Exam (elaborations)
MIP1501 Assignment 2 2024
- Course
- MIP1501 (MIP1501)
- Institution
- University Of South Africa (Unisa)
MIP1501 Assignment 2 2024
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PROSTUDENT
,Question 1 (24)
1.1. Compare the Egyptian and the Babylonian numeration systems in terms of the
number of symbols, functionality, and possible uses.
Number of Symbols:
Egyptian System: The Egyptian numeration system utilized a variety of symbols, each
representing different powers of 10. For example, they had distinct symbols for 1, 10,
100, 1000, and so on, up to very large numbers. This resulted in a relatively large
number of symbols needed to represent numbers.
Babylonian System: The Babylonian numeration system, on the other hand, employed
only two symbols for basic numerals, one for tens and one for ones. This simplicity
allowed them to represent a wide range of numbers with just two symbols.
Functionality:
Egyptian System: The Egyptian system was not positional, meaning the value of a
symbol depended on its placement rather than its inherent value. This made arithmetic
operations more complex and limited the system's versatility.
Babylonian System: The Babylonian system, while also not positional, had more
flexibility due to its use of a base-60 system. This allowed for easier manipulation of
numbers and facilitated calculations involving fractions, squares, and cubes.
Possible Uses:
Egyptian System: The Egyptian numeration system was suitable for representing large
quantities, as evidenced by their use of symbols for very large numbers. However, its
lack of positional notation made complex calculations more challenging.
Babylonian System: The Babylonian numeration system was well-suited for practical
applications such as trade, measurement, and astronomy. Its base-60 system allowed
for convenient representation of fractions and facilitated calculations involving time,
angles, and other measurements.
, 1.2. Write down three similarities and three differences of the numerations listed in 1.1.
Hierarchical Representation
Both systems utilized a hierarchical structure where the value of a symbol depended on its
position within a number. In the Egyptian system, the value of a symbol depended on its
position relative to other symbols, while in the Babylonian system, the value of a symbol
depended on its position within the base-60 system.
Lack of Zero: Neither system included a symbol to represent zero, which meant that they did
not have a placeholder for empty positions in numbers.
Symbolic Representation: Both systems used symbols to represent numerical values, albeit
in different ways. The symbols in each system were visually distinct and were combined to
represent larger numbers.
Differences:
Base System
The Egyptian system was based on powers of 10, with distinct symbols for each power, while
the Babylonian system was based on a sexagesimal (base-60) system, allowing for more
compact representation of numbers.
Symbol Complexity: The Egyptian system employed a larger number of symbols, each
representing a different power of 10, leading to a more complex notation system. In contrast,
the Babylonian system used only two basic symbols (tens and ones), simplifying the
representation of numbers.
Positional Notation: While neither system used positional notation in the modern sense, the
Babylonian system exhibited a greater degree of positional significance due to its base-60
structure. This facilitated arithmetic operations and allowed for more efficient calculations
compared to the Egyptian system, which lacked positional significance beyond the order of
symbols.
1.3. Are these numeration systems (see 1.1.) still used today? Do your own research and
then provide reasons for your answer.
Both the Egyptian and Babylonian numeration systems are not used in their original forms
today.
Egyptian Numeration System
The Egyptian numeration system was not positional, meaning the value of a symbol
depended on its placement rather than its inherent value. This lack of positional notation
made arithmetic operations more cumbersome and limited the system's versatility. As a
result, it was gradually replaced by more efficient positional numeral systems, such as the
Hindu-Arabic numeral system, which is the basis of the numeration system used
worldwide today.
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