# Chinese Numeration System

### By: Elizabeth Williams

## Chinese System

The traditional Chinese system was a base ten system, with symbols for the digits 0-9 and

symbols for the powers of ten. For example: Eleven was “ten one” in traditional Chinese, twelve “ten two”

Used small bamboo rods arranged to represent the numbers 1 to 9, which were then places in columns representing units, tens, hundreds, thousands, etc

## Who/When?

Chinese numbering system, which dates back to at least the 2nd millennium BCE. Li Zhi gives the earliest source of the method, although it must have been invented before his time.

## How long?

Chinese invented the numeral system and were adding, subtracting, multiplying and dividing at least 1,000 years before anyone else, with simple bamboo rods.

roots in the rod bundles used in China from as early as 475 BC

## When Found?

The earliest known text on arithmetic based on the current number system was written by an Arab in AD 825, but the earliest Chinese treatise on the rod numerals and procedures for multiplication and division - the sun zi suanjing - was written about 425 years earlier.

## Still Use It?

While China has for many years uses adopted the Arabic numeral system familiar around the world, it also still uses its native Chinese character number system.

Arabic numerals were introduced to China as early as the Ming Dynasty (1368-1644) by merchants that traveled around the world, but some Chinese mathematicians still used Chinese numeral characters. After the Qing dynasty, though (1644-1912) it was replaced by Arabic numerals. China has historically been very influential in Asia, so Chinese influence likely accounts for use of Arabic numerals in other Asian countries, as well

## Symbols

The number 75 is written in Chinese using the characters 7, 10, and 5 or

You cannot put for 75.

## Facts

Over more than 30 years, pored over ancient Chinese texts written in highly technical language and travelled the world hunting down works on mathematics

Arabic numerals are used in mathematics in China. The Chinese numbers are mainly used in writings.

The importance of these finds, as far as learning about the ancient Chinese number system, was that many of the inscriptions contained numerical information about men lost in battle, prisoners taken in battle, the number of sacrifices made, the number of animals killed on hunts, the number of days or months, etc. The number system which was used to express this numerical information was based on the decimal system and was both additive and multiplicative in nature.

Among the greatest mathematicians of ancient China was Liu Hui, who produced a detailed commentary on the “Nine Chapters” in 263 CE, was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations.

By the 13th Century, the Golden Age of Chinese mathematics, there were over 30 prestigious mathematics schools scattered across China

Mathematics was both Practical and Spiritual

Chinese mathematics came about because of the needs of the empire for administrative services. Things like surveying, taxations, calendar making, etc.

Used counting board like the Romans

## Advantages

The system included 0 which many other systems don’t use.

Multiplication and addition aren't to hard, which is good by the 0 and the base ten understanding

Less symbols

## Disadvantages

Numbers were so easy they could be changed or forged in banknotes. This made them have to make an entirely new number system for business and ceremonial use

Even though it was smaller than other number systems still had twice as many symbols as we use in our number system

## Adding, Subtracting, Multipling

Addition: The counting of rods for the two numbers placed down, one number above the other. The digits added left to right with carries where needed.

Subtraction is similar to Addition

Multiplication: Multiplication table to 9 times 9 memorized. Long multiplication similar to ours with advantages due to physical rods

They used their hands to make the numbers for example ASL Y would be 6

## Citations

Mary Flagg, Marjorie Marks, And Jennifer Marsala. Alphabetic and Multiplicative Systems of Numeration - Section 1.2 - Math 2303, Concepts in Algebra (n.d.): n. pag. Web.

"Ancient Numerals and Numbers - History Dictionary." Ancient Numerals and Numbers - History Dictionary. N.p., n.d. Web. 08 Dec. 2015.

"Chinese Numerals." Cultural China. N.p., 2007. Web. 2010.

"Chinese Invented Number System: Singapore Ressearcher." Chinese Invented Number System: Singapore Ressearcher. N.p., n.d. Web. 08 Dec. 2015.

"Chinese Numbers." Chinese Numbers. N.p., n.d. Web. 08 Dec. 2015.

"When Did They Start Using Arabic Numerals in Asian Countries?" Yahoo! Answers. Yahoo!, n.d. Web. 08 Dec. 2015.

"Chinese Mathematics - The Story of Mathematics." Chinese Mathematics - The Story of Mathematics. N.p., n.d. Web. 09 Dec. 2015.

"Chinese Numeration." *Prezi.com*. N.p., n.d. Web. 10 Dec. 2015.