# Chinese numerals

Chinese numerals are words and characters used to denote numbers in written Chinese.

Today, speakers of Chinese languages use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as Korean, Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials.[citation needed]

The other indigenous system consists of the Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in Hong Kong until the 1990s, but were gradually supplanted by Arabic numerals.

## Characters used as numerals

The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals. Similar to spelling-out numbers in English (e.g., "one thousand nine hundred forty-five"), it is not an independent system per se. Since it reflects spoken language, it does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not.

### Ordinary numerals

There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, ten thousands and hundred millions. There are two sets of characters for Chinese numerals: one for everyday writing, known as xiǎoxiě (小寫; 小写; 'small writing'), and one for use in commercial, accounting or financial contexts, known as dàxiě (大寫; 大写; 'big writing'). The latter arose because the characters used for writing numerals are geometrically simple, so simply using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could easily change the everyday characters 三十 (30) to 五千 (5000) just by adding a few strokes. That would not be possible when writing using the financial characters 參拾 (30) and 伍仟 (5000). They are also referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals". For the same reason, rod numerals were never used in commercial records.

Value Financial Ordinary Pinyin Jyutping Tai Lo Wugniu Notes
0 or líng ling4 khòng, lêng lin Usually is preferred, but in some areas, 〇 may be a more common informal way to represent zero. The original Chinese character is or , is referred as remainder something less than 1 yet not nil [說文] referred. The traditional is more often used in schools. In Unicode, 〇 is treated as a Chinese symbol or punctuation, rather than a Chinese ideograph.
1 jat1 it, ci̍t iq Also (obsolete financial), can be easily manipulated into ; 'two' or ; 'three'.
2 èr ji6 jī, nn̄g gni, er, lian Also (obsolete, financial), can be easily manipulated into ; 'one' or ; 'three'. Also ; .
3 sān saam1 sam, sann Also (obsolete financial), which can be easily manipulated into ; 'one' or ; 'two'.
4 sei3 sù, sì sy Also (obsolete financial).
5 ng5 ngóo, gōo ng
6 liù luk6 liok, la̍k loq
7 cat1 chit chiq
8 baat3 pat, peh paq
9 jiǔ gau2 kiú, káu cieu
10 shí sap6 si̍p, ca̍p zeq Although some people use as financial[citation needed], it is not ideal because it can be easily manipulated into ; 'five' or ; 'thousand'.
100 bǎi baak3 pek, pah paq
1,000 qiān cin1 chian, cheng chi
104 wàn maan6 bān ve Chinese numbers group by ten-thousands; see Reading and transcribing numbers below.
108 亿 jik1 ik i For variant meanings and words for higher values, see Large numbers below.

### Regional usage

Financial Normal Value Pinyin Standard alternative Notes
0 kòng Historically, the use of for 'zero' predates . This is now archaic in most varieties of Chinese, but it is still used in Southern Min.
0 dòng Literally 'a hole', is analogous to the shape of ⟨0⟩ and , it is used to unambiguously pronounce #0 in radio communication.
1 yāo Literally 'the smallest', it is used to unambiguously pronounce #1 in radio communication. This usage is not observed in Cantonese except for 十三幺, which refers to a special winning hand in mahjong.
1 shǔ In most Min varieties, there are two words meaning 'one'. For example, in Hokkien, chi̍t is used before a classifier: 'one person' is chi̍t ê lâng, not it ê lâng. In written Hokkien, is often used for both chi̍t and it, but some authors differentiate, writing for chi̍t and for it.
; 2 liǎng Used instead of before a classifier. For example, 'two people' is 两个人, not 二个人. However, in some lects such as Shanghainese, is the generic term used for two in most contexts, such as 四十兩 and not 四十二. It appears where 'a pair of' might in English, but is always used in such cases. It is also used for numbers, with usage varying from dialect to dialect, even person to person. For example, '2222' can be read as 二千二百二十二, 兩千二百二十二, or even 兩千兩百二十二 in Mandarin. It is used to unambiguously pronounce #2 in radio communication.
; 2 liǎ In regional dialects of Northeastern Mandarin, represents a "lazy" pronunciation of within the local dialect. It can be used as an alternative for 兩个; 'two of', e.g. 我们倆; wǒmen liǎ; 'the two of us', as opposed to 我们兩个; wǒmen liǎng gè. A measure word never follows .
3 In regional dialects of Northeastern Mandarin, represents a "lazy" pronunciation of three within the local dialect. It can be used as a general number to represent 'three', e.g.第仨号; dìsāhào; 'number three'; 星期仨; xīngqīsā; 'Wednesday', or as an alternative for 三个; 'three of', e.g. 我们仨; wǒmen sā; 'the three of us', as opposed to 我们三个; wǒmen sān gè). Regardless of usage, a measure word never follows .
7 guǎi Literally 'a turn' or 'a walking stick' and is analogous to the shape of ⟨7⟩ and , it is used to unambiguously pronounce #7 in radio communication.
9 gōu Literally 'a hook' and is analogous to the shape of ⟨9⟩, it is used to unambiguously pronounce #9 in radio communication.
10 In spoken Cantonese, (aa6) can be used in place of when it is used in the middle of a number, preceded by a multiplier and followed by a ones digit, e.g. 六呀三 '63', it is not used by itself to mean 10. This usage is not observed in Mandarin.

