Download The Real Number System

The Real Number System
Presented by Mr. Laws
8th Grade Math
JCMS
Q
Z
W
N
IR
Goal/Objective
8.NS: Know that there are numbers that are
not rational and approximate them by rational
numbers.
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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.
Essential Question

How do I understand and perform
operations with the Real Number System?
Q
Z
W
N
IR
The Real Number System
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The Real Number System is made up of
a set of rational and irrational numbers.
It has at five subsets:
1.
2.
3.
4.
5.
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
Natural Numbers (N)
Irrational Numbers (IR)
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.
1
2
3
5
4
1.5
2.3333
O

2
Rational Numbers
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Rational Numbers – consists of integers,
terminating, and repeating decimals.
It can also be expressed as a fraction.
1
.5 
2
5
8  8.83333
6
.9
16  4
{…-3, -2, -1, 0, 1, 2, 3, …}
7.5
Rational Numbers
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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, …}
Integers
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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}
Rational Numbers

Terminating Decimals are rational
numbers that stops before or after the
decimal point.

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For example: 5.0, 2.75, .40, .0001…etc.
Repeating Decimals are rational numbers
that repeats after the decimal point.
 For example: .3333…, .75 , 10.635
Irrational Numbers

Irrational numbers consist of numbers that
are non-terminating and non-repeating
decimals.

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They cannot be express as a fraction!
Pi is an great example of an irrational number
 http://www.joyofpi.com/pi.html
  pi
47
4.25837547984...
.001, .0011, .00111, .001111…etc
2
Real Number System Tree Diagram
Real Numbers
Rational
Numbers
Integers
Whole
Numbers
Natural #’s
Terminating
Decimals
Negative #’s
Zero
Irrational
Numbers
Repeating
Decimals
Non-Terminating
And
Non-Repeating
Decimals
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.
Your Turn
Answer True or False to the statements below. If the statement is
False, explain why.
6. −5 is a rational number. _______
7.
8
is rational. _______
8.
16 is a natural number __________
9. 3.25 is an integer. _______
10. 2.434434443… is a rational number.____________
Summary
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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?