In
linguistics,
number
names (or
numerals) are specific
words in a
natural
language that
represent numbers.
In
writing, numerals are symbols
also representing numbers.
Numeral types
In
linguistics, the terms representing
numbers can be classified according to their use:
 Cardinal
numerals: describe quantity  one, two,
three, etc.
 Ordinal
numerals: describe position in a sequential order 
first, second, third, etc.; the terms
next and last may also be considered a kind of
ordinals.
 Partitive numerals: describe division into
fractions  half, third, quarter,
etc.
 Multiplicative numerals: describe repetition 
once, twice, thrice, etc.
 Collective numerals: describe groups or
entities composed of several parts  single,
double, triple, etc.
 Distributive numerals: describe dividing and
assigning in portions  in pairs, by the dozen.
Note that the English language does not have distinct distributive
numerals (though it does have distributive adjectives/pronouns,
such as each, either and every), but
some other languages such as Georgian and Latin do have them; e.g.,
Latin singuli ("one by one"), bini ("in pairs",
"by twos"), terni ("three each"), etc. (whence the English
terms singular, binary, ternary,
etc.).
Basis of counting system
Not all peoples count. Specifically, there is not much need for
counting among huntergatherers who do not engage in commerce. Many
languages around the world have no numerals above two to four,—or
at least didn't before contact with the colonial societies,—and
speakers of these languages may have no tradition of using the
numerals they did have for counting. Indeed, several languages from
the Amazon have been independently reported to have no numerals
other than 'one'; it's arguable that such a system should not be
considered a separate word class of 'numeral' at all. These include
Nadëb, precontact
Mocoví and
Pilagá,
Culina and precontact
Jarawara,
Jabutí,
CanelaKrahô,
Botocudo ,
Chiquitano, the
Campa languages,
Arabela, and
Achuar.
4: quaternary
Some
Austronesian and Melanesian ethnic groups, including the Maori, some Sulawesi and some
Papua New
Guineans count
instead of by five, using the base number four, using the term
asu and aso (derived from Javanese asu: dog) as
the ubiquitous village dog has four legs. This is argued by
anthropologists to be also based on early humans noting the human
and animal shared body feature of two arms and two legs as well as
its ease in simple arithmetic and counting.As an example of the
system's ease a realistic scenario could include a farmer returning
form the market with fifty
asu heads of pig (200), less 30
asu (120) of pig bartered for 10
asu (40) of
goats noting his new pig count total as twenty
asu: 80 pigs
remaining. The system has a correlation to the
dozen counting system and is still in common use in
these areas as a natural and easy method of simple
arithmetic.
5: quinary
Quinary systems are based on the number 5.
Anthropologists argue it is almost certain quinary system developed
from counting by fingers (five fingers per hand). It is common
since the days of the ancient
Babylonians
and found in almost every culture worldwide. It is present in the
Celtic and
Banish
systems and the
Inuit languages.The
ancient Greek Bëotius records that the term
digit is exactly that as used to describe fingers
still present today.
8: octal
Octal is a counting system based around the
number 8.
It is used in the Yuki language of California and in the Pamean
languages of Mexico, because the
Yuki and Pamean
keep count by using the four spaces between their fingers rather
than the fingers (five) themselves.
10: decimal
A majority of traditional number systems are based on the
decimal numeral
system. Anthropologists hypothesize this may be due to humans
having five fingers per hand, ten in total. There are many regional
variations including:
Historically, its use was first employed by the ancient
Egyptians, who invented a wholly decimal system,
and later extended by the
Babylonians
and also a system of pictorial representation, substituting letters
and other reminders with symbols.
English farmer coined the term
notch: defined as ten. from the
tally
sticks of the
livestock a full deep
score for every twenty, a half score
or notch
pret half score or ten.
12: duodecimal
Duodecimal numbers or systems based
around the base unit of 12, are a frequent occurrence.
These include:
Duodecimal numeric system have some practical advantages over
decimal. It is much easier to divide the base digit
twelve (which is a
highly composite number) by many
important
divisors in
market and trade settings, such as the numbers
2,
3,
4 and
6. It is still common usage and is found in idiom.
For example, "A
dime a dozen" refers to
something so common or numerous as to be of little worth or
noteworthiness.
