The real number system
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John scored 17 points (4x4 + 0x1 + -1x3 = 17) Mary scored 20 points (4x5 = 20) Adam scored 18 points (4x4 + -1x2 = 18) Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30) Kim scored 31 points (4x7 + 4x1 = 31) Jenny scored 32 points (4x8 = 32) Zack scored 27 points (4x6 + 4x1 = 27) Amy scored 25 points (4x5 + 4x1 = 25) The students sorted from highest to lowest scores are: 1
The real number system
- 1. The Real Number System
- 2. N : 1,2,3,….Z : …,-2,-1,0,1,2,..Q :Irational:
- 3. Real NumbersRational Numbers ¼ ⅓0.6 - ⅔ √0.25IrrationalNumbersπ0.101001√2Integers- 4 -3-8Whole Numbers0NaturalNumbers2 5
- 8. 1.1Integers and Their SymbolsA+50-5+5-50Positive and Negative NumbersThe numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows. thermometerHorizontal number lineYou may write: the temperature of 5 degrees above zero as 5 ºC,
- 9. the temperature of 5 degrees below zero as -5 ºC. Verticalnumber line
- 10. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Positive integersNegative 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, …
- 11. a. Determine all integers between 5 and 4.Example 1Solution: 4, 3, 2, 1, 0, 1, 2, 3b. 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 10c. 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
- 12. B-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Comparing and Ordering Integers-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6increase decreaseWhat if we use a vertical number line?Change the sign to <, >, or = on 4 7 Solution:Example 2The number 4 is located on the right side of 7. Therefore, 4 > 7.
- 13. Problem 1Arrange the following numbers from the least to the greatest.a. 5, 3, 6, 6, 2, 4, 1b. 9, 5, 6, 12, 17, 8, 14 Problem 1Solution :a. -6, -3, -1, 2, 4, 5, 6b. -14, -12, -5, 6, 8, 9, 17
- 14. 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 21720183031322725