Numbers in Chinese: Mandarin Numerals from 0 to Billions

How do you count from 0 to 10 in Chinese?

In Mandarin Chinese the numbers 0 to 10 are 零 (líng), 一 (yī), 二 (èr), 三 (sān), 四 (sì), 五 (wǔ), 六 (liù), 七 (qī), 八 (bā), 九 (jiǔ) and 十 (shí). Each one is a single character, and each is said with one of the four tones of Mandarin, which the marks above the pinyin letters show.

Pinyin is the standard way of writing Mandarin sounds with the Latin alphabet. Mandarin has four tones — high and level (ā), rising (á), dipping (ǎ) and falling (à) — and a neutral tone, and a different tone is a different word: sì (4, falling) and sǐ (death, dipping) differ only in tone. The marks are not decoration; learn each number with its tone.

How do the numbers 11 to 99 work in Chinese?

Numbers from 11 to 99 are built by saying the tens first and the ones second: 十一 is "ten-one" (11), 二十 is "two-ten" (20) and 三十五 is "three-ten-five" (35). There is nothing to memorize beyond 零 to 十 and one rule: for 10 to 19 say 十 and then the digit, and for 20 to 99 say the tens digit, then 十, then the ones digit (leave it out when it is 0).

Compare this with English, which has the special words eleven, twelve, thirteen and twenty, and with Indonesian, where 11 is sebelas and 12 is dua belas (belas marks the teens) and 20 is dua puluh. Chinese has no such exceptions at all.

Researchers have linked such regular names to how children learn to count. In a 1995 study by Miller and colleagues, Chinese-speaking children counted further than American children of the same age, and the difference showed mainly in the numbers beyond ten, where English names stop being regular.

How do you say hundreds, thousands and zero in Chinese?

Hundreds and thousands use the place words 百 (bǎi) and 千 (qiān) after the digit, and a gap of zeros is read as a single 零 (líng): 105 is 一百零五. Unlike 十, the words 百 and 千 always need their digit, so 100 is 一百 and never just 百.

The zero rule. Say 零 once for each gap of one or more zeros that sits between two non-zero digits. Never say it for zeros at the end of a number: 1,000 is 一千, not "一千零".

Two words for 2. Use 二 (èr) when 2 is a digit or the last digit of a group (二十, 十二, 第二). Use 两 (liǎng) when a lone 2 comes before 千, 万 or 亿 (两千, 两万, 两亿) and before a measure word (两个人, "two people"). Before 百 both are heard: 二百 and 两百.

In speech the last unit is often dropped. 一百五 usually means 150 (一百五十) and 三千五 means 3,500. That is why 105 must keep its 零: 一百零五 is 105, but 一百五 is 150.

Why does Chinese count in 万 and 亿 instead of thousands and millions?

Chinese groups digits in fours, not threes: after 千 (1,000) the next new word is 万 (wàn, 10,000), and the next after that is 亿 (yì, 100,000,000). English, Indonesian and most European languages add a new word every three digits (thousand, million, billion). Chinese adds one every four, so a number is a short list of numbers up to 9999, each followed by 万 or 亿.

The two systems agree only at 10 to the power 12, where 万亿 (10,000 × 100,000,000) is one trillion. In between, a speaker has to translate: "100,000" is not "a hundred thousand" but "ten wàn". The scholars' word myriad for 10,000 is the same unit as 万.

A quick way to read any number. Count the digits from the right in fours. The first four are the plain group, the next four are the 万 group, and the next four are the 亿 group. The widget below shows both groupings at once.

How do you write any number in Chinese, step by step?

To write a number in Chinese, split its digits into groups of four from the right, read each group with 千 百 十, put 亿 or 万 after the groups, and say 零 once for each gap of zeros. Take 20,508,030:

1. Write the digits and cut them into groups of four from the right: 2050 | 8030.
2. Read each group as a number up to 9999 with 千, 百 and 十. 2050 is 两千零五十 and 8030 is 八千零三十.
3. Put 万 after the second group from the right and 亿 after the third. The last group has no unit: 两千零五十万 八千零三十.
4. Say 零 once for each gap of zeros, including a gap between groups (when a group starts below 1,000, or a whole group is empty).
5. Check the special cases: 两 for a lone 2 before 千, 万 or 亿; drop the 一 only before a leading 十 (十, 十一, 十万); and do not read zeros at the end.

