Download Real Number System Worksheet File

The Set of Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Subsets of the Real Number System:
1 Natural Numbers
o
These are the counting numbers from 1 to infinite: {1, 2, 3, …, infinite}
2 Wh le Numbers
These are the the counting numbers and also zero: {0, 1, 2, 3, …, infinite}
3 Integers
These are the whole numbers and their opposites. A synonym for opposite is additive inverse.
{negative infinite, …, -3, -2, -1, 0, 1, 2, 3, …, infinite}
4 Rational Numbers
The rational numbers include integers and positive and negative fractions.
Examples include: -.25, 1/3, 0, 8, -100, √25 , ∛27
Notice that .25 is a terminating decimal, and 1/3 is a repeating decimal.
5 Irrational Numbers
Examples are the number pi (π) and imperfect roots such as √6 and ∛54
Enter these roots in your calculator and notice that the decimals don't terminate and don't repeat
Analyze the set of real numbers and answer the questions below.
1. What are the the additive inverses (opposites) and multiplicative inverses (reciprocals) for the following real numbers?
Hint: Rewrite both of the numbers as reduced fractions, first.
0.4
−1 .6
additive inverse
multiplicative inverse
2. Write the given real numbers in order proceeding from the smallest negative to the greatest positive real number.
Then, graph the real numbers on the number line. Add a scale with negative and positive integers and zero to the number line.
3.25, -7/8, pi, -2√2, -3, -10/3
3a. Assign each number to the proper subsets of the real number system by checking the columns that apply.
Natural
3b. Abstract application:
How many bus stops do the Chattanooga Carta
buses make today?
To which subsets of the real number system
does this number belong?
11
0
0.25
-⅔
-5
-π
Whole Integers Rational Irrational
Real