How were numbers written on Babylonian cuneiform tablets?

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Babylonian cuneiform tablets utilized a sophisticated sexagesimal (base-60) positional numeral system. Because the base was large, the Babylonians used a simpler additive grouping system to represent the digits 1 through 59.12

  • Symbols: Scribes used a stylus to impress wedge-shaped marks into damp clay. A vertical wedge represented 1, while a corner-shaped symbol represented 10. These were combined additively to form numbers up to 59 (e.g., three 10s and two 1s represented 32).32
  • Positional Notation: For values 60 and greater, the Babylonians employed place value, where the position of a symbol determined its power of 60. For instance, a single wedge could represent 1, 60, or 602, depending on its placement.2
  • Limitations: The system initially lacked a zero, which often created ambiguity regarding the magnitude of a number. By the 3rd century BCE, a placeholder symbol was introduced to denote missing powers of 60, though it was used inconsistently and typically only for interior positions. Additionally, the system lacked a mark to separate integral and fractional parts, requiring context to determine the intended value.12