Talk:Decimal/Archive 2

Sinocentrism and how one can miss the subject completely


It was fun for a while, but now the section Decimal has gone too far down the gutter for the mess there to be longer ignored. There are two interrelated problems The historical truth is that many ancient cultures had a base ten number system ( http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Egyptian_numerals.html ): The first were clearly the Egyptians, and later also came the Greeks and Romans. The great exception were the Babylonians who used instead base 60, but, in using this, they were the first to use the positional notation centuries before anyone else.
 * 1) Sinocentrism: The main author, Gisling, shifts as much focus as possible to the Chinese side, effectively appropiating the Hindu-Numeral number system as a Chinese contribution. But this is an extreme minority view which needs major readjustment.
 * 2) In his attempt to overblow the Chinese achievement, however, he moves farther and farther away from the actual topic of the article which is the decimal system, that is number systems based on units of 10 — not necessarily the positional notation which can, and historically was, used with any number base (the Sumerians used base 60).

The traditional Chinese number system, by contrast, did not have a positional notation until they adopted the Hindu-Numeral number system. Heck, even today the traditional Chinese characters are not positional! The use of these rods in Han times was restricted to the merchant class, eventually died out and therefore should be given due, that is much less weight in the article. Preferably, it would be best to limit coverage of positional systems to a minimum and concentrate instead on the actual subject, number systems with base ten. Gun Powder Ma (talk) 01:18, 23 June 2011 (UTC)
 * Complete rubish, without any reliable sources, article from web does not count as scholary nor credible. You must provide reliable sources for your unfounded claim, such as "The traditional Chinese number system, by contrast, did not have a positional notation until they adopted the Hindu-Numeral number system" is complete rubish, exposing the complete ignorant of User:Gunpowder Ma]] of basic history. Joseph Needham pointed out long ago, that Shang numeral ( 13 century BC) is a place value system, and more advanced than contemporary Babylonian and Egypt. Gisling (talk) 08:59, 23 June 2011 (UTC).
 * Your assertion that traditional Chinese numerals are positional is plainly wrong and can be disproven with a glance: Not even today 十 (10), 百 (100) and 千 (1000) are positional, but represented by a single symbol, as the linked Wikipedia article also amply shows. For being positional they would have needed one, two, three digits respectively. I removed the claim. Obviously you don't have the faintest idea of what you are talking about and neither know Chinese nor what positional and decimal systems actually are. Gun Powder Ma (talk) 10:11, 23 June 2011 (UTC)

You are clearly ignorant of what the Chinese written numerals are all about. It is common knowledge, that the the characters 十，百，千，万,亿   are power of ten markers, and easily correlated with posititional system. See Joseph Dauben Chinese Mathematics in p190 of The Mathematics of Egypt Mesopotamia, China and Islam, A Source Book.

The written Chinese symbol is a subset of place value decimal system, called dipositional decimal system by Jean Claud Martzloff. You don't have the faintest idea what Chinese numerals is.

"neither know Chinese " Uh ? I am a ChiefEditor 维基执行主编 of zh.wikipedia.org, written over 500 articles, where is your contribution in zh.wiki ? I doubt you even know how to read ancient Chinese mathmatic classics.-- Gisling (talk) 10:36, 23 June 2011 (UTC).


 * "... easily correlated with positional system" does not mean "is a positional system" or even that the Chinese had the concept of a positional system. You'll have to do better than that to include that Chinese system in the "positional" section.  I can't speak as to whether you know Chinese, but I know mathematics, and a "dipositional system" is not a positional system.  — Arthur Rubin  (talk) 10:52, 23 June 2011 (UTC)
 * For example, take the number 201. If it were to be represented (2) (100) (1), that would not be even a dipositional system.  If it were (2) (100) (0) (10) (1), that might qualify as "dipositional", but it's not positional unless (0) (10) (2) (100) (1) were invalid.  — Arthur Rubin  (talk) 10:54, 23 June 2011 (UTC)
 * Arthur, please check out Chinese numerals. A glance will tell you that this number system is not positional (e.g. the numerals for 10, 100, 1000 are represented by a single character, not by two, three or four respectively). It is as plain and obvious as the pyramids not being cubes. Gun Powder Ma (talk) 11:14, 23 June 2011 (UTC)
 * Gisling, you are beginning to edit-war, you have restored an assertion which must be plainly wrong. The Chinese numerals are not positional, neither in Shang times nor those of today which are nothing but a direct continuation. Gun Powder Ma (talk) 11:03, 23 June 2011 (UTC)


 * Joseph Needham said so --Gisling (talk) 11:06, 23 June 2011 (UTC).
 * I know he is the champion of sinocentrism, but like us all, he is only a mere mortal, I am afraid. Could you quote extensively from him, not just the conclusion, but the whole argument? Gun Powder Ma (talk) 11:09, 23 June 2011 (UTC)

for calculation, and that IS the world's earliest positional decimal system, far earlier than any civilization on earth, can any one deny that. And that is the one system one should concentrate on, not the written character. --Gisling (talk) 11:10, 23 June 2011 (UTC).
 * I must stress here, the written Chinese numbers was strictly for written record, not for calculation. The Chinese use counting rods
 * So you concede the obvious point that the Chinese numerals are not positional? Yes, the Han Chinese counting rods were positional, although they were not the first positional system which were the Babylonian numerals. The rods may qualify as the first decimal positional system, but their use was restricted to merchants, to market transactions in the Han period. Right now, the history section hugely overblows their importance, even in China itself the overwhelmingly used number system remained the traditional, non-positional Chinese numerals. Gun Powder Ma (talk) 11:20, 23 June 2011 (UTC)


 * Again, you exposed your total ignorance on counting rods. "but their use was restricted to merchants, to market transactions in the Han period" What complete rubish.  The Chinese history of mathematics, from  The Nine Chapters on the Mathematical Art (九章算术) to Tang dyansty 算经十书 to Mathematical Treatise in Nine Sections(数书九章) of Song dynasty andCeyuan haijing( 测圆海镜),Yigu yanduan(益古演段）， Jade Mirror of the Four Unknowns(四元玉鉴) OF yuan dynasty are all base on Rod calculus. In short the history of counting rod IS the core of Chinese mathematics. What " but their use was restricted to merchants, to market transactions in the Han period", you are simply a laughing stock.

