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 attests to a relation with the Sumerian system.
Characters
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, which can make calculations more difficult. Only two symbols 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. 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 10and 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, 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, 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, 30, and 60. Integers and fractions were represented identically—a 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 number—merely 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 we do in numbers like.
