negative Percentages

Hello everybody. Could you please tell me which version is correct for a negative percentage? For a decrease of 20%: (20)% or (20%)? I would prefer the latter as % is not an unit. Thank you. 136.8.33.71 (talk) 12:36, 2 January 2015 (UTC)

No heading

I am surprised that no one at Wikipedia has seen this problem.

Percentages are a comparison of two variables. It is possible for one to have a container that contains 40% alcohol however it is not possible to have a container with 113% alcohol. The reason for this is obvious, that is the two variables are "alcohol" and "no alcohol" and when we get to 100% alcohol we no longer have a percentage of alcohol for the 100% figure has meaning only in the prospect of "no alcohol". This is true for all percentages no matter what the material or condition that is being compared. The prospect of comparison is not comparison and percentages are a comparison as are all rates.

I understand that percentages are a fraction, as the article says, however they can never be a compound fraction for when ever the comparison gets to the unit then it is no longer a comparison. The prospect of comparison is not comparison but a 3rd variable and you are only allowed two variables in percentages. It is a common mistake (not always a mistake but sometimes a scam) to add words to a comparison like "next" thinking that the word "next" is not a variable but it is a variable based in time. Any time you are presented with a "percentage" that is over 100% the person who generated it has included a third variable for if they had not done that the values it represents would have been included in the values of the initial percentage. Look for the third variable and you will find the fraud.

It is too bad that Wikipedia has indulged in truthiness in this article for we have enough teaches indulging in this lie.

I have taken the liberty to move your comment to the end as is the custom on Wikipedia talk pages. I am sorry to hear that my investments can never grow to more than 100% of their current value ... perhaps I should consider a different broker. In any event, we only report on what is available in reliable secondary sources, so if you can find your point of view written in a reliable secondary source we can consider it. Bill Cherowitzo (talk) 04:38, 14 April 2016 (UTC)

Percentages can not have fractional parts - look at the Math

Percentages are a rate and nothing more. Percentages are a rate constructed out of two dependent variables and only two dependent variables. Dependent variables are as a coin toss in that you have one or the other, either heads or tails, dead or alive, alcohol or non-alcohol. When one says "per 100" one has limited the number to 100 units and because of the dependent variables their are no fractional parts to percentages. This is the same as saying "10 chances in 100" for their are no fractional parts in "chances" either. Percentages can be expressed as a fraction but not as either a complex or a compound fraction. It is understood that if you describe percentages as a fraction of 10/100 then you also have a fraction of 90/100.

Percentages are descriptive of data. They can not be add, subtracted, divided or multiplied. One can not average percentages. The only way the description can be changed is if the data is changed.

Lets take an example of two containers of alcohol. One container has 10% alcohol in it and the other 90% alcohol in it. If we mix the two containers together can one know the percentage of alcohol in the mixed container? The answer is clearly "no" for we must know the size of the containers. One container could be a cup the other a 55 gallon drum. The only case where you might suggest it possible is if the containers are the same size which one would have to know. One must work from the data which is always the case with percentages.

Their are only 99 percentages. The reason for this is two fold. one: One can not have fractional parts to percentages. two: 0% has the same value as 100%.

Both 0% and 100% do not have two dependent variables so they are not a rate and percentages are only a rate at least until they change the meaning of the word "Per".

The assertion bellow from this article is wrong, wrong, wrong. Many things are "common" but they have nothing to do with Math.

"percentage values may often be limited to lie between 0 and 100, there is no mathematical restriction and percentages may take on other values.[2] For example, it is common to refer to 111% or −35%, especially for percent changes and comparisons."

As it was said in the movie "The Producers" "you can never have anything more then 100 percent". That is Math — Preceding unsigned comment added by Mwdar (talk • contribs) 02:05, 1 October 2016 (UTC)

Percentages are Binaries

Percentages are like Bits, that is they are binaries. You have either 0 or 1 in bits and you have in percentages either dead or alive, head or tails, part alcohol or part non alcohol. When ever you create a rate following per by only a number then you are creating an "either or situation" which means it is a binary. A rate must have only two variables and when you have only a number after the per you have an implied second variable that is the opposite of the first variable.

One can not have a fraction of a binary. When one stipulates a number of unites like 100 then one is restricted to 100 unites. If one wishes to create a binary of 110 unites then one must stipulate 110 unites.

You can not average percentages which means you can not add, subtract, multiply or divide percentages.

