Name: Date: CHAPTER
1
The Real Number System
Lesson 1.1 R
epresenting Rational Numbers
on the Number Line
Use the  symbol. Order the numbers from least to greatest. Graph each
number on a horizontal number line.
1.
10 1
, 1 , 0.4, 0.9
3
2
1 4 5
4 3 8
2. 0.23, , ,
Compare. Write , , or .
3. 2.12
4.0.37
2.31 0.317
Round each number.
5. 2,549 to the nearest ten.
6. 23.17 to 1 decimal place.
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Round 7,363.923
7. to the nearest hundredth.
8. to the nearest whole number.
Find the square and cube of each number.
9. 7
10.10
Find the square root of each number.
11. 36
12.81
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Name: Date: Find the cube root of each number.
13. 125
14.512
Complete each inequality using , , or  .
15. |21|
|221|
16. |8|
|288|
Order the numbers from greatest to least. Use the  symbol.
17. 22,
18.23, 42,
100 , 33
16
Find the absolute values of fractions.
Example
a) 5
6
3
4
Find the absolute values of 2 and .
5
5
3 3
2  and 
6 6
4
4
5
3
b) Using a number line, show how far 2 and are from 0. Which number is
4
6
closer to 0?
5
units
6
0
1
3
units
4
5
6
5
6
5
2
is
6
3
is
4
5
3
Because the distance units  units,
6
4
3
4
3
4
1
units to the left of 0.
units to the right of 0.
3
4
is closer to 0.
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2 Chapter 1 Lesson 1.1
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Name: Date: Complete.
19. a)
b)
Find the absolute values of 2
2
2
3
and 2
5
9
4
9
2
and 2 .
4
3
5
Graph the two numbers on a number line and indicate their distances from
0. Which number is farther from 0?
3
2
1
0
1
2
3
is farther from 0.
Solve.
20. a)
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b)
21. a)
b)
5
2
Find the absolute values of 2 and 3 .
8
Graph the two numbers on a number line and indicate their distances from
0. Which number is farther from 0?
Find the absolute values of 1
1
11
and 2 .
4
6
Graph the two numbers on a number line and indicate their distances from
0. Which number is farther from 0?
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Name: Date: Write each number in nm form where m and n are integers.
Example
a)
22
6
7
b)19
6
27 6
7
7
20
52
7
2 27  2
19 5 19
1
Whole numbers have
1 in the denominator.
Complete.
4
6
22. 3 23. 217

4
3 5
6
5
5
6
2
1
6
217 5
1
or 5
21
Write each number in nm form where m and n are integers.
12
18
15
10
25. 1
2
3
27. 1
26. 24 9
21
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24. 2
4 Chapter 1 Lesson 1.1
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Name: Date: Write each decimal in nm form where m and n are integers with n  0.
Example
a)0.6
6
0.6 5 10
5
6 is in the tenths place. Use 10 as the denominator.
3
5
Simplify.
b) 20.25
25
20.25 5 2100
1
5 2
4
5 is in the hundredths place. Use 100 as the
denominator.
Simplify.
Complete.
28. 7.5
7.5 5
5
1
Write the integer,
. Write 0.5 as
.
Write as an improper fraction.
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Write each decimal in nm form where m and n are integers with n  0.
29. 2 0.375
30.3.6
31. 2 9.36
32.3.625
33. 3.21
34. 2 1.045
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Name: Date: Locate the following rational numbers on the number line.
Example
5
6
21.6 and
Step 1
Find the integers that the rational number lies between.
21.6 is located between
5
is a proper fraction so it is located between
6
Step 2
Graph a number line and label the integers.
2
1
and
21
.
0
0
and
1
.
1
Step 3
Divide the distance between the integers into equal segments.
You divide the distance between 0 and 1 into 6 equal segments and the distance
between 22 and 21 into 10 equal segments.
2
1
0
1
Step 4
5
Use the segments to locate 21.6 and .
6
2
1.6
1
0
5
6
1
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22
6 Chapter 1 Lesson 1.1
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Name: Date: Complete.
35. 2
10
1
and
4
5
Step 1
Find the integers that the rational number lies between.
2
1
is a negative proper fraction so it is located between
5
and
10
1
1
can be written as a mixed number, 2 , and 2 lies between
4
2
2
.
and
.
Step 2
Graph a number line and label the integers.
Step 3
Divide the distance between the integers into equal segments.
You divide the distance between 21 and 0 into
the distance between 2 and 3 into
equal segments and
equal segments.
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Step 4
10
1
Use the segments to locate 2 and
.
5
4
Locate the following rational numbers on the number line.
5
8
36. 2 and 2.2
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Answers
b)
11
units
6
1
1
4
units
Chapter 1
2
Lesson 1.1
1
10
2
3
1. 0.4  0.9  1 
0.4
0
10
3
1
2
1
1
2. 0.23 
4

2
5

8
1
4
0.23
1
0.9
22. 3
3
4
4
3
5
8
0
3. 
26. 2
1
1.5
2
4. 
5
10
3
b)
7
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2
20. a)
4
9
4
units
1
2
0
2
3
3
1
2
3
2
3
100
29
32.
8
34. 2
;
8 3
2
3
units
10
2
Step 2
units
0
5
8
4
can be written as a mixed number: 2
1
2
1
2
3
0
1
1 11
6
1
2
3
0
1
2
0
1
2
3
Step 4
3
4
and
lies between 2 and 3.
1
1
2
You divide the distance between 21 and 0 into 5
equal segments and the distance between 2 and
3 into 2 equal segments.
2
21. a) 1 ;
200
5
5
8
209
1
1
Step 3
5 2
b)
321
5
between 21 and 0.
is farther from 0.
1
25
18
2 is a negative proper fraction so it is located
units
2
2
2
35. Step 1
9
4
2
15
30.
234
31. 2
33.
9
4
3
3
1
3
18. 42  23  16
5
3
7
5
17. 33  100  22
9
11
27.
3
8
15. 5
16. 
and 2
5
3
29. 2 13. 5
14.8
2
6
21
2
14
10. 100; 1,000
52
22
17
or 5
6
28. 7.5 5
11. 6
12.9
2
5
2
7. 7,363.92
8.7,364
19. a) 2
17
2
6
3
5. 2,550
6.23.2
9. 49; 343
1
6
23. 217 5
4
3

1
4
24. 2 25.
4
3
0.5
2
1
5
6
1
11
6
6
4
0
1
36.
3
1
5
10
4
0
1
5
8
1
2
3
2.2
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