Once I understood that the Babylonians used a positional system using powers of sixty rather than ten, I was able to easily interpret the meaning of this number system. The third column represented 60 2 or Again, placing the symbol for one in this column represented Placing the symbol for two in this column represented 7200 and so on. This pattern would continue for all of the 59 unit symbols. If one put the Babylonian symbol for one in this column, it had the value of 60, and if one put the symbol for two, it had the value of 120.

The next column contained multiples of 60. This is exactly the way that we arrange numbers today, but we use ten different units for the first column 0, 1,2, 3,4,5,6,7,8, or 9 instead of 59 different unit symbols. The first column was the unit columnĥ and contained any of the fifty-nine base units. Therefore, the idea of place value is an ancient one. (See chart below)Ĥ The Babylonians then used a positional number system like we have today to arrange the numbers into columns. I first discovered that the Babylonians used only two cuneiform symbols to arrange into fifty-nine base units. My next task was to gain an understanding of how a base sixty number system worked. Nevertheless, there is no clear explanation why the civilizations of Mesopotamia used sixty as a base. Still others argue that using the division of each finger into three sections could allow a person to count to sixty. Others argue that there were about 360 days in a year and that this would account for using 60. This would make the number sixty easy to manipulate when calculating amounts of grain that the ancients used as currency for barter. Apparently, the system of weights and measures in the Fertile Crescent civilizations relied upon the fraction amounts of 1/3 and 2/3. Having so many factors has made sixty a number that is easy to divide into amounts. Some historians have argued that the number sixty has many factors such as 1,2,3,4,5,12, 15, 20, 30, and 60. It is clear that the Babylonians inherited this system from the Sumerians, but why any of the ancient civilizations chose sixty as a base is a bit of a mystery. It is not as easy to see the importance of the number sixty. One can see how a base 10 system would originate from the fact that a human has 10 fingers, or how a base 20 system would originate from 20 fingers and toes. Therefore, the main reason that I have choosen this topic is to gain an understanding of how it worked, and to develop lessons on Babylonian mathematics that I can incorporate into the social studies curriculum.ģ Findings: My first question as to why the Babylonians adopted a number system based upon sixty proved to be difficult to answer. I have always known that the Babylonians had a sexagesimal number system, but I have never fully understood how it worked.

A favorite activity of my students is to make clay tablets and to write stories in the soft clay in cuneiform using a stylus. As part of this unit, I cover the cuneiform language of these civilizations. The Sumerians and Babylonians are two of the civilizations that we have covered in class. 1 By Mark Swanson The Babylonian Number System Essential Questions: Why did the Babylonians use a number system based on 60 instead of 10? How did the Babylonian number system work? How was the Base 60 number system different from a Base 10 number system? Why this topic? As a social studies teacher, I often have to teach about the early civilizations that developed in Mesopotamia.

60 in babylonian numerals