What Han dynasty merchant ?? --Gisling (talk) 12:36, 23 June 2011 (UTC).


 * Without counting rod numeral system, there would be no decimal multiplication, decimal divsion, decimal linear equations, no decimal higher equations in China, these decimal computation algorhtims were transmitted to the middle east in 9th century via India. Without couting rod positional decimal system, there would be no arithematics and algebra we know today. It is utmost important in world mathematic history. The positionl decimal system of counting rod, is one of the greatest Chinese invention, and its influence in the world is paramount --Gisling (talk) 12:50, 23 June 2011 (UTC).


 * That is an assertion that would require a very good reference. And AFAIK you have not shown that rods date to the Shang dynasty, and even if you did, that they were the first. As well as that being rather beside the point for this article.


 * AFAIK, the rod system is only attested to the 2nd c. BCE, though of course it could be older. I don't know if a space was left for zero as it was later; only in the 8th c. CE was a numeral for zero introduced, presumably from India.


 * BTW, the traditional Chinese system can be used as a positional system, with a written zero and 十百千万 being equivalent to spaces/commas in the Hindu-Arabic system, and I have seen them used that way, but AFAIK such usage is not ancient. — kwami (talk) 14:14, 23 June 2011 (UTC)


 * These rods played no role in the world history of mathematics and no transfer to other cultures is recorded. They were not even widespread in China where people continued to use the non-positional Chinese numerals. Gun Powder Ma (talk) 19:29, 23 June 2011 (UTC)

to represent zero. It is obvious, as subtract 5 from 5 left physical emptiness. Further, a major difference of Chinese positional decimal counting rod numerals is its physical dependence on position. 5 [] 6 1 multiplied by 10 becomes 5 [] 6 1 [], and it was done PHYSICALLY not by appending empty space [], as the Indian numeral does, but rather move the whole batch of counting rod numerals PHYSICALLY one space left. Similarily, 5 [] 6 1 divided by 10 was performed by PHYSICALLY move the batches of rods right one space, and becomes 5 [] 6. Indian numerals is a WRITTEN system, shifting right/ shifting right makes no sense in Indian numbers. In this sense rod numeral system is more positional than Indian numerals of after 7th century. The numeral system of India used 9 symbols, also used a space to represent zero. (See George Ifrah). You are quite correct, the numbers 十百千万 are markers, like 1000,000,000,000,000. But the Chinese written system was never used for computation in mathematics or astronomy. They used a bag of counting rods, just like Ming dynasty merchant/mathematician used abacus, which by the way used 9 symbols and a space to denote number of any size. They stuck 个十百千万 on the abacus for markers.
 * AFAIK, the rod numeral system dated back to the Spring and Autumn period. And and a space was indeed left on the counting board

The mention of Shang dynasty oracle bone numerals is only for the purpose to trace the origin of positional decimal system in China, ie, it was home grown and rooted in ancient civilzation. This is in contrast to Indian Kharosthi or Brahmi numerals were all non positional, hence that the postulation that positional decimal system originated in India becomes dubius. EVen Indian scholars on mathematics in India has doubt that positional decimal system originated in India --Gisling (talk) 17:30, 23 June 2011 (UTC).

--Gisling (talk) 17:30, 23 June 2011 (UTC).


 * That makes no sense at all. — kwami (talk) 18:03, 23 June 2011 (UTC)


 * Is the counting board system, itself, a "positional decimal system"? The "rod numerals" appear not to have actually been used, according to your sources, before the "0" was imported from India.  — Arthur Rubin  (talk) 17:40, 23 June 2011 (UTC)


 * Yes, it was. It was a bit awkward as a positional system if not written on a grid, because it was difficult to tell how many zeros there were with inline text, especially if they were at the end of the number. It was therefore sometimes augmented with the higher-order numerals from the oral (traditional) system. But AFAIK it was primarily used by mathematicians, and they would write on a grid so all the zeros were unambiguous. Of course, once a written zero was introduced, the system became much more practical.
 * The system was also used for decimal fractions, but I don't know if that was done before the intro of the zero. Probably, as it was modeled after the abacus. — kwami (talk) 18:00, 23 June 2011 (UTC)


 * If you really wants to understand counting rod numerals, counting rods, Rod calculus and Principles of Hindu Reckoning is good place to start. If you don't understand rod numerals, which was widely used in China, Korea and Japan, how can you say you understand history of mathematics ?? I don't see you have made any contribution to these topics.--Gisling (talk) 18:26, 23 June 2011 (UTC).


 * This is not the place for dubious claims about positional notation, which is not the topic of this article. I've moved the huge and out-of-place claims about Chinese origins to a section below. — kwami (talk) 21:59, 23 June 2011 (UTC)


 * I shall moved it to a new article when I have time --Gisling (talk) 12:15, 24 June 2011 (UTC).

Is wikipedia articles reliable source ??
User:Gun Powder Ma relied on the web and a STARTED CLASS wikipedia as reason for his massive disruptive deletion of other people's article in a B class article, quite ridiculus.

In my opinion, unless a wiki article achieve feature article or good article status, it is not counted as  "reliable source''. Even if a feature article, still there is danger of self referencing.  --Gisling (talk) 19:52, 23 June 2011 (UTC).
 * Please stop, Gisling. You say you were Chinese and yet you evidently don't know the Chinese numerals. What you are doing is calling the pyramids square, the link to the WP article should only serve for users to have a look themselves. So tell me how can 十 (10), 百 (100) and 千 (1000) be positional? How? Gun Powder Ma (talk) 20:01, 23 June 2011 (UTC)

scholar books on history of Chinese mathematics.
 * Pity, you depend on incomplete article for basis of your counter claim, apparently you have never seriously read any English nor Chinese

I added two sourly missed sections Shang oracle numerals and Rod numerals to Chinese numerals. --11:39, 24 June 2011 (UTC).
 * You realize that you evade a very simple question. So please, again, tell us how can 十 (10), 百 (100) and 千 (1000) be positional? Gun Powder Ma (talk) 11:46, 24 June 2011 (UTC)


