Download Fractions and Decimals

LES
SO
N
Fractions and Decimals
Goal: Write fractions as decimals and decimals as fractions.
Vocabulary
When a long division problem results in a
remainder of 0, the quotient is a terminating
decimal.
Terminating decimal:
Repeating decimal:
1
EXAMPLE
Need help
with dividing decimals?
See page 71
of your textbook.
5
8
When a long division problem results in one
or more digits repeating without end, the
quotient is a repeating decimal.
Writing Fractions as Decimals
3
5
Write (a) and (b) 2 as decimals.
Solution
a.
b.
0.625
85
.0
0
0
48
0.6
53
.0
Write zeros in
dividend as
placeholders.
Write a zero in dividend
as a placeholder.
30
20
Remainder is zero .
0
16
40
40
0
Remainder is zero .
5
Answer: 0.625
8
90
|
Chapter 4
Notetaking Guide
3
Answer: 2 2 0.6 2.6
5
Write the fraction or mixed number as a decimal.
Guided Practice
7
10
25
400
1. 3
4
2. 0.7
0.0625
2
EXAMPLE
1
8
3. 4
4. 3
4.75
3.125
Writing Fractions as Repeating Decimals
11
6
14
15
Write (a) and (b) as decimals.
Solution
a.
The digit
1.833 . . .
b.
3 keeps
repeating.
61
1
.0
0
0
The digit
0.933 . . .
3 keeps
repeating.
151
4
.0
0
0
6
13 5
50
50
48
45
20
50
Remainder will
never be zero .
18
Remainder will
20
never be zero .
11
14
Answer: 1.83
6
EXAMPLE
Need help
with place value?
See page 56
of your textbook.
3
Answer: 0.93
15
Writing Decimals as Fractions
Write (a) 0.72 and (b) 3.875 as a fraction or mixed number.
Solution
5 is in the
72
a. 0.72 875
b. 3.875 3 100
18
1
hundredths’
p
4
place.
4
25 p 1
18
25
1000
2 is in the
thousandths’
place.
1
7 p
125
3 25
8 p1
1
7
38
Lesson 4.7
Fractions and Decimals
| 91
EXAMPLE
Only the
digit(s) under the
bar should be
repeated. In Example 4,
Kitten 1's weight
written as a decimal
is 0.83 = 0.8333...,
not 0.838383....
4
Ordering Numbers
Veterinarian Jorja’s cat gave birth to a litter of kittens. She took
the kittens to the veterinarian for a check-up. The kitten’s weights
were recorded for their medical records. What is the order of the
kittens from least to greatest weight?
5
Kitten 1: pound 0.83 pound
6
2
5
1
Kitten 3: pound 0.25 pound
4
Kitten 2: pound 0.4 pound
3
8
Kitten 4: pound 0.375 pound
Answer: Because 0.25 < 0.375 < 0.4 < 0.83 , the kittens are, from
least to greatest weight, Kitten 3 , Kitten 4 , Kitten 2 , and Kitten 1 .
Guided Practice
5
12
Write the fraction or mixed number as a decimal.
17
8
5. 0.416
7
16
2
9
6. 7. 3
2.125
8. 6
3.2
6.4375
Write the decimal as a fraction or mixed number.
9. 0.8
10. 3.35
4
5
92
|
Chapter 4
Notetaking Guide
7
20
3
11. 0.625
5
8
12. 1.175
7
40
1