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How did the abacus represent ones tens and hundreds?

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arithmetic A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”

The abacus represents numerical values through the specific positioning of counters or beads. In its early forms, such as the board-based abacus, counters were placed on marked lines or in designated files where their position indicated their value—specifically representing ones, tens, hundreds, and higher decimal places.1

In later versions, such as the frame-based abacus, these values are represented by beads that slide along a series of parallel wires or rods. Each rod corresponds to a specific decimal place (ones, tens, hundreds, etc.), and the number of beads moved into a designated counting position on that rod determines the value for that place. By manipulating these beads, users can perform arithmetic calculations by tracking the changing values across these positional columns.21