30 三十 A contraction of 三十. The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement (五卅運動). The spoken form is still used in various dialects of Chinese. In spoken Cantonese, ; saa1 can be used in place of 三十 when followed by another digit such as in numbers 31–39, a measure word (e.g. 卅個), a noun, or in phrases like 卅幾 'thirty-something'. It is not used by itself to mean 30. When spoken is pronounced as 卅呀; saa1-aa6. Thus 卅一 '31', is pronounced as saa1-aa6-jat1.
40 四十 A contraction of 四十. Found in historical writings written in Literary Chinese. Spoken form is still used in various dialects of Chinese, albeit very rare. See Reading and transcribing numbers section below. In spoken Cantonese ; sei3 can be used in place of 四十 when followed by another digit such as in numbers 41–49, a measure word (e.g. 卌個), a noun, or in phrases like 卌幾 'forty-something', it is not used by itself to mean 40. When spoken, is pronounced as 卌呀; sei3-aa6. Thus 卌一; 41, is pronounced as sei3-aa6-jat1.
200 二百 Very rarely used; one example is in the name of a library in Huzhou, 皕宋樓; Bìsòng Lóu.

### Large numbers

For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with unique names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu; 'Arithmetic in Five Classics'. In modern Chinese, only the second system is used, in which the same ancient names are used, but each represents a myriad, ; wàn times the previous:

Character Factor of increase
Character (S) 亿
Pinyin wàn zhào jīng gāi ráng gōu jiàn zhèng zǎi
Jyutping maan6 jik1 siu6 ging1 goi1 zi2 joeng4 kau1 gaan3 zing3 zoi2
Tai Lo bān ik tiāu king kai jiông koo kàn cèng cáinn
Shanghainese ve i zau cín tsy gnian kéu tsen tse
Alternative ; 𥝱
Rank 1 2 3 4 5 6 7 8 9 10 11 =n
"short scale"(下數) 104 105 106 107 108 109 1010 1011 1012 1013 1014 =10n+3

Each numeral is 10 (; shí) times the previous.

"myriad scale"(萬進, current usage) 104 108 1012 1016 1020 1024 1028 1032 1036 1040 1044 =104n

Each numeral is 10,000 (; ; wàn) times the previous.

"mid-scale" (中數) 104 108 1016 1024 1032 1040 1048 1056 1064 1072 1080 =108(n-1)

Starting with 亿, each numeral is 108 (万乘以万; 萬乘以萬; wàn chéngyǐ wàn; '10000 times 10000') times the previous.

"long scale"(上數) 104 108 1016 1032 1064 10128 10256 10512 101024 102048 104096 =102n+1

Each numeral is the square of the previous. This is similar to the -yllion system.

