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# The real number system

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• 1. The Real Number System
• 2. N : 1,2,3,….
Z : …,-2,-1,0,1,2,..
Q :
Irational:
• 3. 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
• 4. Concept Summary
• 5. Operation of Integers
• 6. Four Fundamental Operations
• 7.
• 8. 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,
• 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 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, …
• 11. 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
• 12. 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.
• 13. 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
• 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 2
17
20
18
30
31
32
27
25