 * Aparently you don't even bother to read other people's opinion on this matter. kwami has already answer this question--Gisling (talk) 12:17, 24 June 2011 (UTC).
 * So far all I've read from you are various Ad hominem attacks ("you don't understand mathematics", "you say you're Chinese but you don't understand Chinese numbers"), Argument from authority comments ("I've made X edits on ZH Wiki, what have you done?"), and things that are completely irrelevant ("the article is start-class, therefore it is wrong and I am right"). I don't mean to be a prick, but would you be able to engage in better discussion with others by taking into account what people are saying, and making sound, logical arguments, as opposed to all the things you've done so far? It's very difficult to follow what your train of thought is. --  李博杰   &#124; —Talk contribs email 13:05, 24 June 2011 (UTC)

Copy & pasting contentious claims
On another note, Gisling, please do not copy and paste contentious material from this page to another without prior discussion here. Gun Powder Ma (talk) 11:50, 24 June 2011 (UTC)


 * No such thing. If some material here "is considered" out of topic, then move to another new on topic article is the only right thing to do--Gisling (talk) 12:20, 24 June 2011 (UTC).
 * On second thought, move to Google Knol and start a new article with sole authorship probably is a better thing to do---Gisling (talk) 12:42, 24 June 2011 (UTC).
 * Um, sorry? That does not make it any less contentious. If content is not accepted here, it isn't a good idea to put it somewhere else on a separate Wikipedia article either. --  李博杰   &#124; —Talk contribs email 12:49, 24 June 2011 (UTC)
 * I am moving some material over to knol---Gisling (talk) 11:44, 25 June 2011 (UTC).
 * I deleted so called "off topic" history section, from anti expert wikipedia, and posted to Google knol--Gisling (talk) 11:49, 25 June 2011 (UTC).
 * So call "contentious" is pure rubish. Professor Lam Lay Yong's work was published in 1992, her evidence is so powerful, nearly half a decade passed, she reported her findings time and again in internatiol conferences on Chinese mathematics attended by top mathematician around the world, yet her view was never challanged, and she won the highest award in History of Mathematics, no historian of Chinese mathematiccs of Chinese, French, Russian and other origin ever won such high award, she is THE authority on History of Chinese mathematics, particularily on the origin of place value decimal numerals, an research started in 19th centry bo Alexander Wylie, followed by Joseph Needham. --Gisling (talk) 13:14, 25 June 2011 (UTC).

Pronunciation of decimal numbers
Is it possible to add how to pronounce these numbers properly? I mean, is 3,34 three point thirty four like in French or three point three four like in German? I have heard both opinions.


 * Sorry I'm not an expert in these matters but a number like three point thirty four (3.34) sounds like a version number in software than a proper number. I would hate to say a number like this 1.1234567. Darrenaustralia (talk) 06:18, 21 October 2008 (UTC)


 * It's normally three point three four. However, 48.49 would most likely be forty-eight point forty-nine, because of the pattern established by the 48. If you read off the individual digits to the left of the radix, you will to the right as well. kwami (talk) 02:31, 26 February 2009 (UTC)


 * This may be a geographic difference or simply an academic culture difference. I never read digits to the right as a number but always as individual digits. And it seems that most of the people educated with me take the same approach. Personally, I cringe when I hear “forty-eight point forty-nine”. Clifsportland (talk) 21:35, 6 December 2010 (UTC)


 * I suspect there's considerable difference between cultures. One Isaac Asimov story hinges on the fact that 101 is pronounced in American English as "one hundred one"; unfortunately, in British English it's "one hundred and one", which wrecks this story for UK readers. — 188.28.24.1 (talk) 20:50, 21 November 2011 (UTC)
 * Americans normally say "one hundred and one", unless we're in an environment where we think we're supposed to give the "right" answer, which we've been taught is "one hundred one". --Trovatore (talk) 21:12, 21 November 2011 (UTC)
 * (Even that's not quite right &mdash; what we normally say is "a hundred and one".) --Trovatore (talk) 21:13, 21 November 2011 (UTC)

tentywise
I removed, for the second time,


 * The proto-germanic languages reckoned in a hundred of 120 in number, and a thousand of 1200. All early germanic languages, including Gothic (Marginal in 1 Cor 15:6) have words for counting in 'tentywise' eg five hundred [tentywise], which supposes a different count is usual. Gordon's Introduction to Old Norse p 293, gives number names that belong to this system. Likewise, one can find entries in Old English, which had a sizable literature before decimalisation. Actual calculations in base 120 are given as late as the 15th century.

on the following grounds.


 * 1) It makes no sense in English. Perhaps in some of the other languages derived from Proto-Germanic languages, ....
 * 2) The first reference points, as far as I can tell, to an example of use, possibly in that book, rather than in 1 Cor 15:6. And its (the book's) provenance seems questionable.

I think what might be said is
 * The proto-germanic languages used (the cognate to) "hundred" to refer to 120, and "thousand" to refer to 1200.

But sources, either in English, or interpreted by someone with a knowledge of English, would be needed. — Arthur Rubin (talk) 15:29, 14 June 2013 (UTC)


 * Even with English, the expression 'fifteen hundred hours', shows two differences to customary uses, and what is being suggested by Rubin (that the hundred is five-score). First, the hundred here is three-score, the previous moment is 'fourteen-fiftynine'.  The number here is 900, not 1500, which means that '00' is being called a hundred.  Secondly, like the Sumerian system itself, it's a division system: the lead place is units: 1500 hours is 15 o'clock.  By O. Neugebauer, one reads the numbers is a mishmash decimal system, but for a certian class of use, very large numbers (which are units and fractions), are used.  The use of such tables, zeros, etc, exactly matches what one would expect of a division-system to avoid division.  So, even by summerian reckoning, 1:40 is 1 2/3, not 100.
 * In Zupko's "British Weights and Measures", appendix A gives units of import and export from 1600 to 1800, we see entries like 'hundred of 120 in number' and 'thousand of 1200 in number', along with 'hundred of 100 in number' and 'thousand of 1000 in number'.  Under 'Wey' in the same author's Dictionary of weights and measures, we find this quote "A weight for Cheese, eg in Essex, 300 l., at the rate of five score and xii to the hundred, which is 336 li."  The hundred here is the hundred-weight, but the translation is 3 hundredweight as 300 l., where 00 is short for hundred, which the balance of the para makes clear.
 * One does not need to use the expression 'the cognate to'. See, eg Great_hundred, and the entry there.  Well into the 1800's, a 'hundred' was also a measure equal to 120, and a 'long hundred' always meant that.  I fail to see what you are saying it makes no sense in English?
 * Marginals tend to appear as reminders to the reader. While  I Cor 15.6 contains a reference to five hundred, the marginal is a reference using the cognate that in other Germanic languages, means 'by the ten-count', or 'tenty-wise'.  The same word is used in an early OHG text, gives some measure that the 'hundred' is not five score usually.  Sometimes the marginals creep in the text.  The reference is not to what I Cor 15.6 says, but more particularly, what the scribe felt was necessary to remember when reading it.  It's a decimal 'five hundred', not a normal one.Wendy.krieger (talk) 11:51, 16 June 2013 (UTC).


