Britannica Sources used in this answer

How did the decimal place-value system work with Chinese counting rods?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

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 the context of East Asian mathematics, the decimal place-value system was implemented using counting rods arranged on a flat surface, such as a counting board.1

This system functioned by representing numbers through the physical placement and orientation of these rods. By utilizing the principles of a decimal place-value system, the rods allowed mathematicians to perform complex arithmetic operations—including addition, subtraction, multiplication, and division—by physically moving and modifying the rod configurations on the board.1

This method was highly effective for advanced calculations, such as those found in The Nine Chapters, which describes algorithms for finding square and cube roots. These algorithms were structured on the counting surface in rows, mirroring the logic of modern long division, with the quotient, dividend, and divisor placed in specific relative positions. Because the rods could be manipulated dynamically, they provided a flexible framework for computation that significantly influenced the development of mathematical theory in China.21