Download Lesson 1.2 Writing Rational Numbers as Decimals

Name: Date: Lesson 1.2 Writing Rational Numbers as Decimals
Use long division to write rational numbers as terminating decimals.
Example
5
8
0.625
8) 5.000
48
20
16
40
40
0
So,
b)
2
Add zeros after the decimal point.
The remainder is 0.
You could also write
1
2 as the mixed
4
9
and then
number
4
5
5 0.625.
8
1
4
0.25
4 ) 1.00
8
20
20
0
1
So, 2 5 2.25.
4
1. 3 25
Divide 5 by 8.
)
25 3.00 divide: 9 4 4.
Divide 1 by 4.
Add zeros after the decimal point.
The remainder is 0.
2. 17
16
)
16 17.000
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a)
8 Chapter 1 Lesson 1.2
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Name: Date: Using long division, write each rational number as a terminating decimal.
3. 2 1 4.
8
5.
3
16
6.
9
20
18
8
Use long division to write rational numbers as repeating decimals.
Example
7
9
Stop dividing when you
see the digits repeat
themselves.
0.7 7 7
9 7.000
63
70
63
70
63
7
7
So, 5 0.777...
9
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)
7.
6
11
11 6.0000 )
8.
17
15
15 17.000
)
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Name: Date: Using long division, write each rational number as a repeating decimal.
Use bar notation to indicate the repeating digits.
Example
5
11
0.4545
11) 5.0000
44
60
55
50
44
60
55
5
5
So, 5 0.4545... 5 0.45
11
9. 2 9
The digits 5 and 4 form
a repetitive group.
10.
30
22
Using long division, write each rational number as a repeating decimal
with 3 decimal places. Identify the pattern of repeating digits using
bar notation.
11.
13
6
12. 34
33
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Name: Date: Using a calculator, write each rational number as a repeating decimal.
Use bar notation to indicate the repeating digits.
13. 18 14. 5
15. 17 16.
11
18
36
29
27
Compare the positive rational numbers using the symbols  or .
Use a number line to help you.
Example
9 and 10
8
9
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9
5 1.125
8
Write each rational
number as a decimal.
10
5 1.111... 5 1.1
9
Compare the decimals, 1.125 and 1.1.
10
9
9
8
1.110
1.115
1.120
1.125
1.130
1.1
1.125 lies to the right of 1.1.
So, 1.125
9
8
1.1.
10
9
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Name: Date: Complete.
25
17. 22 and
8
7
Write each rational number as a decimal.
22
5
7
25
5
8
Compare the decimals,
Complete the number line and compare the numbers.
and
lies to the right of
So,


.
.
.
Compare the positive rational numbers using the symbols  or .
Use a number line to help you.
18. 3 and 5 19. 10 and 9
9
20. 13 and
8
21. 17 and 1
11
6
8
11
8
10
9
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4
12 Chapter 1 Lesson 1.2
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Name: Date: Compare the negative rational numbers using the symbols  or .
Use a number line to help you.
Example
1
and 1
4
5
Method 1
Write each rational number as a decimal.
1
2 5 20.25
4
1
2 5 20.2
5
|20.25 |5 0.25
|20.2 | 5 0.2
4 5
1
1
0.3
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0.2
0.25
Compare using a
number line.
Use the absolute
value of 0.25 and
0.2 to help you
graph the decimals
on a number line.
0.25 units
0.2 units
0.1
0
From the number line, you see that 20.25 lies farther to the left of 0 than 20.2.
So, 20.2  20.25 ?
1
1
2
5
4
2
Method 2
Write an inequality using the absolute
value of the two numbers.
|20.25 |  |20.2 | The two numbers are negative, so the number with the greater
absolute value is farther to the left of 0. It is the lesser number.
20.2  20.25.
2
You can compare using
place value.
1
1
2
5
4
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22. 22 7 and 22 8
9
8
Method 1
Write each rational number as a decimal. Then find the absolute value of each
decimal to help you graph the decimals on a number line.
22
7 5
8
units
units
|
|5
8
22 5
9
|
From the number line, you see that
of 0 than
0
5
|5
.