 * I say again: "The proto-germanic languages reckoned in a hundred of 120 in number, and a thousand of 1200." is not English. One can say that (cognates of) "hundred" meant 120, and "thousand" meant 1200, but what you wrote doesn't say that.  Furthermore, it requires a source, which you haven't provided.
 * An English sentence, although it still requires a source, would be:
 * The Proto-Germanic language used "hundred" to refer to 120 and "thousand" to refer to 1200.
 * What "tenty-wise" means in the scribe's words requires a source or a knowledgable translator; you are not such a translator, considering the English language sentences you have written.
 * Both numbered paragraphs above, and most of your other sources, are examples of use of "hundred" as 120 (or as 100 as contrasted to 120); WP:CALC does not allow us to assert that it's a common usage, as you assert (when translated into English). — Arthur Rubin  (talk) 19:17, 16 June 2013 (UTC)


 * I use base 120, and have done so for nearly 30 years. I can do all of the long arithmetic in either decimal or twelfty, without conversions.  I can find square roots, for example, and criss-cross multiplication in that base.  And i just use the twelve-by-twelve tables.  A lot of what they teach about bases in school, is just plain wrong.  But that's not the issue here.  Numbers in twelfty appear at my website http://www.os2fan2.com/, and also randomly in various posts i make.
 * You don't need to be a linguist to take an interest in ancient languages, just any connection. I mean, what sort of fluency are you proposing for these various aboriginal languages: the quotes there are not much better than anything given by Gordon's "Introduction to Old Norse": just an unadorned number-list.
 * The references i gave from Goodare on 120 (the reference i see you happily edited out!), gives a clearer set of use of 120, than the examples of 60 use in Neugebauer, or the scattered word-lists in most of the 'other examples of bases'. I mean, you can see from how people are said to react to the presence of counts in the long hundred, to be that it was in common enough use, that merchants and customs folk might expect transactions in the long-hundred in a way that we would not.  What sort of common use do you really want?
 * I mean, the celtic 20 does not even raise a mention, even though it leaves deep marks in the french language (quatre-vignt dix-huit, for example), and one of the welsh counting systems, actually divides the score into quarters, and refers to 'three-fifteen', for 18?. It's modern welsh, for example!
 * Reading Neugebauer will tell us that the use of 60 was less entrenched in the Sumerians, than the use of 120 in Scotland. It just happens that 60 was used by the book-scribes in Sumeria, but 120 was not used by the Christian book-scribes.  You have to take this filter, and the other filter that the readers might not be expecting C to mean 120, to account.
 * Although i do not read gothic or old norse, i am fairly competent in cognate-translation. There are assorted rules, you can follow to make PIE /dent/ into OHG /zahn/ and OE /tooth/ through protogermanic /tanth/.  The greekish text is translated at 'fimf hundram', to which the translator added a marginal 'taihunteweis'.  This is taken by the scholars in the field as a marginal, that has crept into the text.  What sort of person adds a marginal, to say that 'five hundred' must be read as a decimal number?  Really.  It only makes sense if hundred does not mean tenty.  And there is enough evidence in the languages that split from protogermanic, and too close to the split for any separate change, to assert that 'hundred' in the proto-germanic, meant 120, and that the decimal conversion comes with the Christians in every case.  It's best attested in the north, because writing beat the christians there.  There are several words for 'decimal' (ON ten-count, OE teentywise vs ON twelve-count, OE twelftywise), to tell us that any value other than 120 fits.  As Goodare notes, there is no expression for countings in dozens and grosses.
 * Goodare actually goes to the extent to show that calculations were done in the six-score, by studying how the carries and borrows work. This is how one finds any base.  There are working examples of the abacus in use, so i suppose that that's a pretty good indicator of in common use.  There are tables that show instances of export and import against which hundred is meant.  I mean, what do you want?  Even ISO 1000 (which defines the metric system), does not admit we use the decimal system!  Where's the reference that we use the decimal system or that it's common!!!.  People don't just write that sort of thing.
 * The sumerian square root of two, is known from one example, and most of the usage given in Neugebauer is given without any statement to the bleedingly obvious: their system is a division system to avoid division.  He gives a reference to a tablet that states that 0:8:34:16 < 1/7 < 0:8:34:18, while happily saying that they had numerous multiple-tables for '44:26:40'.  In any case, even Neugebauer gives the proper form of sumerian numbers in common use: it's kind of a mixed decimal-sixty system, eg the number 192, might be given as 3:12 in the tables, would be written as csxxxii (ie 100 + 60 + 3*10 + 2*1) in the surrounding text.  Yet this is 'happily quoted as a base on the scale of the mayans'.
 * It's not hard to reconstruct the sumerian process in twelfty, for example. First you have the recriprocal table. This can be taken as all of the numbers of the form 2^x 3^y 5^z to 120, placed beside their recriprocals, eg '72 -> 1.80'.  To calculate a recriprocal of a number not on the table, one uses interpolation.  The 'seven brothers' problem, might be found by noting that 1/7 lies between 16 (7.60), and 18 (6.80), for which we add two of the former, to three of the latter, and divide by 5.  Thus we get 16*2+18*3 = 86, divide by five gives 17:24.  The actual number is 17:17, but a bit of refinement to the method yields that result.  One could actually start from 17:24 by 7, to get 100.48, and then refine the multiple down to somewhere between 17:17 (E9,E9), and 17:18 (1.00.06).
 * Likewise, using the recirpocal tables, yield sqrt(2) at 1:50. Multiplying this by 1:50 gives 2:00.V0.  The square on 1:49 gives 1:E8.01.  You can see that 2 lies roughly 2/3 of the way through this, gives a next approximation at 1:49.80.  The actual difference in the squares is 1:E9/2:99.  We don't have either of these in the table, but 2 and 2:80 do occur, so we can find that the proportion needed is 1 / 1:40, or 90.  This means that 1:49.90 is pretty close too.  It's actually 1:49.85 or 0:84.V2.
 * The previous two paragraphs are examples of 'experimental aerchology', the sort of thing you see in the BBC show 'Time Team'. You don't just dig up bones and read old texts: you can experiment with processes, and look for modern examples. Wendy.krieger (talk) 11:32, 17 June 2013 (UTC)
 * I removed Goodare because it seemed, at first glance, to be self-published. It appears I was wrong, although I'd like some confirmation that the Proc Soc Antiq Scot is a reputable journal.  If you would learn to use Wikipedia's citation format, it would have been easier for me to determine what you were saying.
 * That only makes sense with your interpretation of the sources. If you can provide a  reliable source which says what you're saying above, then something more can be in the article.  (And, in case you wish to quote the BBC show "Time Team", I don't think that would be a reliable source, either.)   I can read your notation, with some effort, but unless some published research reports what you're saying, it's not relevant here.
 * As for your calculations above, they are too complicated to fall under WP:CALC; they are irrelevant for Wikipedia unless some reliable source reports them. As a further aside, there's an error on your twelfty page:  "One thousand" (1200d) is 10.00 in your notation.  Referring to 1.00.00 as "one thousand" is a misuse of decimal or twelvety notation; you might rationally refer to it as "myriad", as 100:"hundred"::myriad:1.00.00 (using : as a quasi-proportionality symbol.)  — Arthur Rubin  (talk) 12:11, 17 June 2013 (UTC)
 * Yes, i know the historical thousand is 10.00, but as i have mentioned on other sites, the names i use are for the powers of 120, not the placement of the digits. In effect, the abacus is reckoned in columns of 120, the numbers are thus named.  I use hundred, thousand, cention, and million for the first four powers of twelfty.  Still, i write it in groups of four, sometimes with points and commas to separate the places, the radix is a semicolon, eg 9.85.10.16 or 985.1016, is 2^16, while pi is 3:16.E9.E3 or 3:16E9.E3.  Unlike decimal, the digits are treated differently, so you need to pick them.  — Preceding unsigned comment added by Wendy.krieger (talk • contribs) 12:58, 17 June 2013 (UTC)
 * You can use whatever words you want, but I would have used hundred, myriad (Greek), million, and yi (Chinese; see 100000000) or myllion for the first four powers of 120 = 1.00 . — Arthur Rubin  (talk) 13:15, 17 June 2013 (UTC)