The system of basing counting on the number 12, is widespread,
across many cultures.Examples include:
 time divisions (twelve months in a year, the twelvehour
clock)
 measurement imperial system
of units (twelve inches to the foot, twelve Troy ounces to the
Troy pound)
 traditional British monetary system (twelve pence to the shilling)
Consequently, languages evolved or loaned terms such
dozen,
gross
and
great gross, which allow
for rudimentary and arguably immediately comprehensible duodecimal
nomenclature (e.g., stating: "two gross
and six
dozen" instead of "three hundred and
sixty").
Ancient Romans used decimal
for
integers, but switched to
duodecimal for
fractions, and correspondingly
Latin developed a rich vocabulary for duodecimalbased
fractions (see
Roman
numerals). A notably novel and invented system of duodecimal
was
J. R. R.
Tolkien's
Elvish languages who used duodecimal as
well as decimal.
20: vigesimal
Vigesimal numbers use the number
20 as the base number for counting. Anthropologists are
convinced the system originated from digit counting, as did bases
five and ten  twenty being the number of human fingers and toes
combinedThe system is in widespread use across the world. Some
include the classical
Mesoamerican
cultures, still in use today in the modern indigenous languages of
their descendants, namely the
Nahuatl and
Mayan languages (see also
Maya numerals).Vigesimal terminology is also
found in some European languages:
Basque,
Celtic
languages,
French (from Celtic
languages),
Danish and
Georgian.The term
score originates from
tally
sticks, where taxmen and farmers would groove
a
notch for every ten, and a full score for every
twenty.The English term
score, now rarely used, is a
remnant of vigesimal numeration in the word
score. It was widely used to learn the
predecimal British currency in this idiom: "a dozen pence and a
score of
bob" , referring
to the 20 shillings in a
pound_sterling. For
Americans the term is most known from the opening of the
Gettysburg Address:
"Four score and
seven years ago, our Forefathers...".
For very large (and very small) numbers, traditional systems have
been superseded by the use of
scientific notation and the system of
SI prefixes. Traditional systems continue
to be used in everyday life.
Numeral symbols
The numbers one through ten in different numeral
systems
Arabic 
١ 
٢ 
٣ 
٤ 
٥ 
٦ 
٧ 
٨ 
٩ 
١٠ 
Bangla (Bengali) 
১ 
২ 
৩ 
৪ 
৫ 
৬ 
৭ 
৮ 
৯ 
১০ 
Chinese 
一 
二 
三 
四 
五 
六 
七 
八 
九 
十 
Devanagari 
१ 
२ 
३ 
४ 
५ 
६ 
७ 
८ 
९ 
१० 
Classical Greek (note: all written
^{} above letters) 
α 
β 
γ 
δ 
ε 
ζ 
η 
θ 
ι 
κ 
Hebrew 
א 
ב 
ג 
ד 
ה 
ו 
ז 
ח 
ט 
י 
West Arabic 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Malayalam 
൧ 
൨ 
൩ 
൪ 
൫ 
൬ 
൭ 
൮ 
൯ 
൧൦ 
Phoenician 
A 
B 
┌ 
Δ 
E 
ζ 
Z 
H 
θ 
I 
Roman 










Suzhou 
〡 
〢 
〣 
〤 
〥 
〦 
〧 
〨 
〩 
〡〇 
Tamil 
௧ 
௨ 
௩ 
௪ 
௫ 
௬ 
௭ 
௮ 
௯ 
௰ 
Thai 
๑ 
๒ 
๓ 
๔ 
๕ 
๖ 
๗ 
๘ 
๙ 
๑๐ 
Counting aids
Counting aids, especially the use of body parts (counting on
fingers), were certainly used in prehistoric times as today. There
are many variations. Besides counting 10 fingers, some cultures
have counted knuckles, the space between fingers, and toes as well
as fingers. The
Oksapmin culture of New
Guinea uses a system of 27 upper body locations to represent
numbers.
To preserve numerical information,
tallies carved in wood, bone, and stone have
been used since prehistoric times. Stone age cultures, including
ancient
American Indian groups, used
tallies for gambling, personal services, and tradegoods.
A method of preserving numeric information in clay was invented by
the
Sumerians between 8000 and 3500 BCE.
This was done with small clay tokens of various shapes that were
strung like beads on a string. Beginning about 3500 BCE clay tokens
were gradually replaced by number signs impressed with a round
stylus at different angles in clay tablets (originally containers
for tokens) which were then baked. About 3100 BCE written numbers
were dissociated from the things being counted and became abstract
numerals.
