NAME ______________________________________________ DATE
9-2
The Real Number System
____________ PERIOD _____
(Pages 441–445)
You know that rational numbers can be expressed as a, where a and b
b
are integers and b 0. Rational numbers may also be written as decimals
that either terminate or repeat. However, there are many numbers
(for example, square roots of whole numbers that are not perfect squares)
that neither terminate nor repeat. These are called irrational numbers.
a
Definition of an
Irrational Number
The set of rational numbers and the set of irrational
numbers make up the set of real numbers. The Venn
diagram at the right shows the relationships among
the number sets.
Real Numbers
Rational Numbers
Integers
Whole
Numbers
Irrational
Numbers
Examples
a. Determine whether 0.121231234 …
is rational or irrational.
This decimal does not repeat nor terminate.
It does have a pattern to it, but there is no
exact repetition. This is an irrational number.
b. Solve h2 50. Round your answer to the
nearest tenth.
h 2 50
h 50
or h 50
Take the square root of each side.
h 7.1 or h 7.1 Use a calculator.
Practice
Name the sets of numbers to which each number belongs: the whole
numbers, the integers, the rational numbers, the irrational numbers,
and/or the real numbers.
3
1. 2. 12
4
3. 0.008
4.
13
5. 16.7
6. 7
Solve each equation. Round decimal answers to the nearest tenth.
7. a2 81
8. n2 54
9. 37 m2
10. p2 6
11. 18 w2
12. x2 99
13. k2 5
14. s2 82
15. 61 b2
16. Physics If you drop an object from a tall building, the distance d in feet
that it falls in t seconds can be found by using the formula d 16t2. How
many seconds would it take a dropped object to fall 64 feet?
17. Standardized Test Practice Find the positive solution of y2 254. Round
to the nearest tenth.
A 15.4
B 15.6
C 15.7
D 15.9
Answers: 1. rational, real 2. whole number, integer, rational, real 3. rational, real 4. irrational, real 5. rational, real
6. irrational, real 7. 9, 9 8. 7.3, 7.3 9. 6.1, 6.1 10. 2.4, 2.4 11. 4.2, 4.2 12. 9.9. 9.9 13. 2.2, 2.2
14. 9.1, 9.1 15. 7.8, 7.8 16. 2 s 17. D
©
Glencoe/McGraw-Hill
73
Glencoe Pre-Algebra
Chapter 9
An irrational number is a number that cannot be expressed as , where a and b are
b
integers and b does not equal 0.