"Decimal Fractions" section contains errors.
A decimal is a tenth-part. Decimals are a string of tenth-parts, specifically a continued-numerator fraction. A decimal carries and borrows to the next higher place by 10.

The assertion that it relies on powers of 10 is misleading. The reason for this, is that decimals will quite happily work with a non-decimal column interspersed, such as the HMS notation on calculators, written as H.MMSSddddd, which has two columns of 6, interspersed with decimal places: ie d.sdsddddddd, where s is a six-column. Railway chainage works with a column of 8 immediately after the radix, ie d.oddddd, this is the furlong, divided into 10 chains, of 100 links. They rely on decimal calculation, but the notion that it's a power of 10 is wrong.

While it might be asserted that something like 1.618 is 1 618/1000, in practice, nothing is further from the truth. The fraction is not recast by the addition of extra precision, but the series of continued numerators is adjusted: thus 1 6/10 1/10 8/10 ... The arguement is that to divide the millimetre into tenths, one has to resort to the metre divided into 10,000!, rather than adding a tenth-deal to the millimetre.

We also note, especially with money, that vulgar fractions, like 1/2 or 1/3, can follow a decimal string, ie 1.33 1/3, or £1.52 1/2, rather than 1.525. This works, because, as noted in the previous paragraph, decimals are seen as a continued-numerator, and other fractions can be added in where-ever need sees fit (eg /8, /10, /10 ...).

No one relates the millimetre directly to the metre, but through the next division up (the centimetre). In practice, the decimal measurement is to consider what decimetre, what centimetre of that dm, and what millimetre of the cm, the measurement falls into. That's the same way we read binary fractions, duodecimal fractions, sexagesimal fractions, centisimal fractions.

Stevins notation, which matches the Arabic source, places a series of 'second numbers' after each unit. This same series of second numbers are elsewhere written in roman numbers, aligning, or raised, eg 5' or 5i. That is, 1(3) is a unit in the third column to the right. The usual presentation for numbers of this kind is to use unadorned ordinals, eg 'tenth-metre', or 'second'. The french division of the circle into grades, are divided to minutes and seconds, by the centisimal scheme, just as the current division of the circle divides to minutes and seconds of sexagesimal. Sir Isaac Newton uses thirds, fourths, fifths of sexagesimal in the Principa (Book iii, on page 458) of http://archive.org/stream/newtonspmathema00newtrich#page/n463/mode/2up. The notation is identical to that used by Stevins, and others who use the -mal fraction schemes.

On the other hand, there is no referrant of any column to the unit column, and no recasting of fractions as more places come available. Thus one must use Latin or Added fractions (which seek insperation from Roman fractions), rather than a sum of powers of 10, to construct decimals.

The section is wrong, in that point that it asserts a power of 10 as divisor. This happens only because added fractions and mixed units are no longer taught in schools. — Preceding unsigned comment added by Wendy.krieger (talk • contribs) 08:32, 18 June 2013 (UTC)


 * Actually, this discussion is interesting, but makes no difference to this article;
 * $$1.618 = \frac {1618}{10^3} = 1 + \frac {6 + \frac {1 + \frac {8}{10}}{10}}{10} = 1 + \frac {6}{10} + \frac {1}{10^2} + \frac {8}{10^3}$$
 * Only in a "mixed unit" representation does it make a difference. — Arthur Rubin  (talk) 09:17, 18 June 2013 (UTC)
 * On the other hand, my assertion is that progressive decimals are just that, an individual instance of an added fraction in tenths. That is, something like 1.618, the 8 is not referred to units, but to the place immediately to the left of it.  That is, you don't need to know what column it is in (relative to the radix), to preform carry, because that is done to the 1 immediately to the left, not the 1 in front of the radix.


