Sexagesimal notation is the technique of expressing numbers in base $60$.
From as early as $3500$ BCE, the Sumerians were using a sexagesimal system for certain purposes, based on divisions of $10$ and $6$:
- $1, 10, 60, 600, 3600, 36 \, 000, \ldots$
This sequence is A281863 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
For conventional business purposes, they used a decimal system.
Their $60$-based system was adopted by the Babylonians, who used it for mathematical and astronomical purposes.
As $60 = 5 \times 12 = 6 \times 10$, it has the advantages of both the decimal (base $10$) and duodecimal (base $12$) systems.
In particular, the ancient division of the sky into the $12$ signs of the zodiac fits the sexagesimal system far better than a decimal system.