The Chinese have traditionally used a number system based on a decimal number system. They use thirteen basic signs denoting the numbers 1 to 9, 10, 100, 1 000, and 10 000.

For other intermediate numbers e.g. 86 754 these would be realised as:

8 lots of 10 000
+ 6 lots of 1 000
+ 7 lots of 100
+ 5 lots of 10
+ 4


Orally - in the past to help school children understand the traditional Chinese numbers the original characters were transcribed using the Pinyin system.

n.b. This has been the official system in use since 1958. As such there is separate name to each of the first ten numerals:

Yi/ er/ san/ si/wu/liu/ qi/ba/jiu/shi

While the numbers 11 - 19 are made up by the 'additive' principle:

11 Shi yi ten - one (i.e. 10 + 1)
12 Shi er ten - two
Etc...
19 Shi jiu ten - nine

Whereas the tens are represented by a 'multiplicative principle':

20 er shi two - ten (i.e. 2 x 10)
30 san shi three - ten
40 si shi four -ten
etc

And for 100, 1 000, and 10 000 the words bai, qian and wan are used.

For the intermediate numbers the multiplicative principle above is also used.

e.g. 86 754 would be realised as:

ba wan + liu qian + qi bai + wu shi + si

i.e. 8 x 10 000 + 6 x 1 000 + 7 x 100 + 5 x 10 + 4

Early on the Chinese also used a written notation based a system of place value. Known as the suan zi, meaning literally ‘calculation with rods’, where the values of the differing numerals are determined by the position the rods occupy.

Below is copy of the initial system (believed to have been passed down by Cai Jiu Feng c. 1200):
Initial Number system, believed to have been passed down by Cai Jiu Feng c. 1200


Unfortunately this system caused confusion. 12 would be confused with 3 or 21; while 25 could be confused with 7, 34, 43, 52, 214, 223 and so on. Can you see why?

To avoid confusion a second system was introduced. Look closely and examine the differences.

Advanced Number System


To distinguish between numerals of differing magnitudes figures were alternated between one system and another. Therefore alternating vertical and horizontal bars

Units/ hundreds/ tens of thousands/ millions …. are drawn with vertical symbols
Whereas the tens/ thousands/ hundreds of thousands…..are drawn with horizontal symbols.

Can you make sense of the three numbers, produced below?
Chinese Numbers with bamboo or Ivory rods called chóu


The numerals like those outlined above were used for writing. For calculation the Chinese initially used little rods made of ivory or bamboo which were called chóu. These were placed on the squares of a tile or a table ruled like a chessboard.

That's another story!
For now...

Children might like to:

i. complete the silhouettes of numbers (see below) – each one made up from seven pieces of the Tangram.
ii. surf the internet and find out more about early Chinese numbers systems
iii. investigate further the Pinyin system.
iv. make copies of the Chinese manuscript signs used to represent the basic 13 numerals.

Parents might like to help with:

i. the surfing of the internet to gather information about early Chinese numbers systems.
ii. devise numbers using the rods.
iii. collating examples of Chinese calligraphy especially numbers as they are written
iv. explaining the difference between numerals, numbers, digits

Teachers might like to:

i. discuss the problem of zero which is NOT allowed for in the above
ii. explore the additve and multiplicative principles outlined above.
iii. set some arithmetical questions using the four rules and numbers written out in rod form..
iv. investigate doing arithmetic using a chóu.
Tangram Two