 * The idea here is that decimal can survive a non-decimal column inserted, whereas the exponent power might not. — Preceding unsigned comment added by Wendy.krieger (talk • contribs) 10:51, 18 June 2013 (UTC)
 * The "error" is not really relevant to this article, though, with the possible exception of your notation for twelvty representations. "A difference which makes no difference is no difference."  — Arthur Rubin  (talk) 19:40, 18 June 2013 (UTC)

For what it is worth, here is how Stevin develops decimals, the second paper in David Eugene Smith 'A Source Book in Mathematics', Dover reprint. The radix is not used anywhere, and it is concieved as a progression of units, each a tenth of the previous. There are explinations after each definition, from which the quotes are sampled. The bit after the decimals show usage, particularly where it departs from modern radix-based decimals - (ie omission of medial zeros, and beginning at any column, not the unit column).

Definition I: 'Disme'(decimals) are a kind of arithmetic based on the idea of a progressions by tens, making use of ordinary arabic numerals, by which any number may be written and all computations that are met in business may be preformed by integers alone, without the aid of fractions.

(Explination) ... Similarly, in the number 2378, each unit of the 8 is a tenth part of each unit of the 7, and so for all others ...

Definition II: Any given number is called the unit, and has the sign (0).

(Explination), The number three-hundred (and) sixty-four units is written 364(0)

Definition III: The tenth part of a unit is called a Prime, and has the sign (1), and the tenth part of a prime is called a Second, and has the sign (2). Similarly for each tenth part of a unit of the next higher figure.

(Explination)  Thus 3(1)7(2)5(3)9(4) is three primes, 7 seconds, 3 thirds, 9 fourths, and we might continue this indefinitely. It ise evident from this definition that the latter numbers are 3/10, 7/100, 5/1999, 9/10,000, abd tghat this number is 3759/10,000. ... For intansce, we do not write 7(1)12(2) but 8(1)2(2) instead, because it has the same values.

Definition IV: The numbers of the second and 3d definitions are called Decimal Numbers

.End of definitions. following are selected examples in order of fall in the paper.

Examples of calculations follow. It is interesting that a value of 0 before a unit, can be suppressed, so he has 5(0)7(2) which lacks a prime, which must be inserted to get 5(0)0(1)7(2).

A calculation of 4(2) divided by 3(4), gives 13(0)3(1)3(2) or 13(0)3(1)3(2)3 1/3(3) is the exact result, but in this work we propose to use whole numbers over ...

Later on, we find 3(4)7(5)6(6), rather as much as one might write seconds without degrees. A value calculated at 1(1)8(2)0(3)4(4)8(5)0(6), is written as 1(1)8(2)4(4)8(5). [Note the missing (3)]

Wendy.krieger (talk) 07:14, 19 June 2013 (UTC)


 * Interesting. It could be noted as a non-standard notation, and with the missing (3), there is absolutely now way to avoid:
 * $$3(4)7(5)6(6) = \frac 3 {10^4} + \frac 7 {10^5} + \frac 6 {10^6},$$
 * and so on. — Arthur Rubin  (talk) 18:37, 19 June 2013 (UTC)

12 and 60
I think it is quite established that the use of 12 and 60 in many cultures on several continents comes from the fact that 12 and 60 have 'relatively' many divisors, {1,2,3,4,6,12} for 12, and {5,10,15,20,30} in addition for 60. This is very useful when it comes to fractional quantities etc, especially before the introduction of p-adic numeral systems with fractional part.

I think the number of months is rather a consequence than a reason for the choice of 12: observe that a (natural, i.e. lunar) month is rather 4 weeks than 30 days, and 52 / 4 = 13, and not 12, (a (solar) year having 52 weeks plus about 1.25 days.) MFH 12:52, 8 Apr 2005 (UTC)


 * A base other than 10 and 20 may be used in a measurement system for the division's sake, but it is rare to use such a base for a language's counting system. Duodecimal systems are used only in several North Nigerian languages and in the Chepang language of Nepal.  The latter seems to be from the Nepalese way of counting using fingers (see the figure).


 * The Babylonian sexagesimal system clearly had an internal decimal system, and 60 was used instead of 100 for ease of division. It is more appropriate to call it a mixed-radix system of bases 10 and 6.


 * By the way, a year has about 12.368 months, not 13 &#8212; divide the solar year (365.2422 days) by the lunar month (29.53059 days). - TAKASUGI Shinji 10:42, 2005 Apr 12 (UTC)

History of decimal numbers in China
Non-positional decimal numerals were used in China, possibly as early as the 14th century BC.


 * In 1930 archeologists earthed 10,000 years old bone tubes with markings from Zhoukoudian Upper cave area belonged to Upper cave man. According to the research by noted Chinese mathematic historian Li Di(correspondent member of Académie internationale d’ histoire des sciences.),the markings on the bone tubes represent numerals:with one cut mark represents 1, two parallel cut marks for 2, three marks for 3, two marks on top, three marks on bottom represents 5,a long circle was possibly symbol for 10; In Li Di's opinion, these symbols has decimal concept.


 * From 1974-78 archeologists excavated 1500 late Neolithic era tombs from Liu Wan area of Le Du county in Qing Hai province, and unearthed more than 30,000 pieces of artifacts, belonged to Ma Chang, Ban Shan Qi Jia and Xin Dian four types of culture. From the Ma Chang site unearthed 48 pieces of flat bones with cut marks, from one marks, two marks, three marks ( one on upper side, two marks on the bottom), 5 marks (two on top, three on botom), the bones from Ban Shan cite have maximum number of eight cuts. Chinese scholars believe, that these marks represent decimal numerals and possibly rudimentary addition operation.


 * The Oracle bone script of Shang dynasty(14th to 11th century BC) has a complete decimal numeral system, with one horizontal line represents 1, two lines one on top another represents 2, three lines stacked represents 3, four lines represents 4, symbol X represents 5, a ^ symbol represent 6, a cross represents 7, ")(" represents 8, nine is already very close the Chinese written 9, | represents 10, || for 20,||| for 30, further,there are separate symbols for 40,50,60,70,80,90,100,200,300...900, 1000,2000,....9000, 10000, up to 40000.

