1. Real Numbers (subsets of real numbers and ordering real numbers)

2. How to use this tutorial!
This tutorial is designed to teach you about Real numbers ( subsets of real numbers and ordering real numbers). The presentation starts with notes and examples followed by practice problems.
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3. Definitions to know Natural (or counting) numbers: N= {1,2,3…}
Whole numbers: W={0,1,2,3…}
Integers: {…-3,-2,-1,0,1,2,3…}
Rational numbers: Q={all numbers that can be expressed in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal.
Irrational number: I={all nonterminating, nonrepeating decimals}. Any number that is not a perfect square has an irrational square root.
Real numbers: R={all rationals and irrationals}

4. Shortcut Real Numbers- (R) Irrational Numbers- (I)
Rational Numbers- (Q)
Integer- (Z)
Whole Numbers- (W)
Natural Numbers- (N)

5. Real Numbers
Real numbers can be divided into two basic groups: Irrational numbers and Rational numbers.
Rational Numbers can further be divided into 3 groups: integers, whole numbers, and natural numbers.

6. Rational Numbers
Rational numbers are all numbers that can be expressed in the form m/n, where m and n are integers and n is not zero}. The decimal form of a rational number is either a terminating or repeating decimal.
A natural number is also always : a whole number, integer, rational number, and real number, etc.
Although a natural number is always an integer; an integer is not always a natural number, etc.
Example:
2, 8/2, 15, 83= real/rational/ integer /whole /natural
-2,-8/2,-15,-83= real/rational/ integer
Rational numbers (Q)
Integers (Z)
Whole numbers (W)
Natural Numbers (N)

7. Irrational Numbers
Irrational numbers are all nonterminating, nonrepeating decimals. Any number that is not a perfect square has an irrational square root.
Examples: …. 
…..
17

8. Examples of Real Number’s Subsets
3/4= real/ rational
0= real/rational/integer/whole
….= real/irrational
1= real/rational/integer/whole/natural
= real/irrational
1/3= real/ rational
91,215,225,201,544= real/rational/integer/whole/natural

9. Practice 1(subsets of real numbers)
Which of the following numbers is irrational? A
-1/2 B
3.63 C
121 D
6/55
               
               

10. Practice 2 (subsets of real numbers)
 36 is what kind of number? A
Real/ Irrational B
Real/rational/integer/ whole/natural C
Real/rational/integer/whole D
Real/rational

11. Practice 3 (subsets of real numbers)
Which of the following is a rational number? A 3 B  C
1/5 D
25/115

12. Practice 4 (subsets of real numbers)
-6 is what kind of number? A
Real/rational/integer B
Real/irrational C
Real/rational D
Real/rational/integer/ whole

13. Ordering Real Numbers Real numbers are ordered from least to greatest.
Example: 1, -4, 49, -16/2, 19/5
ordered from least to greatest would be:
-16/2 (-8), -4, 1, 49 (7), 19/5(3.8)

14. Practice 5 (ordering real numbers)
Order the following numbers from smallest to largest:
-8, 14/3, 10, 5 A
-8, 14/3, 10, 5 B
-8, 5, 14/3, 10 C
-8, 10, 5, 14/3 D
-8, 14/3, 5, 10

15. Practice 6 (ordering real numbers)
Order the following numbers from least to greatest:
144, -47, 19/6, -13 A
-47, -13, 19/6, 144 B
-47, -13, 144, 19/6 C
-13, -47, 144, 19/6 D
-47, 144, 19/6, -13

16. References
Information retrieved 11/30/05 from:

17. YAY!!!
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