Babylonian Notation

Writing on clay tablets using a cuneiform (a wedge-shaped stylus), the Babylonians employed an incomplete sexagesimal (base 60) positional system of numbers. The first 59 digits were written as a combination of two different marks; the wedge and the corner as shown below.

When 60 was reached, the symbols were repeated to denote the number of sixties. For example, 60 was denoted by while 120 was denoted by . The same procedure was used to denote 60², 60³ etc. Generally, symbols of higher order appeared on the left.

Today we use our own digits, along with semicolons and commas to represent sexagesimal numbers. Examples are shown below.

Decimal	Sexagesimal	Babylonian notation
63	1,3
3/4 = 45/60	0; 45

There were several defects in the Babylonian numeration system:

The lack of a sexagesimal point.

For example, could represent 2, 1 + 1/60, or even 2/60.

Ambiguous use of symbols.

For example the following numbers are represented by the same symbols.

Decimal	Sexagesimal	Babylonian notation
12 = 10 + 2	12
602 = 10 60 + 2	1, 2

The absence of zero.

For example the following numbers are represented by the same symbols.

Decimal	Sexagesimal	Babylonian notation
1	1
60	1, 0

Continue to Babylonian Arithmetic Back to Main Page