Chinese Numerals

The Chinese number system writes numbers with the characters 一 二 三 四 五 六 七 八 九 十 for 1 to 10 and adds 百 (100), 千 (1,000), 万 (10,000) and 亿 (100,000,000). It is a decimal system with regular words: 25 is “two-ten-five,” 二十五, and 99 is “nine-ten-nine,” 九十九. In everyday life China also uses the digits 0 to 9, which are explained on the page Hindu-Arabic numerals, so the characters appear mainly in words, on bank documents and in traditional writing.

This page shows the characters, the rules for reading and writing numbers, the formal numerals on banknotes and cheques, and the counting rod numerals with which Chinese scholars calculated for about two thousand years. The history of Chinese mathematics is in the China section of the history of mathematics, and the German overview is Chinesische Mathematik (in German). Other systems are on the page about number systems.

The Chinese number characters 0 to 10 and the place words

Learn the ten digits and four place words, and you can write any number. The word for 2 changes in speech: before a measure word, as in “two people,” Mandarin uses 两 (liǎng) instead of 二. In written numerals, 二 is standard.

How to read and write Chinese numbers

The rules are short, and every number from 11 to 99 follows the same pattern:

1. 11 to 19: say 十 and then the digit. 14 is 十四, not “one-ten-four.”
2. 20 to 99: say the tens digit, then 十, then the ones digit. 47 is 四十七, “four-ten-seven.”
3. Hundreds and thousands: digit plus 百 or 千. After a hundred, the “one” stays: 110 is 一百一十.
4. Zeros inside a number are said as 零, once for any gap: 105 is 一百零五 and 1,010 is 一千零一十. A zero at the end is not said.

Big numbers: groups of four digits

English groups digits in threes (thousand, million, billion). Chinese groups them in fours, because 万 is 10,000 and 亿 is 10,000 times 10,000. Japanese and Korean count the same way. A number is split into groups of four digits from the right, and each group is read like a number below 10,000 and followed by 万 or 亿. So 123,456,789 becomes 1 | 2345 | 6789, which is 一亿二千三百四十五万六千七百八十九. The international number system groups in threes, and the Indian system with lakh and crore groups in twos, so the same number looks different in each.

The words for round numbers show the difference: 100,000 is “ten myriads,” 十万, and 10,000,000 is “one thousand myriads,” 一千万. A million million, 10¹², is 一万亿, “ten thousand times a hundred million.”

Formal numerals on banknotes and cheques

The simple characters 一, 二 and 三 are just one, two and three strokes, so it is easy to turn one into another. For money, contracts and cheques, China therefore uses formal numerals (dàxiě), complex characters that cannot be altered by adding a stroke. The table gives the traditional forms. The simplified forms differ only for some characters, for example 贰, 叁 and 陆.

With the formal numerals, 2,026 reads 貳仟零貳拾陸.

Ancient Chinese numbers: oracle bones and counting rods

The oldest Chinese numerals are carved on oracle bones and tortoise shells from the late Shang period (14th century BC to about 1045 BC). They have signs for 1 to 9 and for 10, 100, 1,000 and 10,000, and a number such as 2,656 was written as “2 thousands, 6 hundreds, 5 tens, 6.” The system is decimal, but it has no place value, because every power of ten has its own sign. The largest number found on the bones is 30,000.

For calculating, scholars used small sticks of bamboo, wood or bone, the counting rods, laid out in the columns of a counting board. Each column was a power of ten, so the board was a place value system long before one existed in Europe. The rod numerals are known from the Warring States period (475 to 221 BC), and bundles of rods were found in graves near Changsha. The figure shows the nine digits.

Two rules kept the digits readable. First, the ones, hundreds and ten-thousands were laid vertically and the tens and thousands horizontally, as the Sunzi suanjing puts it: “one is vertical, ten is horizontal.” Second, an empty place stayed empty. A written zero in the form of a small circle, 〇, appears in Chinese mathematical books from the 13th century (Qin Jiushao, 1247). Some historians think the circle came from India earlier. On the board, red rods meant positive numbers and black rods negative numbers.

The bead abacus, the suanpan, slowly replaced the rods and was in common use by about the 14th century. The horizontal rod forms lived on in the Suzhou numerals, which merchants used for prices and invoices and which you can still see in some Chinese markets. They are in Unicode as Hangzhou numerals.

Practice problems with answers

Frequently asked questions

Sources and further reading

• MacTutor History of Mathematics: Chinese numerals
• Wikipedia: Chinese numerals, Counting rods and Suzhou numerals
• Jean-Claude Martzloff: A History of Chinese Mathematics, Springer, Berlin 1997.