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Section 2-1 – Numeration Systems
Imagine that we are in the past—before we had counting systems.
How would you keep track of the number of chickens on your farm??
Having a counting system requires that we recognize a
one-to-one correspondence
between two
equivalent sets:
the set of objects we are counting and the set of numbers we are using to count
them.
Numbers, Numerals, and Numeration Systems:
Number
– The amount being counted or measured
Numeral
– The symbol used to designate the amount (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Numeration System
– A collection of properties and symbols agreed upon to represent numbers
systematically.
The table on pg. 62 has the symbols used for different numeration systems (Babylonian, Egyptian,
Mayan, Greek, Roman, Hindu, Arabic, Hindu-Arabic)
Hindu-Arabic System – Base 10 System:
•No tally marks
•All numerals are constructed from the 10 digits
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
•Place value is based on powers of 10 (the base of the system)
•Concept of Zero
•Expanded form
For example, the number
546
=
500 + 40 + 6
=
(5 * 100) + (4 * 10) + (6 * 1)
=
(5*10
2
) + (4 * 10
1
) + (6 * 10
0
)
(expanded form)
We can use Base-10 Blocks to represent numbers in base-10.