Most of the positional base 10
numeral systemA numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
s in the world have originated from
IndiaIndia , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
, where the concept of positional numeration was first developed. The Indian numeral system is commonly referred to in the West as the
Hindu-Arabic numeral systemThe Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 5th centuries by Indian mathematicians, adopted by Persian and Arab mathematicians , and spread to the western world...
or just
Arabic numeralsArabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
, since it reached Europe through the Arabs.
Devanagari numerals and their Sanskrit names
Below is a list of the Indian numerals in their modern
DevanagariDevanagari |deva]]" and "nāgarī" ), also called Nagari , is an abugida alphabet of India and Nepal...
form, the corresponding European (Indo-Arabic) equivalents, their
SanskritSanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
pronunciation, and translations in some languages.
Modern
Devanagari |
Hindu-Arabic |
Sanskrit word for the
ordinal numeral (wordstem) |
Translations in some
languages |
| ० |
00 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
|
(शून्य) |
sifr (ArabicArabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...
) |
| १ |
1 |
(एक) |
echad (Hebrew Hebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...
) |
| २ |
2 |
(द्वि) |
dva (RussianRussian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
) |
| ३ |
3 |
(त्रि) |
tre (ItalianItalian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
) |
| ४ |
4 |
(चतुर्) |
katër (AlbanianAlbanian is an Indo-European language spoken by approximately 7.6 million people, primarily in Albania and Kosovo but also in other areas of the Balkans in which there is an Albanian population, including western Macedonia, southern Montenegro, southern Serbia and northwestern Greece...
) |
| ५ |
5 |
(पञ्च) |
penki (LithuanianLithuanian is the official state language of Lithuania and is recognized as one of the official languages of the European Union. There are about 2.96 million native Lithuanian speakers in Lithuania and about 170,000 abroad. Lithuanian is a Baltic language, closely related to Latvian, although they...
) |
| ६ |
6 |
(षष्) |
seis (SpanishSpanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...
) |
| ७ |
7 |
(सप्त) |
şapte (RomanianRomanian Romanian Romanian (or Daco-Romanian; obsolete spellings Rumanian, Roumanian; self-designation: română, limba română ("the Romanian language") or românește (lit. "in Romanian") is a Romance language spoken by around 24 to 28 million people, primarily in Romania and Moldova...
) |
| ८ |
8 |
(अष्ट) |
astoņi (LatvianLatvian is the official state language of Latvia. It is also sometimes referred to as Lettish. There are about 1.4 million native Latvian speakers in Latvia and about 150,000 abroad. The Latvian language has a relatively large number of non-native speakers, atypical for a small language...
) |
| ९ |
9 |
(नव) |
nove (ItalianItalian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
)
|
Since Sanskrit is an
Indo-European languageThe Indo-European languages are a family of several hundred related languages and dialects, including most major current languages of Europe, the Iranian plateau, and South Asia and also historically predominant in Anatolia...
, it is obvious (as also seen from the table) that the words for numerals closely resemble those of
GreekGreek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
and
LatinLatin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
. The word "Shunya" for zero was translated into
ArabicArabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...
as "صفر" "sifr", meaning 'nothing' which became the term "zero" in many European languages from
Medieval LatinMedieval Latin was the form of Latin used in the Middle Ages, primarily as a medium of scholarly exchange and as the liturgical language of the medieval Roman Catholic Church, but also as a language of science, literature, law, and administration. Despite the clerical origin of many of its authors,...
,
zephirum (Arabic: sifr).
Indian classical language(s)
Arabic numeralsArabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Used in |
| Tamil numerals |
o |
௧ |
௨ |
௩ |
௪ |
௫ |
௬ |
௭ |
௮ |
௯ |
Tamil languageTamil is a Dravidian language spoken predominantly by Tamil people of the Indian subcontinent. It has official status in the Indian state of Tamil Nadu and in the Indian union territory of Pondicherry. Tamil is also an official language of Sri Lanka and Singapore...
|
| tyle= |
| Telugu numerals |
౦ |
౧ |
౨ |
౩ |
౪ |
౫ |
౬ |
౭ |
౮ |
౯ |
Telugu languageTelugu is a Central Dravidian language primarily spoken in the state of Andhra Pradesh, India, where it is an official language. It is also spoken in the neighbouring states of Chattisgarh, Karnataka, Maharashtra, Orissa and Tamil Nadu...
|
Note: The symbol for zero in Tamil is modern innovation. Unicode 4.1 and later define encodings for them.