In practice, this situation does not lead to ambiguity, with the exception of ; zhào, which means 1012 according to the system in common usage throughout the Chinese communities as well as in Japan and Korea, but has also been used for 106 in recent years (especially in mainland China for megabyte). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿; wànyì) or ; tài; 'tera-' instead. Partly due to this, combinations of and 亿 are often used instead of the larger units of the traditional system as well, for example 亿亿; yìyì instead of . The ROC government in Taiwan uses ; zhào to mean 1012 in official documents.

### Large numbers from Buddhism

Numerals beyond zǎi come from Buddhist texts in Sanskrit, but are mostly found in ancient texts. Some of the following words are still being used today, but may have transferred meanings.

Character Pinyin Jyutping Tai Lo Shanghainese Value Notes
; gik1 ke̍k jiq5 1048 Literally 'extreme'.

### Small numbers

The following are characters used to denote small order of magnitude in Chinese historically. With the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse.

Characters Pinyin Value Notes
10−12 (Ancient Chinese)

corresponds to the SI prefix pico-.

miǎo 10−11 (Ancient Chinese)
āi 10−10 (Ancient Chinese)
; chén 10−9 Literally 'dust'

; (S) corresponds to the SI prefix nano-.

shā 10−8 Literally, "Sand"
; xiān 10−7 'fiber'
wēi 10−6 still used, corresponds to the SI prefix micro-.
10−5 (Ancient Chinese)
; 10−4 also .

háo 10−3 also .

still in use, corresponds to the SI prefix milli-.

10−2 also .

still in use, corresponds to the SI prefix centi-.

fēn 10−1 still in use, corresponds to the SI prefix deci-.

### Small numbers from Buddhism

Characters Pinyin Value Notes

; corresponds to the SI prefix yocto-.

; corresponds to the SI prefix zepto-.

### SI prefixes

In the People's Republic of China, the early translation for the SI prefixes in 1981 was different from those used today. The larger (, , , , ) and smaller Chinese numerals (, , , , ) were defined as translation for the SI prefixes as mega, giga, tera, peta, exa, micro, nano, pico, femto, atto, resulting in the creation of yet more values for each numeral.

The Republic of China (Taiwan) defined 百萬 as the translation for mega and as the translation for tera. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz".

Today, the governments of both China and Taiwan use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes. The following table lists the two different standards together with the early translation.

SI Prefixes
Value Symbol English Early translation PRC standard ROC standard
1030 Q quetta-   kūn kūn
1027 R ronna-   róng luó
1024 Y yotta-   yáo yòu
1021 Z zetta-   jiē
1018 E exa- ráng ài ài
1015 P peta- pāi pāi
1012 T tera- gāi tài zhào
109 G giga- jīng
106 M mega- zhào zhào 百萬 bǎiwàn
103 k kilo- qiān qiān qiān
102 h hecto- bǎi bǎi bǎi
101 da deca- shí shí shí
100 (base) one
10−1 d deci- fēn fēn fēn
10−2 c centi-
10−3 m milli- háo háo háo
10−6 µ micro- wēi wēi wēi
10−9 n nano- xiān nài
10−12 p pico- shā
10−15 f femto- chén fēi fēi
10−18 a atto- miǎo à à
10−21 z zepto-   jiè
10−24 y yocto-   yāo yōu
10−27 r ronto-   róu róng
10−30 q quecto-   kuī kuì

### Whole numbers

Multiple-digit numbers are constructed using a multiplicative principle; first the digit itself (from 1 to 9), then the place (such as 10 or 100); then the next digit.

