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2-1 Numeration Systems
Tally Numeration System
Egyptian Numeration System
Babylonian Numeration System
Mayan Numeration System
Roman Numeration System
Hindu-Arabic Numeration System
Definition Numerals: written symbols to
represent cardinal numbers.
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Numeration system: a collection of properties
and symbols agreed upon to represent numbers
systematically.
Hindu-Arabic Numeration System
1. All numerals are constructed from the 10 digits
2. Place value is based on powers of 10
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Tally Numeration System
Uses single strokes (tally marks) to represent
each object that is counted.
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
= 13
Egyptian Numeration System
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Babylonian Numeration System
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Mayan Numeration System
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Roman Numeration System
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Roman Numeration System
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Hindu-Arabic Numeration System
1. All numerals are constructed from the 10 digits
2. Place value is based on powers of 10
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Place value assigns a value to a digit depending on its placement in a numeral.
Expanded form
If a is any number and n is any natural
number, then
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
Factor
= ´ + ´ + ´ + ´3 2 16789 6 10 7 10 8 10 9 1
= × × × ×na a a a a
n factors
Base-ten blocks
1 long →101 = 1 row of 10 units
1 flat →102 = 1 row of 10 longs, or 100 units
1 block →103 = 1 row of 10 flats, or 100 longs, or 1000 units
Copyright © 2013, 2010, and 2007, Pearson
Education, Inc.
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