4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 4.2 PlaceValue or Positional Value System 1 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 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. 2 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write 10,425 in expanded form. Write 346,728 in expanded form. Write 143 in expanded form. 3 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 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. 4 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write 9820 in Babylonian. 5 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write 2519 in Babylonian. 6 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write in HinduArabic. Write in HinduArabic. 7 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 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 8 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write 4025 in Mayan. 9 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write 3685 in Mayan. 10 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Write in HinduArabic. Write in HinduArabic. 11 4.2 PlaceValue Numeration Systems FILLED IN.notebook October 23, 2015 Homework 12

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