Non positional decimal system was common place in many civilizations.
 * The bronze script of Zhou dynasty (1045 BCE to 256 BCE) not only inhereited the decimal numerals of Oracle bone script, but showed marked advancement, as positional numeral concepts appeared, for instance the script "金XX" prepresents  355, the right hand side X represents 5, the next one represents 50, however because such application was not wide spread, a full positional decimal system had not yet evolved.


 * Bamboo script of the Qin dynasty and Han dynasty indicates mathematical operation with decimal addition, subtraction, multiplication, of decimals and rudimentary fractions ( in 1/3, 2/3)

there was never any evidence of such counting board( in the sense of game board, chess board type) in literature nor any artifact found, probably due to lack of use according to Wu Wenjun ed, Grand Series of History of Chinese mathematics.

In ancient time, the Chinese used written decimal numerals only for recording, never for calculation. For calculation they used counting rods, conveniently stored in a silk pouch and carry them around; whenever calcultion was needed, the counting rods were taken out from the pouch and laid out on a flat surface such as on the ground, on a table top, this flat surface was referred by historian as "counting board",. rod calculus involves the use of 9 and only 9 man made numerals(plus a natural blank on counting board for zero), each numeral composed from one to five rods. The rod numerals decimal system differ from the written Chinese decimals system, in that it expresses the concept of ranks 万千百十for 10thousand, thousand, hundred and ten instead with words but with positions on the counting board, from right to left in ascending order of ranks For instance the number 12325 expressed in written Chinese decimal system as 一万二千三百二十五 is simply | 二 ||| 二  ||||| on the counting board. Start from the unit digit with vertical form, the next position, alternate with horizontal form, followed by vertical, horizontal etc, this convention of alternating vertical/horizontal avoids confusion of adjaction numerals when laying round counting rods on gridless floor, otherwise || ||||| could be misread as  34, 43, or 52, if rods roll over. This alternation of vertical and horizontal rod numeral form is very important to correctly understand written trascription of rod numerals on manuscripts. For instance in Licheng suanjin, 81 was transribed as, and 108 was transripted with,it is clear that the latter clearly had a blank zero on the "counting board" (ie, floor or mat), even though on the written transcription, there was no blank. On the same manuscript, 405 was transcribed as   , with a blank space in between, for obvious reason, and could no way be interpreted as "45".In other words,      was not just transcription, but was an image of the lay out of count rod number 405 on a table or floor.

Giving the fact that there was close links between ancient civilizations thru the Silk Road. It is more amazing the two books more than four hundred years apart, across different cultures, across two radically different media,one material numerals, the other written numerals possessed such indentical algorithm details ,almost like DNA traceable to its origin.

Base 100 Redirect
'Base 100' redirects here. However, as far as I understand it, Base 100 and Base 10 (decimal) are NOT necessarily the same. Base 10 uses digits 0-9, while base 100 would essentially 100 separate "digits". Should we make a new page for 'base-100'? Or am I mistaken? 50.196.48.211 (talk) 18:52, 6 May 2014 (UTC)
 * Well, in my personal opinion, Base-100 is not particularly notable. If it has some use I am not aware of then perhaps it is deserving of a base of its own.  As far as the redirect goes, I will have to look around to see if we have a page that works better, but you are correct the two are not the same. Thenub314 (talk) 19:07, 6 May 2014 (UTC)

'Base 10', not 'Base-10' or 'Base Ten'
Accuracy and consistency of terminology is always the goal of a dictionary and encyclopedia. Base 10 is the correct and certainly the most accepted description of the decimal system as opposed to the confusing Base-10 (negative?) or non-numeric Base Ten. I've thus tweaked the article using "Base 10". - Pythagoras 50.153.106.144 (talk) 12:52, 9 June 2015 (UTC)

Hebrew Numerals are Base 10
I added Hebrew numerals where references were made to Greek Numerals and Roman Numerals. - King Solomon 50.153.106.144 (talk) 14:27, 9 June 2015 (UTC)

Decimal in Sanskrit
The word "decimal" is similar to Sanskrit "dashamlav", meaning "tenth part". I don't know the etymological significance.Sooku (talk) 06:09, 28 July 2015 (UTC)

Four and twenty blackbirds
Other weird natural language terms for the numbers are the French : the number 98 is described as in this translation, "four-twenties ten-eight" and the German : the pronunciation of 24 is translated as "four and twenty", which survives in the English nursery rhyme.

This is why the Continental European telephone numbers are in pairs (12.34.56.78), so that both of these sets of natural language speakers would not get confused, just everybody learning either language. 173.162.253.101 (talk) 14:59, 17 March 2016 (UTC)

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Grammar
The sentence "J. Lennart Berggren notes that positional decimal fractions for the first time by Arab mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century." is not grammatically correct. I do not know what J. Lennart Berggren notes, or how to resolve this error in a manner that is true to the source material. 67.208.179.138 (talk) 13:09, 28 June 2016 (UTC)


 * Fixed. --Bill Cherowitzo (talk) 04:13, 29 June 2016 (UTC)

Why does JEDEC stop at GB?
Why does JEDEC stop at GB? BIN is exactly the same as DEC as far as I know. Shouldn't we add TB, PB, EB, ZB and YB? Mc peko (talk) 18:44, 21 February 2017 (UTC)

Article needs additional citations for verification
When adding Refimprove on 12 January 2011, commented that "entire sections are sourced only with one author or reference. When that's done, the section should be noted as that author's theory, rather than attributed as fact, even if the author is an expert, when there are notable contradictory theories." Comment moved from unsupported template parameter to increase its visibility and encourage resolution of the issue. --Worldbruce (talk) 19:39, 9 November 2016 (UTC)
 * I don't see any particularly problematic content; I can look at adding references this Wednesday or Thursday. Power~enwiki (talk) 02:39, 31 July 2017 (UTC)