Between 2700 BCE and 2000 BCE in Sumer, the round stylus was
gradually replaced by a reed stylus that was used to press
wedgeshaped cuneiform signs in clay. These cuneiform number signs
resembled the round number signs they replaced and retained the
additive
signvalue notation of
the round number signs. These systems gradually converged on a
common
sexagesimal number system; this
was a placevalue system consisting of only two impressed marks,
the vertical wedge and the chevron, which could also represent
fractions. This sexagesimal number system was fully developed at
the beginning of the Old Babylonia period (about 1950 BC) and
became standard in Babylonia.
Sexagesimal numerals were a
mixed radix system that retained the alternating
base 10 and base 6 in a sequence of cuneiform vertical wedges and
chevrons. By 1950 BCE this was a
positional notation system. Sexagesimal
numerals came to be widely used in commerce, but were also used in
astronomical and other calculations. This system was exported from
Babylonia and used throughout Mesopotamia, and by every
Mediterranean nation that used standard Babylonian units of measure
and counting, including the Greeks, Romans and Egyptians.
Babylonianstyle sexagesimal numeration is still used in modern
societies to measure
time (minutes per hour)
and
angles (degrees).
In
China, armies and provisions were counted using modular
tallies of prime numbers. Unique
numbers of troops and measures of rice appear as unique
combinations of these tallies. A great convenience of
modular arithmetic is that it is easy to
multiply, though quite difficult to add. This makes use of modular
arithmetic for provisions especially attractive. Conventional
tallies are quite difficult to multiply and divide. In modern times
modular arithmetic is sometimes used in
Digital signal processing.
The oldest Greek system was the that of the
Attic numerals, but in the 4th century BC
they began to use a quasidecimal alphabetic system (see
Greek numerals). Jews began using a similar
system (
Hebrew numerals), with the
oldest examples known being coins from around 100 BC.
The Roman empire used tallies written on wax, papyrus and stone,
and roughly followed the Greek custom of assigning letters to
various numbers. The
Roman numerals
system remained in common use in Europe until
positional notation came into common use
in the 1500s.
The
Maya of Central America used a
mixed base 18 and base 20 system, possibly inherited from the
Olmec, including advanced features such as
positional notation and a
zero. They used
this system to make advanced astronomical calculations, including
highly accurate calculations of the length of the solar year and
the orbit of
Venus.
The Incan Empire ran a large command economy using
quipu, tallies made by knotting colored fibers.
Knowledge
of the encodings of the knots and colors was suppressed by the
Spanish conquistadors in the
16th century, and has not survived although simple quipulike
recording devices are still used in the Andean
region.
Some authorities believe that positional arithmetic began with the
wide use of
counting rods in China.
The earliest written positional records seem to be
rod calculus results in China around 400. In
particular, zero was correctly described by Chinese mathematicians
around 932.
The modern
positional Arabic numeral system was developed by mathematicians in India, and passed on to
Muslim mathematicians, along
with astronomical tables brought to Baghdad by an Indian
ambassador around 773.
From
India, the thriving trade between Islamic sultans and
Africa carried the concept to Cairo.
Arabic mathematicians extended the system to include
decimal fractions, and wrote an important work about
it in the 9th century. The modern
Arabic
numerals were introduced to Europe with the translation of this
work in the 12th century in Spain and
Leonardo of Pisa's
Liber Abaci of
1201. In Europe, the complete Indian system with the zero was
derived from the Arabs in the 12th century.{{citation]]
The
binary system (base 2),
was propagated in the 17th century by
Gottfried Leibniz. Leibniz had developed
the concept early in his career, and had revisited it when he
reviewed a copy of the
I ching from China.
Binary numbers came into common use in the 20th century because of
computer applications.
