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 (๐น to count units and ๐ 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 ๐๐๐น๐น๐น represented the digit for 23 (see table of digits above). These digits were used to represent larger numbers in the base 60 (sexagesimal) positional system. For example, ๐น๐น ๐๐๐น๐น๐น ๐น๐น๐น would represent 2ร602+23ร60+3 = 8583. 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: ๐๐๐น๐น๐น could have represented 23, 23ร60 (๐๐๐น๐น๐นโฃ), 23ร60ร60 (๐๐๐น๐น๐นโฃโฃ), 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 (360ยฐ in a
circle or 60ยฐ in an
angle of an
equilateral triangle),
arcminutes, and
arcseconds 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: 2ร2ร3ร5, which makes it divisible by
1,
2,
3,
4,
5,
6,
10,
12,
15,
20,
30, and
60.
Integers and
fractions were represented identicallyโa radix point was not written but rather made clear by context.
Zero 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 numberโmerely the lack of a number. Later Babylonian texts used a placeholder () to represent zero, but only in the medial positions, and not on the right-hand side of the number, as is done in numbers like . == See also ==