Other modern Indian languages
The five Indian languages (
HindiStandard Hindi, or more precisely Modern Standard Hindi, also known as Manak Hindi , High Hindi, Nagari Hindi, and Literary Hindi, is a standardized and sanskritized register of the Hindustani language derived from the Khariboli dialect of Delhi...
,
MarathiMarathi is an Indo-Aryan language spoken by the Marathi people of western and central India. It is the official language of the state of Maharashtra. There are over 68 million fluent speakers worldwide. Marathi has the fourth largest number of native speakers in India and is the fifteenth most...
,
KonkaniKonkaniKonkani is a name given to a group of several cognate dialects spoken along the narrow strip of land called Konkan, on the west coast of India. This is, however, somewhat an over-generalisation. Geographically, Konkan is defined roughly as the area between the river Damanganga to the north...
,
NepaliNepali or Nepalese is a language in the Indo-Aryan branch of the Indo-European language family.It is the official language and de facto lingua franca of Nepal and is also spoken in Bhutan, parts of India and parts of Myanmar...
and
SanskritSanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
itself) that have adapted the Devanagari script to their use also naturally employ the numeral symbols above; of course, the names for the numbers vary by language. The table below presents a listing of the
symbols used in various modern Indian scripts for the numbers from zero to nine:
Arabic numeralsArabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Used in |
| Eastern Nagari(Ref) numerals |
০ |
১ |
২ |
৩ |
৪ |
৫ |
৬ |
৭ |
৮ |
৯ |
Bengali languageBengali or Bangla is an eastern Indo-Aryan language. It is native to the region of eastern South Asia known as Bengal, which comprises present day Bangladesh, the Indian state of West Bengal, and parts of the Indian states of Tripura and Assam. It is written with the Bengali script...
Assamese languageAssamese is the easternmost Indo-Aryan language. It is used mainly in the state of Assam in North-East India. It is also the official language of Assam. It is also spoken in parts of Arunachal Pradesh and other northeast Indian states. Nagamese, an Assamese-based Creole language is widely used in...
|
| Gujarati numerals |
૦ |
૧ |
૨ |
૩ |
૪ |
૫ |
૬ |
૭ |
૮ |
૯ |
Gujarati languageGujarati is an Indo-Aryan language, and part of the greater Indo-European language family. It is derived from a language called Old Gujarati which is the ancestor language of the modern Gujarati and Rajasthani languages...
|
| Marathi numerals |
० |
१ |
२ |
३ |
४ |
५ |
६ |
७ |
८ |
९ |
MarathiMarathi is an Indo-Aryan language spoken by the Marathi people of western and central India. It is the official language of the state of Maharashtra. There are over 68 million fluent speakers worldwide. Marathi has the fourth largest number of native speakers in India and is the fifteenth most...
, Sanskrit and Hindi languages |
| Gurmukhi numerals |
੦ |
੧ |
੨ |
੩ |
੪ |
੫ |
੬ |
੭ |
੮ |
੯ |
Punjabi languagePunjabi is an Indo-Aryan language spoken by inhabitants of the historical Punjab region . For Sikhs, the Punjabi language stands as the official language in which all ceremonies take place. In Pakistan, Punjabi is the most widely spoken language...
|
| Malayalam numerals |
൦ |
൧ |
൨ |
൩ |
൪ |
൫ |
൬ |
൭ |
൮ |
൯ |
Malayalam languageMalayalam , is one of the four major Dravidian languages of southern India. It is one of the 22 scheduled languages of India with official language status in the state of Kerala and the union territories of Lakshadweep and Pondicherry. It is spoken by 35.9 million people...
|
| Oriya numerals |
୦ |
୧ |
୨ |
୩ |
୪ |
୫ |
୬ |
୭ |
୮ |
୯ |
Oriya languageOriya , officially Odia from November, 2011, is an Indian language, belonging to the Indo-Aryan branch of the Indo-European language family. It is mainly spoken in the Indian states of Orissa and West Bengal...
|
| Lepcha numerals |
|
SikkimSikkim is a landlocked Indian state nestled in the Himalayan mountains...
and BhutanBhutan , officially the Kingdom of Bhutan, is a landlocked state in South Asia, located at the eastern end of the Himalayas and bordered to the south, east and west by the Republic of India and to the north by the People's Republic of China...
|
| ᱀ |
᱁ |
᱂ |
᱃ |
᱄ |
᱅ |
᱆ |
᱇ |
᱈ |
᱉ |
History
A decimal place system has been traced back to ca. 500 in India. Before that epoch, the
Brahmi numeralThe Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE . They are the direct graphic ancestors of the modern Indic and Hindu-Arabic numerals. However, they were conceptually distinct from these later systems, as they were not used as a positional system with a...
system was in use; that system did not encompass the concept of the place-value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as separate symbols for
hundred and
thousand.