Numerals in most popular systems
West Arabic 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
East Arabic 
٠ 
١ 
٢ 
٣ 
٤ 
٥ 
٦ 
٧ 
٨ 
٩ 
Asomiya (Assamese) 
০ 
১ 
২ 
৩ 
৪ 
৫ 
৬ 
৭ 
৮ 
৯ 
Bengali 
০ 
১ 
২ 
৩ 
৪ 
৫ 
৬ 
৭ 
৮ 
৯ 
Chinese
(everyday) 
〇 
一 
二 
三 
四 
五 
六 
七 
八 
九 
Chinese
(formal) 
零 
壹 
贰/貳 
叁/叄 
肆 
伍 
陆/陸 
柒 
捌 
玖 
Chinese
(Suzhou) 
〇 
〡 
〢 
〣 
〤 
〥 
〦 
〧 
〨 
〩 
Devanagari 
० 
१ 
२ 
३ 
४ 
५ 
६ 
७ 
८ 
९ 
Ge'ez
(Ethiopic) 

፩ 
፪ 
፫ 
፬ 
፭ 
፮ 
፯ 
፰ 
፱ 
Gujarati 
૦ 
૧ 
૨ 
૩ 
૪ 
૫ 
૬ 
૭ 
૮ 
૯ 
Gurmukhi 
੦ 
੧ 
੨ 
੩ 
੪ 
੫ 
੬ 
੭ 
੮ 
੯ 
Kannada 
೦ 
೧ 
೨ 
೩ 
೪ 
೫ 
೬ 
೭ 
೮ 
೯ 
Khmer 
០ 
១ 
២ 
៣ 
៤ 
៥ 
៦ 
៧ 
៨ 
៩ 
Lao 
໐ 
໑ 
໒ 
໓ 
໔ 
໕ 
໖ 
໗ 
໘ 
໙ 
Limbu 
᥆ 
᥇ 
᥈ 
᥉ 
᥊ 
᥋ 
᥌ 
᥍ 
᥎ 
᥏ 
Malayalam 
൦ 
൧ 
൨ 
൩ 
൪ 
൫ 
൬ 
൭ 
൮ 
൯ 
Mongolian 
᠐ 
᠑ 
᠒ 
᠓ 
᠔ 
᠕ 
᠖ 
᠗ 
᠘ 
᠙ 
Burmese 
၀ 
၁ 
၂ 
၃ 
၄ 
၅ 
၆ 
၇ 
၈ 
၉ 
Oriya 
୦ 
୧ 
୨ 
୩ 
୪ 
୫ 
୬ 
୭ 
୮ 
୯ 
Roman 

I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
Tamil 
௦ 
௧ 
௨ 
௩ 
௪ 
௫ 
௬ 
௭ 
௮ 
௯ 
Telugu 
౦ 
౧ 
౨ 
౩ 
౪ 
౫ 
౬ 
౭ 
౮ 
౯ 
Thai 
๐ 
๑ 
๒ 
๓ 
๔ 
๕ 
๖ 
๗ 
๘ 
๙ 
Tibetan 
༠ 
༡ 
༢ 
༣ 
༤ 
༥ 
༦ 
༧ 
༨ 
༩ 
Urdu 
۰ 
۱ 
۲ 
۳ 
۴ 
۵ 
۶ 
۷ 
۸ 
۹ 
Additional numerals

10 
20 
30 
40 
100 
1000 
10000 
10^{8} 
10^{12} 
Chinese
(simple) 
十 
廿 
卅 
卌 
百 
千 
万 
亿 
兆 
Chinese
(complex) 
拾 



佰 
仟 
萬 
億 
兆 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
10000 
Ge'ez
(Ethiopic) 
፲ 
፳ 
፴ 
፵ 
፶ 
፷ 
፸ 
፹ 
፺ 
፻ 
፼ 
See also
Numerals in various languages
Numeral notation in various scripts
Related topics
Notes
 LinguaLinks Library
 Walsinfo.com
 Hammarström (2006) "Rarities in numeral
systems"
 Ryan, Peter. Encyclopaedia of Papua and New Guinea.
Melbourne University Press & University of Papua and New
Guinea,:1972 ISBN 0522840256.: 3 pages pp219.
 Aleksandr Romanovich Luriicac, Lev Semenovich Vygotskiĭ, Evelyn
Rossiter. Ape, primitive man, and child: essays in the history
of behavior . CRC Press: 1992: ISBN 1878205439: 171 pages
 Heath, Thomas, A Manual of Greek Mathematics, Courier
Dover: 2003. ISBN 0486432319 576 page, p:11
 Georges Ifrah, The Universal History of Numbers: The Modern
Number System, Random House, 2000: ISBN 1860467911: 1262
pages
 Scientific American Munn& Co: 1968, vol 219:
219
 Karl Menninger, Paul Broneer, Number Words and Number
Symbols Courier Dover Publications: 1992: ISBN 0486270963: 480
pages