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The real number system
 

The real number system

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    The real number system The real number system Presentation Transcript

    • The Real Number System
    • N : 1,2,3,….
      Z : …,-2,-1,0,1,2,..
      Q :
      Irational:
    • Real Numbers
      Rational Numbers
      ¼ ⅓
      0.6
      - ⅔ √0.25
      Irrational
      Numbers
      π
      0.101001
      √2
      Integers
      - 4 -3
      -8
      Whole Numbers
      0
      Natural
      Numbers
      2
      5
    • Concept Summary
    • Operation of Integers
    • Four Fundamental Operations
    • 1.1
      Integers and Their Symbols
      A
      +5
      0
      -5
      +5
      -5
      0
      Positive and Negative Numbers
      The numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows.
      thermometer
      Horizontal number line
      You may write:
      • the temperature of 5 degrees above zero as 5 ºC,
      • the temperature of 5 degrees below zero as -5 ºC.
      Verticalnumber line
    • -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
      Positive integers
      Negative integers
      0 is neither positive nor negative
      A set of integers; ..., 3, 2, 1, 0, 1, 2, 3, ... , can be symbolized as Z.
      • The complete number line of integers can be drawn as follows.
      Natural numbers ( bilanganAsli ) : 1, 2, 3, 4, …Whole numbers ( bilanganCacah ) : 0, 1, 2, 3, 4, …Integers ( bilanganBulat ) : …, -2, -1, 0, 1, 2, …
    • a. Determine all integers between 5 and 4.
      Example 1
      Solution:
      4, 3, 2, 1, 0, 1, 2, 3
      b. Write all even integers between 6 and 11.
      Solution:
      The even integers between 6 and 11 are 4, 2, 0, 2, 4, 6, 8, and 10
      c. Write all odd integers between 7 and 8.
      Solution:
      The odd integers between 7 and 8 are -5, -3, -1, 1 , 3 , 5, and 7
    • B
      -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
      Comparing and Ordering Integers
      -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
      increase
      decrease
      What if we use a vertical number line?
      Change the sign  to <, >, or = on 4 7
      Solution:
      Example 2
      The number 4 is located on the right side of 7. Therefore, 4 > 7.
    • Problem 1
      Arrange the following numbers from the least to the greatest.
      a. 5, 3, 6, 6, 2, 4, 1
      b. 9, 5, 6, 12, 17, 8, 14
      Problem 1
      Solution :
      a. -6, -3, -1, 2, 4, 5, 6
      b. -14, -12, -5, 6, 8, 9, 17
    • In a mathematics test, the score for the right answer is 4, for the wrong answer is -1, and 0 for failing to answer.
      Complete the table below (use a spreadsheet, if possible) and then sort the students based on their scores from the highest to the lowest.
      Problem 2
      17
      20
      18
      30
      31
      32
      27
      25