Babylonian Numerals

Babylonian numeration is a numbering system used by the ancient Babylonians/Sumerians in Mesopotamia to represent numbers. In mesopotamian/babylonian/sumerian number system, numbers are written in a cuneiform style with | (pipe or nail) and < (corner wedge or bracket), written in base 60 (sexagesimal).

The number is written in base 60, the 60 digits are broken down into vertical bars 𒐕 (often noted |) which are worth one unit (1) and chevrons 𒌋 (often noted <) which are worth ten (10) in base 10.

The power change of sixty ($ 60^1 = 60 $, $ 60^2 = 3600 $, $ 60^3 = 216000 $ etc.) is represented by an empty space.

To convert a Babylonian number:

— Identify the positions (from right to left). Each position represents a power of $ 60 $

— Multiply the value in each position by its power of $ 60 $

— Add the results to obtain the number in base $ 10 $

Since Unicode 5 (2006) cuneiform symbols can be represented on compatible browsers, here is the table of characters used by dCode:

Babylonians did not use the zero (this concept had not been invented), but from the 3rd century in Babylon, they used the symbol (as a writing separator for numbers)

Converting is easy by counting symbols and considering it in base 60 to get numbers into classical Hindu-Arabic notation.

To convert a number $ n $ from base $ 10 $ to base $ b=60 $ apply the algorithm::

— Divide the decimal number by $ 60 $ and note the whole quotient as well as the remainder

— Repeat the process with the quotient until it is equal to $ 0 $

— Read the remainders obtained in reverse order to obtain the representation in base $ 60 $

// pseudo-code
function decimal_to_base60(n) {
q = n
b60 = []
while (q > 0) {
r = q mod 60
b60 []= r
q = q div 60
}
return b60
}


Babylonian numbers chart (base60)

0 (zero)		1		2		3		4
5		6		7		8		9
10		11		12		13		14
15		16		17		18		19
20		21		22		23		24
25		26		27		28		29
30		31		32		33		34
35		36		37		38		39
40		41		42		43		44
45		46		47		48		49
50		51		52		53		54
55		56		57		58		59

For other numbers, use the form above.

60 has the advantage of having many divisors: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Convert the Babylonian numbers to Hindu-Arabic numerals (1,2,3,4,5,6,7,8,9,0), then use the Roman numeral converter of dCode.

Clay tablets played a crucial role in understanding Babylonian numbers, as they were the medium on which the ancient Babylonians wrote their numerations. These tablets have survived through the centuries, providing a valuable source of information about the numerical and mathematical systems of this civilization.

Babylonian/Summerian numbers are thought to have been developed around 2000 BC.