The Mesopotamian Number System
In Mesopotamia during ancient times, different symbols were used for
different landmark numbers. Later they used a base-60 system, also called the sexagesimal
system.
It has puzzled many people. They thought why they
chose base 60. Different theories exist to explain the connection between 60
and the periods of some important events (like the length of their lunar month
which had 30 days, etc.), the ease of representing fractions, their earlier
sequence of landmark numbers — 1, 10, 60, 600, 3600, 36000, … — getting reduced
to only the powers of 60, and so on.
The influence of the Mesopotamian sexagesimal system,
also known as the Babylonian number system, can be seen even now in our
units of time measurements as 1 hour = 60 minutes and 1 minute = 60 seconds.
These digits were used to represent larger numbers in the
base-60 (sexagesimal) positional system.
Let us represent our own symbols to indicate the landmark
numbers.
For example, we can represent 8583 = 2 × 602 + 23 × 60 + 3 as follows:
A space was left to indicate a place without value,
similar to the modern-day zero. Babylonians later
devised a sign to represent this empty place.
Therefore, any number can be represented using the numerals 1 to 59
along with the numerals for landmark numbers. Thus, the Mesopotamian system has
removed the need for unending sequence of symbols by making use of the positions
where the symbols are placed or written. This system, however, cannot be
considered to fully developed as still there were challenges. The spacing
between symbols to represent the place value caused a lot of confusion leading
to the same numeral to be read in different ways. Then they introduced a new
symbol for denoting a blank space.
Example: Write the following Mesopotamian symbols
in Hindu-Arabic numerals.
a. 
b. 
Solution:
a.
= 3 × 602 + 22 × 60 + 2
= 3 × 3600 + 22 × 60 + 2
= 10800 + 1320 + 2
= 12,122
b.
= 1 × 602 + 21 × 60 + 3
= 1 × 3600 + 21 × 60 + 3
= 3600 + 1260 + 3
= 4863