### 4.2 - Place-Value Numeration Systems

```4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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4.2 ­ Place­Value or Positional Value System
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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In a place­value system sometimes called a positional value system, the value of the symbol depends on its position in the representation of the number.
ex. The 2 in 20 represents two tens and the 2 in 200 represents two hundreds
A true positional value system requires a base and a set of symbols, including a symbol for zero and one for each counting number less than the base.
A decimal number system is the most common positional value system which is base 10. Our Hindu­Arabic System is a decimal number system.
Digits are the symbols used to make up numbers. In the Hindu­Arabic system the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Positional values are based on the base, and the location of the digit. To determine the positional value you take the base to the power that corresponds to the digit location. The positional values for the Hindu­Arabic system are:
0
1
2
..., (10)5, (10)4, (10)3, (10) , (10) , (10)
We more commonly express this as:
..., (10)5, (10)4, (10)3, (10)2, (10)1, 1
Which can be simplified to:
..., 100,000, 10,000, 1,000, 100, 10, 1
Expanded form of a number is when you express the number as the sum of each digit times its corresponding positional value.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write 10,425 in expanded form.
Write 346,728 in expanded form.
Write 143 in expanded form.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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The Babylonian System
The positional values are:
..., (60)4, (60)3, (60)2, (60)1, 1
In a Babylonian numeral, a gap is left between the characters to distinguish between the various place values.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write 9820 in Babylonian.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write 2519 in Babylonian.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write in Hindu­Arabic.
Write in Hindu­Arabic.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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The Mayan System
The number system is based on their religious and agricultural calendar.
Numbers are written vertically, like the Chinese, with the unit position on the bottom.
The place values are:
..., 18x(20)4, 18x(20)3, 18x(20)2, 18x20, 20, 1
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write 4025 in Mayan.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write 3685 in Mayan.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Write in Hindu­Arabic.
Write in Hindu­Arabic.
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4.2 ­ Place­Value Numeration Systems ­ FILLED IN.notebook
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Homework
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