the real number system
Post on 26-Jan-2015
602 Views
Preview:
DESCRIPTION
TRANSCRIPT
THE REAL NUMBER SYSTEM
Complex numbers ( C )
Real Numbers (R )
Rational numbes (Q)
Integers (Z)
Whole numbers
Natural numbers(N)
Prime numbers
Even numbers
Composite numbers
Odd Numbers
Zero
Negative integers
Fractions
Irational numbers
Imaginer Numbers
N : 1,2,3,….Z : …,-2,-1,0,1,2,..
Q : 0,,, bZbab
a
Irational: ,3,2
IrasionalQR
Real Numbers
IrrationalNumbers
π
0.101001
√2
Rational Numbers
¼ ⅓
0.6
- ⅔ √0.25
Integers
- 4 -3
-8
Whole Numbers
0
NaturalNumbers
2 5
Concept SummaryExample Natural Whole Integer Rational Irrational Real
0 / / / /
4 / / / / /
-7 / / /
√25 / / / / /
√41 / /
¼ / /0.1212… / /0.0101101
…/ /
Operation of IntegersOperations Properties Form/ Expression
1. Addition 1. Clossure2. Commutativ
e3. Associative4. Identity
element
1. For a,b Є Integers so, a + b Є integers
2. a + b = b + a3. ( a + b ) + c = a + ( b + c)4. a + 0 = 0 + a = a
2. Substraction
Invers of addition
a – b = a + ( -b ), -b is invers of b
3. Multiplication
1. Clossure2. Commutativ
e3. Associative4. Distributive
5. Identity element
1. For a, b Є integers so, a x b Є integers
2. a x b = b x a3. ( a x b ) x c = a x ( b x c )4. a x ( b + c ) = (a x b ) + ( a x c)
a x ( b – c ) = ( a x b ) – ( a x c )5. a x 1 = 1 x a = a
4. Division Invers of multiplication
a : b = a x 1/b
+ - x ¸
plussummore thanincreased bytotalin all
minusdifferenceless thansubtractdecreased by
timesproductmultipliedeachof
dividedquotient
Four Fundamental Operations
Symbol Symbol
√ Radical sign ≤ Less than or equal to
∑ summation ≥ Greater than or equal to
Π phi Є Element of
∞ infinity ∩ intersection
! factorial U union
≠ Not equal to % percent
=>
Equal to
Greater than
°<
Degree
Less than
Positive and Negative Numbers
1.1
You may write:• the temperature of 5 degrees above
zero as 5 ºC, • the temperature of 5 degrees below
zero as -5 ºC.
0
+5
-5
0+5-5
Vertical number line
Horizontal number line
th
erm
om
eter
The numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows.
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.
0 is neither positive nor negative
Negative integers Positive integers
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Natural numbers ( bilangan Asli ) : 1, 2, 3, 4, …
Whole numbers ( bilangan Cacah ) : 0, 1, 2, 3, 4, …
Integers ( bilangan Bulat ) : …, -2, -1, 0, 1, 2, …
Example 1
a. Determine all integers between 5 and 4.
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
Comparing and Ordering Integers
What if we use a vertical number line?
Change the sign to <, >, or = on 4 7
Solution:
Example 2
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
The number 4 is located on the right side of 7. Therefore,
4 > 7.
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
decrease increase
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 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
Students’
Names Number of
Correct
Answers
Number of Wrong
Answers
Number of Unanswered
Questions Total Score
Abdullah 5 3 2
Aminah 6 4 0
Galuh Erna 5 2 3
Zainul 8 2 0
Nabila 8 1 1
Zaty 8 0 2
Hamidah 7 1 2
Yusuf 7 3 0
17
20
18
30
31
32
27
25
top related