The Babylonians used a base-60 (or sexagesimal) positional numeral system borrowed from the Sumerians. Sexagesimals still survive to this day, in the form of degrees, 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 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.
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da:Babyloniske tal og cifre
fr:Numération babylonienne