2. ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)

3. ® Ramziah AL Kaissi Natural Numbers Are the set of counting numbers. Example:{1, 2, 3,…} Zero is not a natural number

4. ® Ramziah AL Kaissi Whole Numbers: Whole numbers are the same as the natural number. The only difference is that whole numbers include the number zero. All Natural Numbers are Whole Numbers.

5. ® Ramziah AL Kaissi Integers Include all positive whole numbers, negative whole numbers and zero Example {…,-3, -2, -1, 0, 1, 2, 3,…}

6. ® Ramziah AL Kaissi All Natural Numbers are Integers. Natural numbers is subset of the Whole Numbers. Whole Numbers is subset of Integers. Natural Number is subset of Integers

7. ® Ramziah AL Kaissi Examples of Integers 6 -12 0 186 -934 Integers Whole Numbers Natural

8. ® Ramziah AL Kaissi Rational Numbers Can be written as a ratio of two integers. e.g.: Can be written in decimal form is terminating or repeating.

9. ® Ramziah AL Kaissi Terminating Decimal: Are decimals that contain a finite number of digits. Examples:  36.8 = 368/10  0.125= 125/1000  4.5= 45/10 Terminating Decimals are Rational Numbers because they can be written as fractions

10. ® Ramziah AL Kaissi Repeating Decimal: Are decimals that contain an infinite number of digits. Examples: 0.333…, 7.689689… Repeating Decimals are Rational Numbers because they can be written as fractions

11. ® Ramziah AL Kaissi Examples of Rational Numbers 16 1/2 3.56 -8 1.3333… - 3/4 Rational Numbers Integers Whole Numbers Natural

12. ® Ramziah AL Kaissi All Natural Numbers and All Integers are Rational Numbers Natural numbers is one subset of the Rational Numbers. Integers are another subset of Rational Numbers. Whole Numbers is another subset of Rational Numbers.

13. ® Ramziah AL Kaissi All Natural Numbers and All Integers are Rational Numbers Natural numbers, whole numbers and integers are Rational numbers because you can write them as a fraction

14. Irrational Numbers Irrational numbers are any numbers that cannot be expressed as fractions (ratio of two integers). They are expressed as non-terminating, non- repeating decimals; decimals that go on forever without repeating a pattern. Examples of irrational numbers: 0.34334333433334… 45.86745893… (pi) = 3.14… ® Ramziah AL Kaissi

15. Real Numbers Irrational Numbers & Rational Numbers

16. Summary Real Numbers Rational Numbers Integers Whole Numbers Natural Irrational Numbers ® Ramziah AL Kaissi