The Indian place-system numerals spread to neighboring Persia, where they were picked up by the conquering
ArabArab people, also known as Arabs , are a panethnicity primarily living in the Arab world, which is located in Western Asia and North Africa. They are identified as such on one or more of genealogical, linguistic, or cultural grounds, with tribal affiliations, and intra-tribal relationships playing...
s. In 662, a Nestorian bishop living in what is now called
IraqIraq ; officially the Republic of Iraq is a country in Western Asia spanning most of the northwestern end of the Zagros mountain range, the eastern part of the Syrian Desert and the northern part of the Arabian Desert....
said:
I will omit all discussion of the science of the Indians ... of their subtle discoveries in astronomy - discoveries that are more ingenious than those of the Greeks and the Babylonians - and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe that because they speak Greek they have arrived at the limits of science would read the Indian texts they would be convinced even if a little late in the day that there are others who know something of value.
The addition of
zero0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
as a tenth positional digit is documented from the 7th century by
BrahmaguptaBrahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...
, though the earlier Bakhshali Manuscript, written sometime before the 5th century, also included zero. But it is in
Khmer numeralsKhmer numerals are characters used for writing numbers for several languages in Cambodia, most notably Cambodia's official language, Khmer. They date back to at least the oldest known epigraphical inscription of the Khmer numerals in 604 AD, found on a stele in Prasat Bayang, Cambodia, located not...
of modern
CambodiaCambodia , officially known as the Kingdom of Cambodia, is a country located in the southern portion of the Indochina Peninsula in Southeast Asia...
is where the first extant material evidence of zero as a numerical figure, dating its use back to the seventh century, is found.
As it was from the Arabs that the Europeans learned this system, the Europeans called them
Arabic numeralsArabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
; the Arabs refer to their numerals as
Indian numerals. In academic circles they are called the
Hindu-Arabic or
Indo-Arabic numerals.
The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:
It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity.
Tobias DantzigTobias Dantzig was a Baltic German Russian American mathematician, the father of George Dantzig, and the author of NUMBER: The Language of Science and Aspects of Science .Born in Latvia, Dantzig studied mathematics with Henri Poincaré in Paris...
, the father of
George DantzigGeorge Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....
had this to say in
Number:
This long period of nearly five thousand years saw the rise and fall of many civilizations, each leaving behind a heritage of literature, art, philosophy, and religion. But what was the net achievement in the field of reckoning, the earliest art practiced by man? An inflexible numeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even elementary calculations called for the services of an expert [...] Man used these devices for thousands of years without contributing a single important idea to the system [...] Even when compared with the slow growth of ideas during the dark ages, the history of reckoning presents a peculiar picture of desolate stagnation. When viewed in this light, the achievements of the unknown Hindu, who some time in the first centuries of our era discovered the principle of position, assumes the importance of a world event.
See also
- Western Arabic numerals
- Eastern Arabic numerals
The Eastern Arabic numerals are the symbols used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in the countries of the Arab world....
- Indian numbering system
The South Asian numbering system, used today in the Indian subcontinent , is based on grouping by two decimal places, rather than the three decimal places commonplace in most parts of the world. This system of measurement introduces separators into numbers in places appropriate to the two-digit...
- Khmer numerals
Khmer numerals are characters used for writing numbers for several languages in Cambodia, most notably Cambodia's official language, Khmer. They date back to at least the oldest known epigraphical inscription of the Khmer numerals in 604 AD, found on a stele in Prasat Bayang, Cambodia, located not...
- Thai numerals
Thai numerals constitute a numeral system of Thai number names for the Khmer numerals traditionally used in Thailand, also used for the more common Arabic numerals, and which follow the Hindu-Arabic numeral system.-Usage:...