Babylonian Numerals

Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.

The Babylonians, who were famous for their astronomical observations and calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units).

This system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers. However, the use of a special Sumerian sign for 60 (beside two Semitic signs for the same number) attests to a relation with the Sumerian system.

The Babylonian system is credited as being the first known positional numeral system, in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base (ten, one hundred, one thousand, and so forth), which can make calculations more difficult.

Only two symbols ( to count units and to count tens) were used to notate the 59 non-zero digits. These symbols and their values were combined to form a digit in a sign-value notation quite similar to that of Roman numerals; for example, the combination represented the digit for 23 (see table of digits below). A space was left to indicate a place without value, similar to the modern-day zero. Babylonians later devised a sign to represent this empty place. They lacked a symbol to serve the function of radix point, so the place of the units had to be inferred from context : could have represented 23 or 23×60 or 23×60×60 or 23/60, etc.

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