Download Lesson 7 Reteach The Real Number System

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Lesson 7 Reteach
The Real Number System
Numbers may be classified by identifying to which of the following sets they belong.
Natural Numbers
Numbers used for counting. {1, 2, 3, 4, 5, …}
Whole Numbers
The set of natural numbers and 0. {0, 1, 2, 3, 4, …}
Integers
The set of whole numbers and their opposites {…, –2, –1, 0, 1, 2, …}
Rational Numbers
Numbers that can be expressed in the form , where a and b are integers and b ≠ 0.
Irrational Numbers
Numbers that cannot be expressed in the form , where a and b are integers and b ≠ 0.
a
b
a
b
Examples
Classify each number by determining all sets of numbers to which it belongs.
a. 5
The number 5 is used for counting. It is a natural number, a whole number, an integer,
and a rational number.
b. 0.666…
Decimals that terminate or repeat are rational numbers, since they can be expressed as
fractions.
2
0.666, … = .
3
c. –√25
Since –√25 = –5, it is an integer and a rational number.
d. –√11
Since –√11 ≈ 3.31662479… Since the decimal does not terminate or repeat, it is an
irrational number.
Exercises
Classify each number by determining all sets of numbers to which it belongs.
4
1. 30
2. 5
3. √21
4. –√9
5. 0
6. –16
7.
6
2
7
8. √7
Course 3 • Chapter 1 Real Numbers