Some Ancient Numerical Notation

Courtney, Crystal, Jon, Marie and Tana
Students in MathEd 300, Fall 1996
University of Regina

During the fourth millenium B.C. the Babylonians produced and began to use the first written numerical notation. They needed a form of documentation to keep track of taxes, trading, canals, dams, etc. Their system of notation is, of course, much different than ours is today. We use base 10 numeration where as the Babylonians, they used base 60. The basis of their system of numerical notation is as follows. (1 is represented by V and so on)

V  VV  VVV  VVV  VVV  VVV  VVV  VVV  VVV
1   2   3    V    VV  VVV  VVV  VVV  VVV
             4     5   6     V   VV  VVV
                             7    8   9
(10 is represented by < and so on)
<  <V  <VV ... <VVV  << ... <<< ... <<<VVV
10 11   12      VVV  20      <<      <<VVV
                VVV          50        VVV
                 19                     59

Because this system is base 60, something different occurs at 60... it is represented by V. Evidently it was difficult to distinguish between 1 and 60, so the Babylonians had to take context into consideration.

When notating numbers greater than 60 a space was used.

ex. V_V = 61 rather than VV which represents 2

V_VVV  V_<   VV    VV_<VVV  VVV_<<<VVV
  VVV   70  120   120 + 13    V   <VVV
  VVV                  133  240  +  46
   69                              286
You might want to look at a question submitted to Quandaries and Queries, Why is a circle divided into 360 degrees?, to see that the influence of the Babylonians and their base 60 mathematics is still evident in some of our current mathematical conventions.

Have fun!


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