Method 2
Write an inequality using the absolute values of the two numbers.
|
||
|
The number with the greater absolute value is
left of 0. Hence it is the
So,


and it is farther to the
number.
Compare the negative rational numbers using the symbols  or .
Use a number line to help you.
23. 2
3
4
and 2 4
5
24. 2
1
22
and 23
10
7
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So,
lies farther to the left
14 Chapter 1 Lesson 1.2
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Lesson 1.2
9.0.2
10.1.36
0.12
1.
25 3.00
25
11. 2.166
12.1.030
)
13. 1.63
14.0.27
15. 0.472
16.1.074
50
50
17.
0
2.
3
5 0.12
25
1.0625
16 17.0000
)
22
7
25
5 3.142857...
Compare the decimals,
3.142857… and 3.125.
8
5 3.125
25
8
16
22
7
100
96
40
32
80
80
3.120
17
5 1.0625
16
3.140
3.150
3.142857...
3.142857… lies to the right of 3.125.
So, 3.142857…  3.125
0
3.130
22
18.
7
 25
8
5
6
3
4
3.2.1254.0.45
5.0.18756.2.25
0.5454
11 6.0000
55
)
0.7
19.
50
44
60
55
50
44
6
8.
6
11
)
4
 5
6
9
10
10
11
10
11
 0.910
9
10
20.
1.10
13
11
 1.15
8
21.
5
17
15
1.20
9
1
1.870
50
45
13
11
9
8
20
15
50
45
0.9
0.900
5 0.5454...
1.133
15 17.000
15
3
0.8
1
1.880
7
8
8
9
1  1
7
8
8
9
1.890
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7.
5 1.133...
156 Answers
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22. Method 1
7. 5; 6
7
22 5 22.875
8
5.7
32
22.875 5 2.875
22 5 2 2.888... 5 2 2.8
8
9
22.8 5 2.8
2 8 522.828427125...
2 8 lies between the tenths 22.8 and 22.9.
The value of 2 8 with two decimal places is
22.83.
Which tenth is 2 8 closer to? 22.8.
7
2
8
8
2
9
2.8 units
2.875 units
3
2
0
1
2.8 2.875
2.9
From the number line, you see that 22.8 lies
farther to the left of 0 than 22.875.
9. 22; 23
So, 22.875  22.8
7
8
8
9
22  22
So, 22.875  22.8
7
8
8
9
4
22
1
4
5
7
10
9
,
2 , 22.31,
11
7
8 , 3.001
Find an approximate value of
14 by using a
The value of 14 with two decimal places is 3.74.
Which tenth is 14 closer to? 3.7
calculator:
14 5 3.741657387...
3.7
4.7
7.0
6.9
48
7.2
7.3
53
10.8
117
3.8
14
1. 
2. 
3. 
4. 
5. Use a calculator to represent each number in
decimal form with 3 decimal places.
0.831  0.832, 2 8  22.828,
1
p
 1.571,  0.143,
2 7  22.646
Ordering the numbers from least to greatest
using the symbol ,
1
p
2 8  2 7   0.831 
14 lies between the tenths 3.7 and 3.8.
4. 2; 3
5.8
34
Lesson 1.4
14 between?
2.4
6. 4; 5
5.9
14. 210.817
3. Which two whole numbers is
3 and 4
2.8
5. 2; 3
4.5
21
10.9
1
2. 2 19 , 2 23 , 13,
4.6
Lesson 1.3
2.6
7
13.7.280
3
4 , 5,
12. 27; 28
23. 2  2 24. 2  23
1.
2.7
11. 25; 26
The number with the greater absolute value is
22.8 and it is farther to the left of 0. Hence it is
the lesser number.
22  22
2.8
8
10. 24; 25
Method 2
22.875  22.8
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5.6
8. Which two integers is 2 8 between? 22 and 23
Find an approximate value of 2 8 by using a
calculator:
7
2.9
8
2.5
6
23
7
2
8 3
2
1
7
7
2
1
0
0.831
1
π
2
2
4.8
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