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modern fraction system is not chinese but indian
it is very illogical to say that on one hand the indians invented the modern numeral system and the fractions were based on the chinese system. all the external links mention Indian mathematicians as the pioneers of fraction system used today, the indians used to write fraction without putting a line in between numerator and denomenator which was later added by the arabs, somebody needs to correct this misleading information on this page. — Preceding unsigned comment added by 60.50.175.163 (talk) 11:13, 2 February 2018 (UTC)

A Commons file used in this page has been nominated for speedy deletion
The file on Wikimedia Commons has been nominated for speedy deletion. View the deletion reason at the. Community Tech bot (talk) 15:22, 28 May 2018 (UTC)

Nonnegative
Come on, people. This is the longstanding form. If you want to change it, get consensus. --Trovatore (talk) 20:56, 2 January 2019 (UTC)
 * A Google search gives 5 million pages with "non-negative" (and 3.4 millions with "nonnegative"). Thus "non-negative" exists and is really common, and MOS:HYPHEN should be followed.
 * Note also that the main articles about this notion Sign (mathematics) and Natural number use "non-negative". Really, this is not incorrect. Vincent Lefèvre (talk) 00:15, 3 January 2019 (UTC)
 * OK, MOS:HYPHEN does not say that the non-hyphenated version is not allowed. It doesn't even clearly state that the hyphenated version is preferred.  So when you say "follow MOS:HYPHEN", you're really not saying anything.
 * What other articles do is not the point. The unit of consistency for spelling choices is the article.  See WP:ARTCON.
 * I agree that "non-negative" is not incorrect. But "nonnegative" is not incorrect either.  You should not be changing it without consensus, against objections.  Please revert to the status quo ante and discuss it. --Trovatore (talk) 00:33, 3 January 2019 (UTC)
 * MOS:HYPHEN says that even though the non-hyphenated version is the rule, in the particular case when the letters brought into contact are the same, using the hyphenated version adds clarity (ditto when the word is not common). I cited the other articles to show that this was common.
 * Concerning the consistency in the article, one already has: "non-integer", "non-mathematical", "non-positional", "non-decimal", and "non-standard". So adding the hyphen to get "non-negative" also brought consistency within the article. Vincent Lefèvre (talk) 00:45, 3 January 2019 (UTC)
 * The wording in MOS:HYPHEN is confusing ("clarifies when" usually means that it distinguishes between possibilities listed after "when") but it does not in any case make a specific recommendation to use the hyphenated version in these cases. It indicates that this is a consideration, but it is not a "rule".   As for consistency, the only thing under discussion is the single word non(-)negative, which is attested hyphenated and not.  There is no consistency with other words under consideration. --Trovatore (talk) 00:50, 3 January 2019 (UTC)
 * This is consistency on the hyphenation or not with "non" (basically, what rules are applied). Vincent Lefèvre (talk) 00:57, 3 January 2019 (UTC)
 * It isn't rule-based. It's the spelling of an individual word, which is attested both ways. --Trovatore (talk) 00:58, 3 January 2019 (UTC)
 * WP:ARTCON doesn't say "individual word" but "variety". Vincent Lefèvre (talk) 01:07, 3 January 2019 (UTC)
 * But there is no "variety" involved here. --Trovatore (talk) 01:11, 3 January 2019 (UTC)
 * That would be the analogue for a variety. Otherwise I don't think the Manual of Style requires consistency for individual words when different spellings are allowed. Vincent Lefèvre (talk) 01:24, 3 January 2019 (UTC)
 * Probably it doesn't require it, but I do think it makes sense to use a consistent spelling, at the article level. Trying to abstract a "variety" from it, I don't think makes sense.  --Trovatore (talk) 01:25, 3 January 2019 (UTC)
 * But what is meant by "consistent spelling" is subjective. You think that this should concern individual words. I think this should also concern words with something common (like the "non" prefix here, thus with a set of rules behind that). Vincent Lefèvre (talk) 01:31, 3 January 2019 (UTC)
 * Well, there just aren't any consistent rules on that. People use hyphens or not fairly haphazardly; I'm not aware that it has become, say, a consistent US/UK difference.  I leave the hyphen out of "nonnegative" and "wellordered" (the latter in the mathematical meaning only) but insist on it in "e-mail", for example.  Since "nonnegative" is clearly acceptable, I think you shouldn't insist on changing it, once reverted, without discussion. --Trovatore (talk) 01:37, 3 January 2019 (UTC)

Just because of being cheekily asked who says..., I say so (especially as non-native speaker) and the few people I asked this, univocally also say so. Maybe the trend will take away this easing on the eye, and as a follow up will elide one of the en-s ... Even WP:MOS mentions the neighboring equal consonants as a reason for using a hyphen, and thus I remain to support a hyphenation in this well-founded and well-definable equivalent application in non-negative.

BTW, Vincent Lefèvre was not alone in re-inserting a hyphen against blatant anti-hyphenism; I agree to his edits. For the time being I withhold any interaction on this. Purgy (talk) 08:02, 3 January 2019 (UTC)
 * Purgy, thanks for bringing up that you're not a native speaker. I don't wish to be rude, but in the past I have not found your intuitions about the English language to be especially reliable. --Trovatore (talk) 18:36, 3 January 2019 (UTC)

History of repeating/infinite decimals?
I've noticed that the "history" section features quite a lot about the history of the use of decimal fractions, but all those it mentions seem to terminate, with no mention of repeating decimals or other decimal fractions understood to continue ad infinitum. Does anyone know where a source might be found on that part of the notation's history? Twin Bird (talk) 05:59, 24 June 2020 (UTC)

Base 10
Base 10 is the most common way of describing itself - google it. It's not confusing like base-10. whereas the (-) could be misinterpreted as a negative sign. Calling it Base Ten defeats the whole purpose of using the numerals, e.g. 10. 2601:589:4800:9090:3851:AB2:AEE3:4904 (talk) 15:37, 25 October 2020 (UTC)
 * The edit that you have done has several issued. Firstly, Wikipedia's manual of style discourages the capitalization of "base" and the use of digits for replacing the word "ten". Secondly, "base-ten" is a qualificative of "positional numeral system", and without dash, the sentence is confusing it is unclear whether "ten" refers to the base or positional "positional numeral system". So the dash is not only grammatical, it is also required. So, I'll revert your edit. D.Lazard (talk) 20:29, 25 October 2020 (UTC)