Babylonian numerals converter

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Max number: 215999

Min number: 1

Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus or a wooden stick to make a mark on a soft clay tablet. The Babylonians inherited a sexagesimal (base-60) positional numeral system, which later together with tablets of sky observation were borrowed by Greek astronomers. Much later the sexagesimal numeral system was used by Arabs and also by ancient and medieval astronomers primarily for facilitating calculations with fractions.

These fractions were used in order to record astronomical coordinates – or angles, and this tradition has survived to this day.  There are 60 minutes of arc in a degree, and 60 arcseconds in a minute.

The Babylonian numeral system had been used before 2 000 B.C.  Only 2 symbols were used to notate numbers: a narrow, wedge-shaped markBabylonian digit 1.svgto count units and a wide, wedge-shaped markBabylonian digit 10.svgto count tens in the 60-based system.

For 1 and 60 was used one and the same symbol, which could also represent such numbers as 3600=602, 216000=603 and any other power of 60. To interpret the number, it should have been divided into digit positions (from right to left). A new digit started with a narrow, wedge-shaped mark following a wide, wedge-shaped mark. The value of the number was the sum of the values of its component parts taking into account that numbers in the each following digit position were 60 times higher than in the previous one.

60 × 1 + 23 = 83
2 × 3600 + 60 × 1 + 23 = 7283

The Babylonians didn’t have a symbol for zero, which could cause ambiguity in the representation of numbers and its interpretation must sometimes have been determined by its context. After a while, between the 4th and the 3d centuries BC, they started marking ‘zero’ with the symbol Babylonian digit 0.svg. However, it was used only for marking spaces between sexagesimal numerals, only in medial position. But the symbol wasn’t used at the end of a number, which was the main reason for ambiguity.

2 × 3600 + 0 + 23 = 7203

If you want to save the number in the Babylonian numeral system, right-click the image and choose in the drop-down menu ‘save the image as…’.

Developing: Vitaly Baydin, Dmitry Konoshonkin


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