Name: Date: Lesson 1.4 Introducing the Real Number System
Using a calculator, compare each pair of real numbers using either  or .
1. 11
2 8
2. 2 7
3.32
3. 20.182476
2 24
4. 24.89898
20.1824762…
Represent each real number as a decimal up to three decimal places.
Locate each number on a real number line.
Example
1
2
67
, 2 35,
25
5 , 27, 2
Use a calculator to represent each number in decimal form with 3 decimal places.
5 2 5 5.500, 27  5.196, 2 25 5 22.680, 2 35  25.916, 3 150  5.313
Ordering the numbers from the least to the greatest using the symbol ,
2 35 2 25  27  3 150  5 2
Locate each number approximately on a real number line.
3
150
67
1
67
1
35
6 5 4
27
0
3 2 1
1
2
3
3
4
1
150 5 2
5
6
π 1
5. 0.831, 2 8 , , , 2 7
2 7
Use a calculator to represent each number in decimal form with 3 decimal places.
0.831 
, 1
2
7
Ordering the numbers from least to greatest using the symbol ,
,π 
,2 8 




,2 7 
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67
25
Locate each number approximately on the real number line.
3
2
1
0
1
2
18 Chapter 1 Lesson 1.4
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Name: Date: Represent each real number as a decimal up to three decimal places.
Locate each number on a real number line.
6. 10 , 10, 2π , 3 , 3
3
3
7. 2 7, 2
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8.
158
,
60
7
5 14
11
, 0.54, 2 ,
2 15
3
2,
π2 3
, , 20.84173
5 13
9. 22.384, 2
4
183
, 2 15 , 2
,2
17
58
99
8
Reteach Course 2A 19
MIF_Reteach C2_Ch01.indd 19
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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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MIF_Reteach C2_Ch01-05_Ans.indd 157
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6. 10 ,  3.333,
9. 8 and 3 are significant digits.
There are 2 significant digits.
3  1.732
3
7
8. 1, 9, 6, and 9 are significant digits.
There are 4 significant digits.
10 ,  3.162,
3
2p
3
 2.094,  0.429,
3
7
0
1
7. 2 7  2 2.646, 2
0.54 
2π
3
10
2
3
3
11
10. The 5th significant digit is 4, which is less than 5.
128,043 is closer to 128,000 than to 128,100.
So, the integer rounded to 4 significant digits is
128,000.
10
3
4
 2 3.667,
3
5
0.545, 2  21.118,
2
14
 0.933
15
11
3
7
5
2
14
15
0.54
11. The 6th significant digit is 9, which is greater than 5.
150,659 is closer to 150,660 than to 150,650.
So, the integer rounded to 5 significant digits is
150,660.
12. The 3rd significant digit is 5.
23,513 is exactly between 23,000 and 24,000.
So, the integer rounded to 2 significant digits is
24,000.
13.290
14.208,600
15. 8,860
16.3,929,720
8.
4
3
2
3
p 2
 1.974, 13  0.231,
20.84173  0.842
3
13
2
0
1
2 15 
2
1
158
60
2
3
4
 0.235,
17
183
23.873, 2
58
183
58
4
22.93.99010
 23.155,
23. a) Total mass 5 8  12.256
5 98.048 g
2.384
3
19. The 7th significant digit is 5.
199.9995 is exactly between 199.999 and 200.000.
So, the decimal rounded to 6 significant digits is
200.000.
20.35.4
21.6.0239
99
 21.244
8
15
π2
5
17. The 5th significant digit is 0, which is less than 5.
19.6207 is closer to 19.62 than to 19.63.
So, the decimal rounded to 4 significant digits is
19.62.
18. The 6th significant digit is 6, which is greater than 5.
232.156 is closer to 232.16 than to 232.15.
So, the decimal rounded to 5 significant digits is
232.16.
5
9. 22.384  22.385, 2
1
158
 2.633, 2  1.414,
60
0.84173
0
1
2
99
8
1
Lesson 1.5
1. 2, 3, 0, and 4 are significant digits.
There are 4 significant digits.
2. 2 and 1 are significant digits.
There are 2 significant digits.
4
17
0
b) 98 g
24. 0.905 mm
Chapter 2
Lesson 2.1
1.  2. 
3.  4. 
5.88 6. 69
3
1
8
3
3. 3 and 1 are significant digits.
There are 2 significant digits.
7. 1 8. 3
4. 4, 5, and 0 are significant digits.
There are 3 significant digits.
9.
11
3
38
10.
12. 1
13
7
11
5. 6, 0, 2, and 3 are significant digits.
There are 4 significant digits.
11.
6. 9, 0, and 1 are significant digits.
There are 3 significant digits.
13.
7. 2, 1, 0, and 4 are significant digits.
There are 4 significant digits.
15. 9.15
16.4.32
17. $42
18. 30
14
3
4
18
14.
1
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19. 20%
158 Answers
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