Download Rational Numbers

NAME ______________________________________________ DATE
5-2
Rational Numbers
____________ PERIOD _____
(Pages 205–209)
5
5
9
1
25
5
• The set of whole numbers is {0, 1, 2, 3, 4, 5, …}. Such numbers as , , and are also whole
Sets of
Numbers
numbers because they can be written as a member of this set.
• The set of integers is the set of whole numbers and their opposites.
a
b
• The set of rational numbers consists of all numbers that can be expressed as , where a and b
1
3
are integers and b 0. The numbers and 5 are rational numbers.
Some decimals are rational numbers.
• Decimals either terminate (come to an end) or they go on forever. Every terminating decimal
can be written as a fraction, so all terminating decimals are rational numbers. For example,
45
100
9
20
0.45 or .
Types of
Decimals
• Repeating decimals can always be written as fractions, so repeating decimals are always
rational numbers. You can use bar notation to indicate that some part of a decimal repeats
forever, for example, 0.333… 0.3
.
• Decimals that do not terminate and do not repeat cannot be written as fractions and are not
rational numbers.
Example
Express 0.2
3
as a fraction in simplest form.
Let N 0.232323….
Then 100N 23.232323….
100N 23.232323…
N 0.232323…
Multiply N by 100 because two digits repeat.
Subtract N from 100N to eliminate the repeating part.
99N 23
⇒
23
99
N To check this answer divide 23 by 99.
Practice
Express each decimal as a fraction or mixed number in simplest form.
1. 0.6
5
3. 0.1
2. 0.444...
4. 1.26
Name the set(s) of numbers to which each number belongs.
3
5. 6. 1280
8
3
8. 0.5
7. 2.5
Replace each ● with , , or to make a true sentence.
1
9. ● 0.3
3
10. 2 ● 2.25
6
12. ● 0.75
11. 1.8 ● 1.7
8
5
6
6
13. Standardized Test Practice Which number is the greatest, ,
,
,
or
10
4
?
9
4
A 9
6
B 11
13
5
C 11
6
D 10
13
13. B
4
9
2. 5
33
3. 13
50
4. 1 5. rational 6. integer, rational 7. rational 8. rational 9. 10. 11. 12. 34
3
5
Glencoe/McGraw-Hill
Answers: 1. ©
Glencoe Pre-Algebra