In Mandarin, the multiplier (liǎng) is often used rather than ; èr for all numbers 200 and greater with the "2" numeral (although as noted earlier this varies from dialect to dialect and person to person). Use of both ; liǎng or ; èr are acceptable for the number 200. When writing in the Cantonese dialect, ; yi6 is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou (Teochew), (no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:

Number Structure Characters
Mandarin Cantonese Chaozhou Shanghainese
60 [6] [10] 六十 六十 六十 六十
20 [2] [10] or [20] 二十 二十 or 廿 二十 廿
200 [2] (èr or liǎng) [100] 二百 or 兩百 二百 or 兩百 兩百 兩百
2000 [2] (èr or liǎng) [1000] 二千 or 兩千 二千 or 兩千 兩千 兩千
45 [4] [10] [5] 四十五 四十五 or 卌五 四十五 四十五
2,362 [2] [1000] [3] [100] [6] [10] [2] 兩千三百六十二 二千三百六十二 兩千三百六十二 兩千三百六十二

For the numbers 11 through 19, the leading 'one' (; ) is usually omitted. In some dialects, like Shanghainese, when there are only two significant digits in the number, the leading 'one' and the trailing zeroes are omitted. Sometimes, the one before "ten" in the middle of a number, such as 213, is omitted. Thus:

Number Strict Putonghua Colloquial or dialect usage
Structure Characters Structure Characters
14 [10] [4] 十四
12000 [1] [10000] [2] [1000] 一萬兩千 [1] [10000] [2] 一萬二 or 萬二
114 [1] [100] [1] [10] [4] 一百一十四 [1] [100] [10] [4] 一百十四
1158 [1] [1000] [1] [100] [5] [10] [8] 一千一百五十八

Notes:

1. Nothing is ever omitted in large and more complicated numbers such as this.

In certain older texts like the Protestant Bible, or in poetic usage, numbers such as 114 may be written as [100] [10] [4] (百十四).

Outside of Taiwan, digits are sometimes grouped by myriads instead of thousands. Hence it is more convenient to think of numbers here as in groups of four, thus 1,234,567,890 is regrouped here as 12,3456,7890. Larger than a myriad, each number is therefore four zeroes longer than the one before it, thus 10000 × ; wàn = ; . If one of the numbers is between 10 and 19, the leading 'one' is omitted as per the above point. Hence (numbers in parentheses indicate that the number has been written as one number rather than expanded):

Number Structure Taiwan Mainland China
12,345,678,902,345(12,3456,7890,2345) (12) [1,0000,0000,0000] (3456) [1,0000,0000] (7890) [1,0000] (2345) 十二兆三千四百五十六億七千八百九十萬兩千三百四十五 十二兆三千四百五十六亿七千八百九十万二千三百四十五

In Taiwan, pure Arabic numerals are officially always and only grouped by thousands. Unofficially, they are often not grouped, particularly for numbers below 100,000. Mixed Arabic-Chinese numerals are often used in order to denote myriads. This is used both officially and unofficially, and come in a variety of styles:

Number Structure Mixed numerals
12,345,000 (1234) [1,0000] (5) [1,000] 1,234萬5千
123,450,000 (1) [1,0000,0000] (2345) [1,0000] 1億2345萬
12,345 (1) [1,0000] (2345) 1萬2345

Interior zeroes before the unit position (as in 1002) must be spelt explicitly. The reason for this is that trailing zeroes (as in 1200) are often omitted as shorthand, so ambiguity occurs. One zero is sufficient to resolve the ambiguity. Where the zero is before a digit other than the units digit, the explicit zero is not ambiguous and is therefore optional, but preferred. Thus:

Number Structure Characters
205 [2] [100] [0] [5] 二百零五
100,004(10,0004) [10] [10,000] [0] [4] 十萬零四
10,050,026(1005,0026) (1005) [10,000] (026) or (1005) [10,000] (26) 一千零五萬零二十六 or 一千零五萬二十六

### Fractional values

To construct a fraction, the denominator is written first, followed by ; fēn; 'part', then the literary possessive particle ; zhī; 'of this', and lastly the numerator. This is the opposite of how fractions are read in English, which is numerator first. Each half of the fraction is written the same as a whole number. For example, to express "two thirds", the structure "three parts of-this two" is used. Mixed numbers are written with the whole-number part first, followed by ; yòu; 'and', then the fractional part.

