Rational Numbers

5.1
Rational Numbers
Goal: Write fractions as decimals and vice versa.
Vocabulary
Rational
number:
Terminating
decimal:
Repeating
decimal:
78 Chapter 5 Notetaking Guide
A rational number is a number that can be written as
the quotient of two integers.
A decimal that has a final digit
A decimal that has one or more digits that repeat
without end
Example 1 Identifying Rational Numbers
Show that the number is rational by writing it as a quotient of two
integers.
a. 3 b. 12 c. 4 2
3
d. 2 1
4
Solution
a. Write the integer 3 as .
3
1
b. Write the integer 12 as
12
or 1
. These fractions
are equivalent .
12
1
c. Write the mixed number 4 2
as the improper fraction .
3 14
3
d. Think of 2 1
as the opposite of
4
. First write as .
Then you can write 2 1
as
4
. To write as a quotient
of two integers, you can assign the negative sign to either the
or the . You can write or
9
4
.
numerator denominator
9
4
9
4
9
4
9
4 2 1
4
2 1
4

Example 2 Writing Fractions as Decimals
5
a. Write as a decimal. b. Write
16
4
as a decimal.
9
a. 0.3125 b. 0.44. . .
16 5.0000 9 4.00
4
8
3
6 20
40
1
6
3
6 40
3
2
80
8
0 Answer: Use a bar to
show the
0
Answer: The remainder
is 0 , so the decimal is a
in the
decimal:
4
repeating digit
repeating
0.4.
9
terminating decimal:
5
0.3125.
16
Checkpoint Write the fraction or mixed number as a decimal.
7
1. 2.
20
3
5
0.35 0.6
3. 2 12
4.
25
23
40
Compare 42
and
48
27
.
30
2.48 0.575
Example 3 Using Decimals to Compare Fractions
42
7
0.875 and 2 0.9 Divide.
48
30
Answer: Compare the decimals. > ,
so 27
30
2
4
48
.
0.9 0.875
>
Lesson 5.1 Rational Numbers 79

Example 4 Writing Terminating Decimals as Fractions
a. 0.03
b. 9.4
80 Chapter 5 Notetaking Guide
3
100
4
9
10
3 is in hundredths’ place,
so denominator is 100 .
4 is in tenths’ place,
so denominator is 10 .
9 Simplify fraction.
2
5
Example 5 Writing a Repeating Decimal as a Fraction
To write 0.81 as a fraction, let x 0.81.
1. Because 0.81 has 2 repeating digits, multiply each side of
x 0.81 by , or 100 . Then 100 x 81.81 .
10 2
100 x 81.81
2. Subtract x from 100 x. (x 0.81 )
x
3. Solve for x and simplify. x
99 81
99 99
x
Answer: The decimal 0.81 is equivalent to the fraction
9
.
11
99
81
9
11

Checkpoint Write the decimal as a fraction or mixed number.
5. 0.8 6. 3.75
Order the numbers 17
11
, 1.35, 5.67, 6, ,
2
3
13
from least
4
to greatest.
Graph the numbers on the number line. You may want to write
improper fractions as mixed numbers.
17
2
8
6
6
4
3 3
5 4
7. 0.12 8. 5.3
4
5
33
1
3
Example 6 Ordering Rational Numbers
4
13
4
1.35
2
0
2
Answer: Read the numbers graphed on the number line from
left to right: , , , , , 5.67 .
1
17
2
6
13
4
1.35
1
3
11
3
4
5.67
6
8
Lesson 5.1 Rational Numbers 81