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How were counting rods used to represent numbers in ancient China?

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East Asian mathematics Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.

In ancient China, counting rods were essential tools used to perform mathematical computations on a surface, such as a counting board. These rods functioned within a decimal place-value system, allowing mathematicians to represent numbers by arranging the rods in specific configurations.12

By placing and modifying these rods on the board, scholars could execute the four arithmetic operations: addition, subtraction, multiplication, and division. This method was central to the procedures described in foundational texts like The Nine Chapters, which presupposed the use of these physical tools for computation even though the numbers themselves were often recorded in Chinese characters. The reliance on this rod-based place-value notation significantly influenced the development of Chinese algebra, as the rods provided the physical framework necessary to manipulate complex numerical expressions.123