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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 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).
- 1 Origin
- 2 Characters
- 3 Zero
- 4 See also
- 5 Notes
- 6 Bibliography
- 7 External links
Origin[ edit ]
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. 
|Hindu–Arabic numeral system|
|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
Characters[ edit ]
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.
Their system clearly used internal decimal to represent digits, but it was not really a mixed-radix system of bases 10 and 6, since the ten sub-base was used merely to facilitate the representation of the large set of digits needed, while the place-values in a digit string were consistently 60-based and the arithmetic needed to work with these digit strings was correspondingly sexagesimal.
The legacy of sexagesimal still survives to this day, in the form of degrees (360° in a circle or 60° in an angle of an equilateral triangle ), minutes , and seconds in trigonometry and the measurement of time , although both of these systems are actually mixed radix. 
A common theory is that 60 , a superior highly composite number (the previous and next in the series being 12 and 120 ), 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.
Zero[ edit ]
The Babylonians did not technically have a digit for, nor 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.[ citation needed ]
See also[ edit ]
- History of zero
- Numeral system
Notes[ edit ]
- ^ a b c Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 247.
- ^ a b Stephen Chrisomalis (2010). Numerical Notation: A Comparative History . p. 248.
- ^ http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/
Bibliography[ edit ]
- Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 0-262-13040-8 .
- McLeish, John (1991). Number: From Ancient Civilisations to the Computer. HarperCollins. ISBN 0-00-654484-3 .
External links[ edit ]
|Wikimedia Commons has media related to Babylonian numerals .|
- Babylonian numerals
- Cuneiform numbers
- Babylonian Mathematics
- High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection
- Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection
- Babylonian Numerals by Michael Schreiber, Wolfram Demonstrations Project .
- Weisstein, Eric W. “Sexagesimal” . MathWorld .
- CESCNC – a handy and easy-to use numeral converter
- Babylonian mathematics
- Non-standard positional numeral systems
- Numeral systems
- All articles with unsourced statements
- Articles with unsourced statements from May 2015
- Commons category link is on Wikidata
- This page was last edited on 22 November 2018, at 09:58 (UTC).
- Text is available under the Creative Commons Attribution-ShareAlike License ;
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