Definition:Sexagesimal Notation

Definition

Sexagesimal notation is the technique of expressing numbers in base $60$.

The sexagesimal notation system can also be seen referred to as logistic arithmetic or logistic notation.

$6, 30$ in sexagesimal is $6 \frac 1 2$ expressed as a mixed fraction.

$11, 22, 30$ in sexagesimal is $11 \frac 3 8$ expressed as a mixed fraction.

From as early as $3500$ BCE, the Sumerians were using a sexagesimal system for certain purposes, based on divisions of $10$ and $6$:

$1, 10, 60, 600, 3600, 36 \, 000, \ldots$

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.