You can only have a maximum of 99% for 100% and 0% are the same value in that you no longer have two variables. 100% alcohol is 0% non alcohol.

It is a indictment of our educational system in the US that so many people provide such erroneous information about percentages as this "talk back" attests too. — Preceding unsigned comment added by Mwdar (talk • contribs) 20:50, 27 August 2017 (UTC)

Comments such as this are binaries, like trash. Either you can keep them around to smell up the house or you can toss them to get some clean air. Wikipedia policy says that I should be civil and not taunt an obviously confused individual for making some totally inane remarks, but I can not just stand by and let any innocents believe that there is any value in this malarkey. I could have just tossed this out as it has no connection to improving this page, nor any connection to reality, but I'm afraid that this editor will just come back yet again (this is his fourth attempt) with his trash, so maybe another tact may be in order.--Bill Cherowitzo (talk) 22:30, 27 August 2017 (UTC)

Percent is Per in cent

This item wrongly states "a percentage is a number or ratio expressed as a fraction of 100."

A ratio requires two variables for as a fraction has two parts so do rates have two variables. Percentages are a rate in 100 unites and not per 100 unites.

One must know the difference between "10 percent alcohol" and "10 parts alcohol per 90 parts alcohol" for if one states 10% one has created a rate of "10 parts per 90 Parts" by the fact that 10+90=100. The first assertion is "10 parts in 100 parts" while the second assertion is "10 parts per 90 parts" and the two assertions are not the same though the values are seen by many as the same. In the first one you assert only one variable so the second variable is implicit while in the second one you assert two variables. If I say 10% alcohol then I have in 100 unites either "alcohol" or "non-alcohol" which is a binary having 100 unites.

If I say 10% are sick I am asserting more then a rate. I am asserting a rate in 100 unites. The two variables of the rate are "sick", the explicit variable, and "well", the implicit variable, in 100 unites. If I mix a solution of "10 parts alcohol per 100 parts non-alcohol" then I have 110 parts in the solution and this is a rate of "10 per 100". If I limit the rate to 100 parts and I assert only one variably the other variable must be implicit and I their for have created a binary. Their are no fractional parts to a binary. Percentages are binaries because they express only one variable.

Simple example concerning 100 units. If one has a pie and cuts it into 100 parts then one cuts one of those parts in half then one no longer has 100 parts in the pie thus it is with percentages for they can have only 100 parts. I also ask people to mix for me a 10.1% solution of alcohol given only a 100 parts, for it can not be done.

Percentages can not be averaged. Percentages can not have fractional parts. Percentages have only 99 unites for they are a rate which requires two variables and at 100% you have only one variable. Percentages are correctly stated as Per in 100 parts.

Marshall D'Arcy (mwda) — Preceding unsigned comment added by Mwdar (talk • contribs) 02:33, 20 January 2019 (UTC)

Wikipedia requires the use of reliable secondary sources to verify its material. In order to even discuss the above sillyness, you would have to find such sources. --Bill Cherowitzo (talk) 06:38, 20 January 2019 (UTC)

12-4.19 is what persentag — Preceding unsigned comment added by Nayeem kabir (talk • contribs) 19:27, 2 April 2019 (UTC)

Example 2

Hello, in example 2 the result off 0.06 is suddenly 6%. The obvious explanation, to multiply 0.06 with 100, is actualy forgotten to explain in this example for which the example is not complete. quote 'by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is a 6% increase. ' is more clear as 'by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage and after multiplying with 100, this is a 6% increase.' or 'by a fraction of 0.15/2.50 = 0.06. After multiplying with 100 it will be expressed as a percentage, this is a 6% increase.' My examples are not the best english, true, but you do forget to mention it in the EXAMPLE...cb 85.149.83.125 (talk) 15:24, 2 August 2019 (UTC)

Wrong for Percentages are Binaries and can not be expressed as fractions

I have posted many times but it seems that no one can understand the obvious when it comes to percentages.

Percentages are a "ratio expressed as a fraction of 100" is a wrong statement.

Ratios are not fractions and can not be expressed as fractions. Ratios are an equivalency or they are like an equation. One is saying if "this is" then "that is". If one says 10% are dead then one is also saying 90% are alive or 10 people dead per 90 people alive, that is if we have 10 dead people then we also have 90 alive people. That is, one has either dead or alive in 100 unites, which is a binary. Ratios using "dependent variables" not "independent variables" must be binaries. One must have two variables and only two variables in a rate. If one expresses one self in terms of percentages one has asserted only one variable which means the second variable must be opposite the asserted variable creating either/or, which is a binary.