Fraction Structure
23

sān

3

fēn

parts

zhī

of this

èr

2

sān fēn zhī èr

3 parts {of this} 2

1532

sān

3

shí

10

èr

2

fēn

parts

zhī

of this

shí

10

5

sān shí èr fēn zhī shí wǔ

3 10 2 parts {of this} 10 5

13000

sān

3

qiān

1000

fēn

parts

zhī

of this

1

sān qiān fēn zhī yī

3 1000 parts {of this} 1

3 56

sān

3

yòu

and

liù

6

fēn

parts

zhī

of this

5

sān yòu liù fēn zhī wǔ

3 and 6 parts {of this} 5

Percentages are constructed similarly, using ; bǎi; '100' as the denominator. (The number 100 is typically expressed as 一百; yībǎi; 'one hundred', like the English 'one hundred'. However, for percentages, is used on its own.)

Percentage Structure
25%

bǎi

100

fēn

parts

zhī

of this

èr

2

shí

10

5

bǎi fēn zhī èr shí wǔ

100 parts {of this} 2 10 5

110%

bǎi

100

fēn

parts

zhī

of this

1

bǎi

100

1

shí

10

bǎi fēn zhī yī bǎi yī shí

100 parts {of this} 1 100 1 10

Because percentages and other fractions are formulated the same, Chinese are more likely than not to express 10%, 20% etc. as 'parts of 10' (or 1/10, 2/10, etc. i.e. 十分之一; shí fēnzhī yī, 十分之二; shí fēnzhī èr, etc.) rather than "parts of 100" (or 10/100, 20/100, etc. i.e. 百分之十; bǎi fēnzhī shí, 百分之二十; bǎi fēnzhī èrshí, etc.)

In Taiwan, the most common formation of percentages in the spoken language is the number per hundred followed by the word ; , a contraction of the Japanese パーセント; pāsento, itself taken from 'percent'. Thus 25% is 二十五趴; èrshíwǔ pā.

Decimal numbers are constructed by first writing the whole number part, then inserting a point (; ; diǎn), and finally the fractional part. The fractional part is expressed using only the numbers for 0 to 9, similarly to English.

Decimal expression Structure
16.98

shí

10

liù

6

diǎn

point

jiǔ

9

8

shí liù diǎn jiǔ bā

10 6 point 9 8

12345.6789

1

wàn

10000

liǎng

2

qiān

1000

sān

3

bǎi

100

4

shí

10

5

diǎn

point

liù

6

7

8

jiǔ

9

yī wàn liǎng qiān sān bǎi sì shí wǔ diǎn liù qī bā jiǔ

1 10000 2 1000 3 100 4 10 5 point 6 7 8 9

75.4025

7

shí

10

5

diǎn

point

4

líng

0

èr

2

5

qī shí wǔ diǎn sì líng èr wǔ

7 10 5 point 4 0 2 5

0.1

líng

0

diǎn

point

1

líng diǎn yī

0 point 1

; bàn; 'half' functions as a number and therefore requires a measure word. For example: 半杯水p=bàn bēi shuǐ; 'half a glass of water'.

### Ordinal numbers

Ordinal numbers are formed by adding ; ; 'sequence' before the number.

Ordinal Structure
1st

sequence

1

dì yī

sequence 1

2nd

sequence

èr

2

dì èr

sequence 2

82nd

sequence

8

shí

10

èr

2

dì bā shí èr

sequence 8 10 2

The Heavenly Stems are a traditional Chinese ordinal system.

### Negative numbers

Negative numbers are formed by adding ; ; before the number.

Number Structure
−1158

negative

1

qiān

1000

1

bǎi

100

5

shí

10

8

fù yī qiān yī bǎi wǔ shí bā

negative 1 1000 1 100 5 10 8

−3 5/6

negative

sān

3

yòu

and

liù

6

fēn

parts

zhī

of this

5

fù sān yòu liù fēn zhī wǔ

negative 3 and 6 parts {of this} 5

−75.4025

negative

7

shí

10

5

diǎn

point

4

líng

0

èr

2

5

fù qī shí wǔ diǎn sì líng èr wǔ

negative 7 10 5 point 4 0 2 5

### Usage

Chinese grammar requires the use of classifiers (measure words) when a numeral is used together with a noun to express a quantity. For example, "three people" is expressed as ; ; sān ge rén, "three (ge particle) person", where / ge is a classifier. There exist many different classifiers, for use with different sets of nouns, although / is the most common, and may be used informally in place of other classifiers.