So 20,508,030 is 两千零五十万八千零三十 (liǎng qiān líng wǔ shí wàn bā qiān líng sān shí). Try your own numbers below, and switch between simplified, traditional and formal writing.

How can you practice reading Chinese numbers?

To read a Chinese number, find 亿 and 万, read each part as a number up to 9999, and write each part with four digits. Reading is the writing steps run backward:

1. Find 亿 and 万 in the number and cut it after each of them.
2. Read each part on its own: 千 is thousands, 百 hundreds, 十 tens, and what is left is the ones.
3. Write every part except the first with four digits, putting zeros in front where needed (零 tells you a place is empty).
4. Join the parts. For example 两千零五十万八千零三十 is 2050 | 8030, which is 20,508,030.

Practice with the widget below: eight numbers of growing size, with pinyin on request. The wrong answers are the mistakes people really make — a place too many or too few, two digits swapped, one digit off.

How do you say fractions, decimals, percentages, years and phone numbers?

Fractions, decimals, percentages, negatives and ordinals follow fixed patterns built from the same number words, while years and phone numbers are read digit by digit.

A fraction is said "of three parts, one": 三分之一 means "one of three parts". A percentage is "of a hundred parts": 百分之五十 is 50%. The digits after 点 are never grouped: 3.14 is "three point one four", never "three point fourteen".

A year is a label, not a quantity, so it is read as separate digits and written with 〇 (or 零): 二〇二五年. The quantity "two thousand and twenty-five" would be 两千零二十五.

What are the formal Chinese numerals 壹, 贰, 叁?

Formal Chinese numerals (大写数字, dàxiě shùzì) are a second set of characters for the same numbers, used on checks, receipts and contracts because they are hard to alter. The ordinary 一 can become 三 with one stroke, and 十 can become 千; 壹 and 叁 cannot.

The reading rules are the same, with two differences: the formal form of 2 is always 贰 (never 两), and 10 is written 壹拾 with its 壹 kept. A check for 1,205 yuan reads 壹仟贰佰零伍元整 (yī qiān èr bǎi líng wǔ yuán zhěng), where 整 means "exactly", closing the amount so nothing can be added after it. The converter above has a formal setting.

This is the same idea as writing an amount in words on a check in English or Indonesian.

What are Chinese counting rods and Suzhou numerals?

Counting rods (算筹, suànchóu) were small sticks of bamboo, bone or ivory laid out in columns on a flat surface to calculate; they form an early decimal place-value system in which an empty place is a gap. Bundles of rods have been found in tombs of the Han dynasty (206 BCE to 220 CE), and the Sunzi suanjing, written between the 3rd and 5th centuries CE, describes how the digits are laid out. The rods were gradually replaced by the abacus (算盘, suànpán), which was widespread by the Ming dynasty (1368 to 1644).

How a number is laid out:

• Each place gets its own column, with the highest place on the left, exactly like written digits.
• The digits 1 to 5 are that many rods. For 6 to 9, one rod laid across stands for 5, and the remaining rods are added to it.
• The direction alternates from place to place: rods stand upright in the ones, hundreds and ten-thousands places and lie flat in the tens, thousands and hundred-thousands places, so two neighboring digits are never mixed up.
• Zero is an empty column. A written circle for zero appears in Chinese mathematical books by the 13th century, for example in Qin Jiushao's Shùshū Jiǔzhāng (1247).
• Red rods are positive and black rods negative in the Nine Chapters on the Mathematical Art, so a column of rods can hold a debt: see the history of negative numbers in the article on integers.

Suzhou numerals (苏州码子, Sūzhōu mǎzi) are the written shorthand that grew out of the rods, long used by traders and still seen on some market price tags: 〇 〡 〢 〣 〤 〥 〦 〧 〨 〩 for 0 to 9. The widget draws the rods for a number beside its Suzhou numerals.

Why are some numbers lucky or unlucky in Chinese?

