# Invention of the decimal system. **URL:** \ **Category:** Factual Questions\ **Created:** [July 27, 2013, 8:22am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657 "2013-07-27T08:22:00Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [July 27, 2013, 8:22am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/1 "2013-07-27T08:22:00Z")
Hi, Chinese kids grow up believing that the Chinese invented the decimal system. Most Western historians I’ve read, believe that the decimal system originated in India. Who’s right? Could there have been different decimal systems invented independently of each other? I look forward to your feedback. Thanks. davidmich ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [July 27, 2013, 11:49am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/2 "2013-07-27T11:49:01Z")
MODERATOR COMMENT: I’m moving this post from “About This Message Board” (a forum devoted to discussions about the Message Board itself) to “General Questions” (a forum devoted to questions that can be answered.) You’ll have a better chance of getting some interesting comments and historical perspectvies. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [July 27, 2013, 12:22pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/3 "2013-07-27T12:22:55Z")
How are they defining decimal system? Because the Romans used a decimal system. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [July 27, 2013, 12:31pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/4 "2013-07-27T12:31:41Z")
Surely the decimal system requires a zero - the Romans saw no need for a zero ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [July 27, 2013, 12:32pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/5 "2013-07-27T12:32:41Z")
> [@davidmich](#): > > Hi, > > Chinese kids grow up believing that the Chinese invented the decimal system. Most Western historians I’ve read, believe that the decimal system originated in India. Who’s right? Could there have been different decimal systems invented independently of each other? > > I look forward to your feedback. > Thanks. > > davidmich The question is not ‘who used a base ten system first’ . Decimal means using digits 0 to 9 (or some equivalent set of 10 digits ) and ONLY those digits. I think chinese only restrict themselves to the 10 digits only after the decimal point (to represent fractions of 1 … ) but they used digits that represented, eg 10,20,30 ,etc, 100, 200,etc, 1000 ,2000,etc. Sure its a base 10 system, in general, but it has more than 10 digits, so its not a pure decimal system. So the modern western system is the first to use 0-9 at EVERY place… a pure decimal system. ---
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [July 27, 2013, 12:50pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/6 "2013-07-27T12:50:29Z")
Thank you all very much for your replies. davidmich ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [July 27, 2013, 1:06pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/7 "2013-07-27T13:06:17Z")
> [@Isilder](#): > > The question is not ‘who used a base ten system first’ . > > Decimal means using digits 0 to 9 (or some equivalent set of 10 digits ) and ONLY those digits. > > I think chinese only restrict themselves to the 10 digits only after the decimal point (to represent fractions of 1 … ) > but they used digits that represented, eg 10,20,30 ,etc, 100, 200,etc, 1000 ,2000,etc. > Sure its a base 10 system, in general, but it has more than 10 digits, so its not a pure decimal system. > > So the modern western system is the first to use 0-9 at EVERY place… a pure decimal system. Well, if _modern western_ encompasses _ancient Hindu_.🙂 I think **davidmich** needs to clarify what he means by “decimal system”: [ul] [li]Counting by tens[/li][li]Place notation, with a zero as placeholder[/li][li]Use of a decimal point (or some equivalent) to allow the writing of fractopns by place notation[/li][li]or something else.[/li][/ul] And no, as this is a four item list, a call-out to Opal is neither required nor appropriate. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [July 27, 2013, 1:11pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/8 "2013-07-27T13:11:33Z")
Most historians think that the positional decimal system (one like we use with just ten digits which can be put together to represent any whole number) was invented by the Indians: > **[Positional notation](https://en.wikipedia.org/wiki/Positional_notation)** > > Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred ... > **[History of the Hindu–Arabic numeral system](https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system)** > > The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205". > Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described outside India in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca. 825), and second Al-Kindi's four-volume work On the Use of the Indian Numerals (ca. 830). Today the name Hindu–Arabic numerals is usually used. > Historians trace modern numerals in... Although some Chinese historians think that the Chinese had such a notation first, that’s not generally accepted among historians. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [July 28, 2013, 2:37am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/9 "2013-07-28T02:37:39Z")