Chinese uses cardinal numbers in certain situations in which English would use ordinals. For example, 三楼/三樓; sān lóu (literally "three story/storey") means "third floor" ("second floor" in British § Numbering). Likewise, 二十一世纪/二十一世紀; èrshí yī shìjì (literally "twenty-one century") is used for "21st century".

Numbers of years are commonly spoken as a sequence of digits, as in 二零零一; èr líng líng yī ("two zero zero one") for the year 2001. Names of months and days (in the Western system) are also expressed using numbers: ; yīyuè ("one month") for January, etc.; and 星期; xīngqīyī ("week one") for Monday, etc. There is only one exception: Sunday is 星期日; xīngqīrì, or informally 星期天; xīngqītiān, both literally "week day". When meaning "week", "星期" xīngqī and "禮拜; 礼拜" lǐbài are interchangeable. "禮拜天" lǐbàitiān or "禮拜日" lǐbàirì means "day of worship". Chinese Catholics call Sunday "主日" zhǔrì, "Lord's day".

Full dates are usually written in the format 2001年1月20日 for January 20, 2001 (using ; nián "year", ; yuè "month", and ; "day") – all the numbers are read as cardinals, not ordinals, with no leading zeroes, and the year is read as a sequence of digits. For brevity the nián, yuè and may be dropped to give a date composed of just numbers. For example "6-4" in Chinese is "six-four", short for "month six, day four" i.e. June Fourth, a common Chinese shorthand for the 1989 Tiananmen Square protests (because of the violence that occurred on June 4). For another example 67, in Chinese is sixty seven, short for year nineteen sixty seven, a common Chinese shorthand for the Hong Kong 1967 leftist riots.

## Counting rod and Suzhou numerals

In the same way that Roman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the rod numerals, which is a positional system. The Suzhou numerals (simplified Chinese: 苏州花码; traditional Chinese: 蘇州花碼; pinyin: Sūzhōu huāmǎ) system is a variation of the Southern Song rod numerals. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.

## Hand gestures

There is a common method of using of one hand to signify the numbers one to ten. While the five digits on one hand can easily express the numbers one to five, six to ten have special signs that can be used in commerce or day-to-day communication.

## Historical use of numerals in China

Most Chinese numerals of later periods were descendants of the Shang dynasty oracle numerals of the 14th century BC. The oracle bone script numerals were found on tortoise shell and animal bones. In early civilizations, the Shang were able to express any numbers, however large, with only nine symbols and a counting board though it was still not positional.

Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 became part of the system of rod numerals.

In this system, horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that "one is vertical, ten is horizontal".

7 1 8 2 4

The counting rod numerals system has place value and decimal numerals for computation, and was used widely by Chinese merchants, mathematicians and astronomers from the Han dynasty to the 16th century.

In 690 AD, Wu Zetian promulgated Zetian characters, one of which was . The word is now used as a synonym for the number zero.

Alexander Wylie, Christian missionary to China, in 1853 already refuted the notion that "the Chinese numbers were written in words at length", and stated that in ancient China, calculation was carried out by means of counting rods, and "the written character is evidently a rude presentation of these". After being introduced to the rod numerals, he said "Having thus obtained a simple but effective system of figures, we find the Chinese in actual use of a method of notation depending on the theory of local value [i.e. place-value], several centuries before such theory was understood in Europe, and while yet the science of numbers had scarcely dawned among the Arabs."

During the Ming and Qing dynasties (after Arabic numerals were introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After the Qing period, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.

## Cultural influences

Traditional Chinese numeric characters are also used in Japan and Korea and were used in Vietnam before the 20th century. In vertical text (that is, read top to bottom), using characters for numbers is the norm, while in horizontal text, Arabic numerals are most common. Chinese numeric characters are also used in much the same formal or decorative fashion that Roman numerals are in Western cultures. Chinese numerals may appear together with Arabic numbers on the same sign or document.