depending on their positions. For example 126 is represented by =⊤ instead of ∥⊤ which could be confused with 37. Usually red rods are for positive numbers and black rods are for negative numbers.
The counting rods could be used for a wide range of calculations, including finding Pi and solving system of linear equations. As a result, the character 籌 is commonly associated with the concept of planning in Chinese. For example, the science of using counting rods 運籌學 is not about the counting rods: it means operational research!
Before the introduction of 0, there was no way to separate 10007 and 107 except inserting a bigger space between 1 and 7, and so rod numerals were used only for doing calculations with counting rods. Once 0 came into play, the rod numerals had become independent and their use indeed outlives the counting rods. One variation of rod numerals is still in use, see the article on Chinese numerals.
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