Both India and China had full-fledged decimal systems early, but which borrowed from which may not be clear. [This Wikipedia article](https://en.wikipedia.org/wiki/Abacus) states > [@](#): > > Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907 AD) when travel in the Indian Ocean and the Middle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians. Other sources dispute this, reversing the chronology. In either case, I don’t think there’s any clear evidence of borrowing – the Indian and Chinese inventions might have been independent. The invention of the decimal system can be considered to have three parts: [ul][li] The use of base 10, rather than a base 60/10 hybrid (Babylonia) or 20/5 hybrid (ancient Mayans).[/li][li] The use of place-value, where 10, 20, 30, … use the same symbols as 1, 2, 3, …[/li][li] The use of an explicit zero symbol.[/li][/ul] Most early arithmetic systems (Egyptian, Greek, Roman) used different symbols for 10, 20, 30 than for 1, 2, 3… Early Babylon, China and the Mayans all used place-value, however. If the abacus was really invented 3000 BC in China, it (or written depictions of its state) would be the earliest place-value system. Without a zero symbol, 23, 203, and even 230 would all appear the same. Perhaps 203 was written “2 3” with a wider space than when 23 was written. Thus zero was the key invention. Naturally a scribe might prefer “2-3” over “2 3” for clarity when depicting 203, so I’ll guess a crude zero-symbol might have been invented many times! Ancient Persia had a zero symbol before the Hindus (and Mayans invented zero independently) but neither of these would qualify as “invention of the decimal system” since neither used base-10. To summarize, my answer to OP’s question (despite Wikipedia) would be “almost certainly China _if it really did have an early decimal abacus_.” Did it? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [July 28, 2013, 3:11am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/10 "2013-07-28T03:11:45Z")
[QUOTE=Wikipedia] The zero was probably introduced to the Chinese in the Tang Dynasty (618-907 AD) … acquir[ing] the concept of zero and the decimal point from Indian merchants and mathematicians. [/QUOTE] I clicked Reply intending to post much as I did, giving precedence to China in part because of their early decimal abacus. I clicked Wikipedia to check abacus date, was surprised to see the above, but posted it. … But shaking my head. It contradicts what I’ve read in at least two History-of-Math books. Perhaps I’m too gullible. I wonder if the above is a corrupt Wiki edit. (At the risk of racism accusation …) _It would not be the first time I’ve seen early Indians given undue credit on Internet blogs and wikis._ I hope an SDMB expert will look into this, correcting Wikipedia if needed. BTW, a source of difficulty in assessing early Chinese technology is the [Great Book Burning](http://en.wikipedia.org/wiki/Burning_of_books_and_burying_of_scholars) by [del]Curtis LeMay[/del] **Qin Shi Huang**. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [July 28, 2013, 3:23am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/11 "2013-07-28T03:23:09Z")
> [@septimus](#): > > Thus zero was the key invention. Naturally a scribe might prefer “2-3” over “2 3” for clarity when depicting 203, so I’ll guess a crude zero-symbol might have been invented many times! History shows that those conceptual innovations that seem the most obvious in hindsight, were, very often, the most difficult to originally grasp. Just because a placeholder zero seems such an obviously good idea to us now, it does not follow that it would have been obvious to those around before its invention. We know that apparently ‘obvious’ ideas such as natural selection and gravitational force were, in fact, very hard won, and, the very time it took to find its place in systems of numerical notation strongly suggests that the same applies, perhaps _a fortiori_, to the placeholder zero. There is, after all, something very odd about the idea of having, and needing, a symbol that stands for nothing. > [@septimus](#): > > To summarize, my answer to OP’s question (despite Wikipedia) would be “almost certainly China _if it really did have an early decimal abacus_.” Did it? I am not really seeing the basis you have for thinking “almost certainly China”, especially since your evidence seems to be a passage from Wikipedia that in fact (and as you admit) says “probably India”. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [July 28, 2013, 6:45am UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/12 "2013-07-28T06:45:26Z")
> [@njtt](#): > > I am not really seeing the basis you have for thinking “almost certainly China”, especially since your evidence seems to be a passage from Wikipedia that in fact (and as you admit) says “probably India”. As I tried to clarify, especially in my 2nd, corrective post that was too late for ETA, _ **I am suspicious of that Wikipedia page** _. I have confidence in Wikipedia’s science pages _but not in history-of-science pages where national pride may be involved.__In contradiction to that Wiki page_ you’ll get plenty of Google hits for “China abacus 3000 BC.” _An ordinary decimal abacus has a “zero” automatically_, as will a depiction of a number represented via abacus. But does the implicit zero on an abacus depiction count? If not, I admit I was likely wrong. Did they indeed go almost another 40 centuries without inventing a written zero symbol? Seems surprising, but your observation is sound. In some ways, Chinese mathematics was advanced by the time of Liu Hui, centuries before the apparent dating of the Hindu zero. They knew of negative numbers, Gaussian elimination, etc. With all that, perhaps I just assumed they had an explicit zero symbol – I can’t find it now Googling. :smack: ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [July 28, 2013, 1:51pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/13 "2013-07-28T13:51:22Z")
The Chinese seem to have most commonly (and early) used a portable device with strung beads as an abacus. The Wiki article mentions Romans and Greeks, for example, using flat (or grooved) tables. A strung abacus would be so much more convenient and therefore more widely used, even on river trips, and it’s easy to imagine the leap from abacus to recording its value by writing the value of each row. (If I were Roman, I’d have simply underlined each group to indicate the “number” belonged) - ie. 006490 would be: \_ \_ VI IV IX \_ (Or write numbers vertically in column.) I’m imagining this sort of notation would be making the need for Zero obvious. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [July 28, 2013, 1:56pm UTC](https://boards.straightdope.com/t/invention-of-the-decimal-system/664657/14 "2013-07-28T13:56:11Z")
“The people in situation X would have obviously seen the need for X” is not equivalent to “They then invented X.” Sometimes people miss the obvious things.