1. Presented by Mr. Laws 8th Grade Math JCMS
The Real Number System
Presented by Mr. Laws
8th Grade Math
JCMS N W Z Q IR

2. Goal/Objective
8.NS: Know that there are numbers that are not rational and approximate them by rational numbers.
8.NS.1: Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in zeros or eventually repeat. Know that other numbers are called irrational numbers.

3. Essential Question
How do I understand and perform operations with the Real Number System? Q N Z W IR

4. The Real Number System
The Real Number System is made up of a set of rational and irrational numbers.
It has at five subsets:
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
Natural Numbers (N)
Irrational Numbers (IR)

5. Real Numbers Definitions
Real Numbers – consists of all rational and irrational numbers.
It includes any number that can be written as a fraction, mixed numbers, terminating and repeating decimals, whole numbers, integers. O -6 4

6. Rational Numbers
Rational Numbers – consists of integers, terminating, and repeating decimals.
It can also be expressed as a fraction.
{…-3, -2, -1, 0, 1, 2, 3, …}

7. Rational Numbers
Integers – consist of natural numbers, their opposites (negative #’s), and zero.
It does not include fractions or decimals.
All whole numbers are integers.
For example:
{…-3, -2, -1, 0, 1, 2, 3, …}

8. Integers
Whole numbers – consist of natural numbers and zero. {0, 1, 2, 3, 4,…}
Natural numbers – are all the counting numbers. {1, 2, 3, 4…}
Negative numbers ={…-4, -3, -2, -1}

9. Rational Numbers
Terminating Decimals are rational numbers that stops before or after the decimal point.
For example: 5.0, 2.75, .40, .0001…etc.
Repeating Decimals are rational numbers that repeats after the decimal point.
For example: .3333…, ,

10. Irrational Numbers
Irrational numbers consist of numbers that are non-terminating and non-repeating decimals.
They cannot be express as a fraction!
Pi is an great example of an irrational number
.001, .0011, , …etc

11. Real Number System Tree Diagram
Rational Numbers
Irrational Numbers
Terminating
Decimals
Repeating
Decimals
Integers
Non-Terminating
And
Non-Repeating
Decimals
Whole
Numbers
Negative #’s
Natural #’s
Zero

12. Your Turn 1. How are the natural and whole numbers different?
2. How are the integers and rational numbers different?
3. How are the integers and rational numbers the same?
4. How are integers and whole numbers the same?
5. Can a number be both rational and irrational? Use the diagram to explain your answer.

13. Your Turn
Answer True or False to the statements below. If the statement is False, explain why.
6. −5 is a rational number. _______
is rational. _______
is a natural number __________
is an integer. _______
… is a rational number.____________

14. Summary What did you learn in this lesson?
What are some important facts to remember about the real number system?
Is there something within the lesson that you need help on?