算筹 · 苏州码子
Chinese numerals: the number systems
“Chinese numerals” usually means the characters 一 to 十, which the rest of this site covers. This page is about the other meaning: the written systems Chinese mathematicians and merchants calculated and kept accounts with before Arabic figures took over.
Four ways to write a number in China
- Arabic figures, 0 to 9: what everyday Chinese text, prices and school maths use today.
- Number characters, 一 二 三: the number words, written out. See 1 to 10.
- Formal characters, 壹 贰 叁: harder to alter, required on financial documents. See writing the characters.
- Rod and Suzhou numerals: place-value notations built from counting rods, below.
Counting rods: place value with sticks
For around two thousand years, from about the 5th century BCE to the 16th century CE, Chinese mathematicians calculated by laying out short rods on a table or a counting board. Each digit was a small bundle of rods; the next place to the left was ten times bigger. It is a true place-value system, and it worked without a zero sign: an empty place on the board was zero.
Two conventions kept the digits apart. A rod laid across the others stands for five, so seven is a cross-rod and two units. And the direction alternates: digits in the units, hundreds and ten-thousands places stand upright, while tens and thousands lie flat. The mathematical classic Sunzi Suanjing sums it up: “one is vertical, ten is horizontal”.
Counting rods also handled negative numbers, which mathematicians kept apart by colour, red for positive and black for negative. When the abacus spread, the rods fell out of use in China.
Suzhou numerals: the merchants' shorthand
Suzhou numerals (苏州码子, also 花码, “flowery numbers”) descend from the rod numerals of the Southern Song. They were the bookkeepers' and market traders' script, quick to write on a ledger or a price board, while the standard characters were used for formal writing. Unicode gives them their own code points, U+3021 to U+3029, with a few added later.
| Value | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Suzhou | 〇 | 〡 | 〢 | 〣 | 〤 | 〥 | 〦 | 〧 | 〨 | 〩 |
A full Suzhou figure takes two lines: the digits, then characters giving the place and unit of the first digit. Wikipedia's example is 〤〇〢二 over 十元, “ten yuan”, which reads 40.22 yuan; the second 2 is written as the character 二 so that two upright 2s do not run together. The converter on this page shows the digits only.
Questions from learners and teachers
Is the Chinese number system base 10?
Yes. Both the spoken numbers and the old written systems are decimal. What differs from English is the grouping of large numbers: Chinese counts in units of ten thousand (万) and a hundred million (亿) rather than thousands and millions.
What were counting rods?
Short sticks of bamboo, bone or wood, laid on a table or board to calculate. Their arrangements were also written down as rod numerals, a place-value system with an empty space for zero, used from around the 5th century BCE to the 16th century, when the abacus replaced it.
Are Suzhou numerals still used?
Rarely. They were a merchants’ shorthand for prices and accounts, common in places such as Hong Kong markets until late in the 20th century, and have since given way to ordinary figures. They can still turn up on traditional handwritten invoices and market price boards.
Do Chinese people use the characters 一 二 三 for maths?
Not for calculating. Schools in China teach arithmetic with the Arabic figures 0 to 9, as in the West. The characters are used for writing numbers out in words, for formal text, and in fixed expressions; the formal forms 壹, 贰, 叁 go on financial documents.