Chinese Numeration System

Sydney Aymar

Number System Explanation/Base

  • Base: 10
  • Digits: 0-9
  • A number passed 10 was written as a basic math problem.
  • Twelve is "ten two"


By the 11th century BC, China had started using their own numeration system. Unlike many early systems, the Chinese numeration system was very vast. The system that was developed consisted of an array of large numbers, negative numbers, a decimal system, and a binary system. The Chinese numeration system is still commonly used. Algebra, geometry, and trigonometry were all developed within China's early numeration systems.

The picture below shows the dynasties and the time period on the right, and the type of math system that was used in the corresponding time period on the left.

Big image


The early Chinese numeration system was quite simple. There were only the numbers 0-9, so any larger numbers were represented by putting smaller numbers together to make larger numbers.

Example :

"The number 75 is written in Chinese using the characters 7, 10, and 5. In Chinese you need to say that you have 7 tens first. 7 tens is how 70 is represented. Once you have the tens place in Chinese, you can finish writing the number with the character for 5. Chinese has no character for ones, but a character is used for the other place values. The character for ten is needed. You cannot write 75 as.”

"The Chinese Numeration System ." edHelper. n.p., n.d. Web. 9 May 2016. <>.

Big image

Advantages and Disadvantages

There are some good things as well as bad things with this numeration system. The system is very simple and easy to interpret for smaller numbers but the disadvantage has to do with larger numbers. When you're representing larger numbers, you have to use a lot of symbols and it could get easy to mix them up.


Just like mostly anything, numeration systems are constantly evolving. The earliest Chinese numeration system was extremely simple. It was a way to keep count of simple things and form currency. As the system evolved, there wee new advancements brought in that could lead the system into more elaborate systems such as algebra.

Calculations (+, -, x, /)

  • +
  • x
  • "The base ten system is easy for us to understand, and multiplication and addition can be performed with comparative ease. It also requires less symbols than the additive systems of Egypt and Rome."

Alphabetic and Multiplicative Systems of Numeration, Section 1.2

Additional Information

Interesting Findings (Symbols):

When researching the numeration system, I came across different web pages. I found that not all web pages had the same representation of the numbers. Many different numeration systems and expansions to systems happened within China. Ever so often, usually aroud a dynasty change, a new math was introduced. I did find out that although there were many different types of math and symbols, they still had to add individual symbols (numbers) to create larger numbers.

Big image


"The Chinese Numeration System ." edHelper. n.p., n.d. Web. 9 May 2016. <>.

O'Connor , J J, and E F. Robertson. "Chinese numerals." Chinese numerals. n.p., Jan. 2004. Web. 9 May 2016. <>.

"Chinese Mathematics." The Story of Mathematics. n.p., n.d. Web. 9 May 2016. <>.

Joyce, David E. "Mathematics in China." History of Mathematics. n.p., Dec. 1994. Web. 9 May 2016. <>.

Calvert, J B. "Chinese Numbers." n.p., Feb. 2000. Web. 9 May 2016. <>.