Preserving numeric information in clay was invented by the Sumerians between 8000 and 3500 BC. This was done with small clay tokens of various shapes that were strung like beads on a string. Beginning about 3500 BC clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets which were then baked. About 3100 BC written numbers were dissociated from the things being counted and became abstract numerals.
Between 2700 BC and 2000 BC in Sumer, the round stylus was gradually replaced by a reed stylus that had been used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. These systems gradually converged on a common sexagesimal number system that was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.
Sexagesimal numerals were a Mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons and was by 1950 BC a positional notation system. Sexagesimal numerals became widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. In Hindu-Arabic numerals, we still use sexagesimal to count time (minutes per hour), and angles (degrees).
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.
The sexagesimal (base-sixty) is a numeral system with sixty as the base. It originated with the ancient Sumerians in the 2000s BC, and was transmitted to the Babylonians: see Babylonian numerals. Sexagesimal was not a pure base 60 system, because that would require 60 different numeric signs. Instead, sexagesimal was a Mixed radix system in which base ten and base six alternated. The units digits were in base ten (Y, YY, YYY, YYYY, ... YYYYYYYYY) and the tens digits were in base six (<, <<, <<<, <<<<, <<<<<) meaning (10, 20, 30, 40, 50). The sixtys were in base ten (60, 120, 180, ... 540) and the six-hundreds were in base six (600, 1200, 1800, 2400, 3000). The 3600 order was in base ten (3600, 7200, 10800, ... 32400).