Example:

Let us say that we have invested $100 and got a 50% return.

I then ask "how much did we get back"?

The first thing that most do is say to themselves what is 50% "OF" $100 in other words they see the problem as a fraction of 50/100. The problem with this is that "of" is not "per" or rates are not fractions.

The rate at 50% is 50 Per 50 for a ratio of 1 to 1. A 50% return on a $100 investment would then be $100.

Rates are not fractions and any one in Mathematics should know this. "Of" is not "Per"

The person or persons who wrote this article in Wikipedia is wrong, wrong and wrong.

Marshall D'Arcy 9/26/20 — Preceding unsigned comment added by Mwdar (talk • contribs) 20:31, 26 September 2020 (UTC)

Mathematics and Pie

One of the greatest rules in Mathematics of all the rules in Mathematics is, put simply, that if you are concerned with the relationship of pieces in a pie you must have a pie. So many person are unaware of this rule and even refuse to consider it in their mathematical calculations.

Let us consider percentages. We should all know that percentages are like a pie with 100 pieces which of course means that one must have a pie. The first thing to look at when considering percentages is “where is the pie“. You would think that this is obvious but the way people operate is never obvious.

If one says 10% of the people are sick then I first must ask “where is the pie“. Some one might suggest that the pie is all the people in the town of “This and That“. I would think that now we have a pie called all the people living in the town of “This and That” so that I can not only know how many are sick but how many are well.

OK this is obvious one might suggest so I will now ask the question “what is a 50% “return” on a $100 “investment““. Most will say $50 however they never think to ask “where is the pie”. One should see that there is no pie in this assertion. One might suggest that the $100 is the pie however what then does one do with the “return“. Clearly the “return” is not part of the “investment“ so it can not be part of the pie. The truth is that “return” on “investment” are “independent variables” in a rate, that is they are like “miles per gallon” and can fluctuate independently of each other. Percentages are “dependent variables“ and percentages has to have a pie.

In this example one can only ask “if I have $100 and of that money 50% is a return” then one could say that the return is equal to $50 for the pie is now $100.

EVERY TIME YOU SEE A PERCENTAGE ONE MUST ASK “WHERE IS THE PIE“.

Marshall W. D'Arcy — Preceding unsigned comment added by Mwdar (talk • contribs) 21:54, 31 October 2020 (UTC)

Semi-protected edit request on 12 February 2021

The fractions appear to be incorrectly formatted, a bug with "[[]]" and sfrac. For example, for 45%, instead of 45 (numerator) appearing above the line over 100 (denominator), it appears over a "/"

Please change "⁠45/100⁠" to "45⁄100" until the conflict between "[[]]" and sfrac is resolved.

Please also change all "sfrac" to "frac" within the pre-set formatting language here for now. Ceratopseer (talk) 19:33, 12 February 2021 (UTC)

 Done. I'll leave the other sfrac templates in for now though as they're much more readable than frac and it doesn't seem broken with out the original conflict. Volteer1 (talk) 01:33, 13 February 2021 (UTC)

Actually, there's a better (but very clunky) workaround that I've placed there now that should fix the problem for now. Volteer1 (talk) 02:40, 13 February 2021 (UTC)

Well done all of you

Dunn et al (2021). The paper is behind a paywall. Someone should nominate this article at https://en.wikipedia.org/wiki/Wikipedia:Good_article_nominations Chidgk1 (talk) 19:53, 8 January 2022 (UTC)

History of percentage

tgd 27.63.60.203 (talk) 13:07, 29 December 2022 (UTC)

how

t 74.101.120.202 (talk) 01:59, 28 February 2023 (UTC)

"Podozreetelynaya tube" - nazыvayetza ..

Например телескоп Хаббла .. с которой стороны смотреть на инфляцию и на пенсию ?

Со стартового стола !! )))

🧐🤸 85.140.9.142 (talk) 07:26, 15 August 2023 (UTC)

Semi-protected edit request on 17 February 2024

Add a link to an online percentage calculator (e.g. https://percentage-calculator.app) Tomek rr84 (talk) 16:30, 17 February 2024 (UTC)

 Not done: If we do that, then people will come and fight over whether this or that website should be included. QuietCicada chirp 16:33, 17 February 2024 (UTC)