Babylonian numerals

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Numeral systems List of numeral system topics
Hindu-Arabic system History Symbol sets: Western Arabic Eastern Arabic Indian family Thai Abjad Armenian Babylonian Brahmi Chinese Cyrillic Egyptian Etruscan Ge'ez Greek Attic Ionian Hebrew Japanese Khmer Korean Mayan Roman D'ni (fictitious)
Positional systems with various bases:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 24, 26, 27, 30, 32, 36, 60, 64 Non-standard systems: 1, -2, -3, Balanced ternary, mixed, Factoradic, Fibonacci coding, bijective, 2i, φ
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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 astrological observations and calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from the Sumerian and also Akkadian 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 1900 BC to 1800 BC. It is also credited as being the first known place-value 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 prior to place-value systems people were obliged to use unique symbols to represent each power of a base (ten, one-hundred, one thousand, and so forth), making even basic calculations unwieldy.

Since their system clearly had an internal decimal system and they used 60 as the second smallest unit instead of 100 as we do today, it is more appropriately considered a mixed-radix system of bases 10 and 6. A large value to have as a base, sixty is the smallest number that can be wholly divided by two, three, four, five, and six, hence also ten, fifteen, twenty, and thirty. Six and ten were also used as sub-bases. Only two symbols used in a variety of combinations were used to denote the 59 numbers. A space was left to indicate a zero, although they later devised a sign to represent an empty place.

Sexagesimals still survive to this day, in the form of degrees (360° in a circle), minutes, and seconds in trigonometry and the measurement of time.

A common theory is that sixty was chosen due to its prime factorization 2×2×3×5 which makes it divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. Integers and fractions were represented identically - a radix point was not written but rather made clear by context.

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Numerals

Image:Babylonian numerals.jpg Babylonian numerals

The Babylonians did not technically have a digit for, or a concept of, the number zero. Although they understood the idea of nothingness, it was not seen as a number—merely the lack of a number. What the Babylonians had instead was a space (and later a disambiguating placeholder symbol) to mark the nonexistence of a digit in a certain place value.

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