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CHAPTER 4

CHAPTER 4. Number Representation and Calculation. §4.1, Our Hindu-Arabic System and Early Positional Systems. Learning Targets:. I will evaluate an exponential expression. I will write a Hindu-Arabic numeral in expanded form. I will express a number’s expanded form as a Hindu-Arabic numeral.

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CHAPTER 4

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  1. CHAPTER 4 Number Representation and Calculation

  2. §4.1, Our Hindu-Arabic System and Early Positional Systems

  3. Learning Targets: I will evaluate an exponential expression. I will write a Hindu-Arabic numeral in expanded form. I will express a number’s expanded form as a Hindu-Arabic numeral. I will understand and use the Babylonian numeration system. I will understand and use the Mayan numeration system. 3

  4. VOCABULARY exponential notation exponential expression Hindu-Arabic number system digits expanded form place value

  5. Crititcal Thinking: A number system has only two digits, 0 and 1. What place values (using our current number system) would you use for each digit for the number 101011?

  6. Exponential Notation 6

  7. Example 1: Understanding Exponential Notation Evaluate the following: 108. Solution: Since the exponent is 8, we multiply eight 10’s together: 108 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 100,000,000 Notice the relationship: 7

  8. Our Hindu-Arabic Numeration System An important characteristic is that we can write the numeral for any number, large or small, using only ten symbols called digits: 0,1,2,3,4,5,6,7,8,9 Hindu-Arabic numerals can be written in expanded form, in which the value of the digit in each position is made clear. We can write663 in an expanded form such that 663 = (6 × 100) + (6 × 10) + (3 × 1) = (6 × 102) + (6 × 101) + (3 × 1) 8

  9. Our Hindu-Arabic Numeration System Hindu Arabic numeration system is called a positional-value,or place-value, system. The positional values in the system are based on the powers of ten: …,105, 104, 103, 102, 101,1 9

  10. Example 2: Writing Hindu-Arabic Numerals in Expanded Form Write 3407 in expanded form. Solution: 3407 = (3 × 103) + (4 × 102) + (0 × 101) + (7 × 1) or = (3 × 1000) + (4 × 100) + (0 × 10) + (7 × 1) GP: Pg 199, #17, 19 10

  11. Example 3: Expressing a Number’s Expanded Form as a Hindu-Arabic Numeral Express the expanded form as a Hindu-Arabic numeral: (7 × 103) + (5 × 101) + (4 × 1). Solution:We start by showing all powers of ten, starting with the highest exponent given. Any power left out is expressed as 0 times that power of ten. (7 × 103) + (5 × 101) + (4 × 1) = (7 × 103) + (0 × 102) + (5 × 101) + (4 × 1) = 7,054 GP: Pg 199, #27, 31 11

  12. The Babylonian Numeration System The place values in the Babylonian system use powers of 60. The place values are The Babylonians left a space to distinguish the various place values in a numeral from one another. 12

  13. Example 4: Converting from a Babylonian Numeral to a Hindu-Arabic Numeral Write as a Hindu-Arabic numeral. Solution: From right to left the place values are 1, 601, and 602. 13

  14. Remember Tallying Data? Sometimes it is necessary to tally when you are counting, like when your homeroom teacher tallies the Homecoming court ballots. 1 = | 5 = |||| 34 = |||| |||| |||| |||| |||| |||| ||||

  15. The Mayans had a very similar way of counting and writing their totals. It is much like tallying but they use vertical lines and dots…

  16. The Mayan Numeration System The place values in the Mayan system are Numerals in the Mayan system are expressed vertically. The place value at the bottom of the column is 1. 16

  17. Example 5: Using the Mayan Numeration System Write as a Hindu-Arabic numeral. Solution:The given Mayan numeral has four places. From top to bottom, the place values are 7200, 360, 20, and 1. Represent the numeral in each row as a familiar Hindu-Arabic numeral. 17

  18. Homework GP: Pg 200, #37, 41, 51, 55 Pg 199 – 200, #16, 18, 24, 26, 34 – 44(e), 48 – 60 (e)

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