Numbers are lucky or unlucky in Chinese because of how they sound: a number that sounds like a good word is lucky, and one that sounds like a bad word is avoided. The meaning comes from the sound, not from the number.

The Beijing Summer Olympics opened on 8 August 2008 at 8:08 pm, a date and time chosen for all those eights.

How do you show numbers with one hand in China?

Chinese speakers show the numbers 1 to 10 with one hand, using a sign for each number that does not depend on language, which lets a market seller and a buyer agree a price across a noisy street. These are common signs; details vary by region and by person.

The sign for 10 draws the character itself: two crossing lines, 十.

What are the common mistakes with Chinese numbers?

The most common mistakes with Chinese numbers are the seven below, each with the correct form.

Practice: test your understanding

These questions mix everything above. A wrong answer costs nothing here: read the hint and try again.

Summary: Chinese numbers at a glance

• 0 to 10 are 零 一 二 三 四 五 六 七 八 九 十; 11 to 99 are the digits joined with 十 (十一, 二十, 三十五).
• Hundreds and thousands use 百 and 千 after the digit; 100 is 一百, never 百.
• Zero: say 零 once per gap of zeros, including across 万 and 亿; never for zeros at the end.
• Two: 二 as a digit, 两 before 千, 万, 亿 and measure words; 二百 and 两百 are both heard.
• Groups of four: 万 is 10,000 and 亿 is 100,000,000, so 100,000 is 十万 and one billion is 十亿.
• Patterns: 三分之一 (1/3), 百分之五十 (50%), 第三 (3rd), 负五 (−5); years and phone numbers are digit by digit.
• Formal numerals 壹 贰 叁 … are for checks and contracts; counting rods and Suzhou numerals are older written systems with zero left empty.

Glossary: key terms

Pinyin

The standard system for writing the sounds of Mandarin with the Latin alphabet and tone marks, such as sān for 3.

Tone

The pitch pattern of a Mandarin syllable; there are four tones and a neutral tone, and changing the tone changes the word.

Hanzi (汉字)

The Chinese characters; each number word is written with one character, such as 三 for 3.

万 (wàn)

The Chinese word for 10,000, the unit that follows 千 and that groups digits in fours.

亿 (yì)

The Chinese word for 100,000,000, ten thousand times 万.

零 (líng)

Zero; it is also read once for each gap of zeros between two non-zero digits.

两 (liǎng)

The form of 2 used for quantities and before 千, 万 and 亿 instead of 二.

Formal numerals (大写)

A second set of characters for numbers, such as 壹 贰 叁, used on checks and contracts because they are hard to alter.

Counting rods (算筹)

Small sticks laid out in columns to calculate, an early decimal place-value system in which zero is an empty place.

Suzhou numerals

A written shorthand derived from counting rods, used by traders, with 〡 to 〩 for 1 to 9 and 〇 for 0.

Myriad

An older English word for 10,000, the same unit as 万.

Place value

The principle that a digit is worth more or less depending on where it stands in the number.

Frequently asked questions

References

1. Georges Ifrah (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. John Wiley & Sons.
2. Joseph Needham (1959). Science and Civilisation in China, Volume 3: Mathematics and the Sciences of the Heavens and the Earth. Cambridge University Press.
3. Lam Lay Yong and Ang Tian Se (1992). Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. World Scientific.
4. Jean-Claude Martzloff (1997). A History of Chinese Mathematics. Springer.
5. Standardization Administration of China (2011). GB/T 15835-2011 出版物上数字用法 (Rules for the use of numerals in publications).
6. Kevin F. Miller, Catherine M. Smith, Jianjun Zhu and Houcan Zhang (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science 6(1), 56–60.
7. Qin Jiushao (1247). Shùshū Jiǔzhāng (Mathematical Treatise in Nine Sections).

Related articles

• Real Numbers: Definition, Types, Examples and Properties: Real numbers explained: definition, types (rational and irrational), examples, properties and the number line, with interactive practice, a proof and FAQ.
• Exponents and Radicals: Laws, Rules, Examples and Practice: Exponents and radicals explained: the five laws, zero, negative and fractional exponents, simplifying roots, rationalizing and scientific notation, with practice.