The Babylonians used a base-60 (or sexagesimal) positional numeral system borrowed from the Sumerians.
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.
Sexagesimals still survive to this day, in the form of degrees, minutes, and seconds in trigonometry and the measurement of time.
See also: Numeral system, Arabic numerals, Armenian numerals, Chinese numerals, Greek numerals, Hebrew numerals, Indian numerals, Mayan numerals, Roman numerals