Download Rational and Irrational Numbers

Name ________________________________________ Date __________________ Class __________________
LESSON
1-1
Rational and Irrational Numbers
Practice and Problem Solving: D
Write each fraction as a decimal. The first one is done for you.
1.
1
9
2.
0.1
________________________
11
20
3.
_______________________
9
16
________________________
Write each decimal as a fraction. The first one is done for you.
4. 0.258
5. 4.8
258 129
=
1000
500
________________________
6. 0.333
_______________________
________________________
Find the two square roots of each number. The first one is done
for you.
7. 16
8. 49
4, −4
________________________
9.
_______________________
25
4
________________________
Find the cube root of each number. The first one is done for you.
10. 343
11. 1
7 × 7 × 7 = 343, 7
________________________
12.
_______________________
8
27
________________________
Approximate each irrational number to the nearest hundredth without
using a calculator. The first one is done for you.
13.
32
5.66
________________________
14.
15.
59
_______________________
118
________________________
Solve.
17
square
100
mile. What is Vatican City’s area written as a decimal?
16. The world’s smallest country is Vatican City. It covers
_________________________________________________________________________________________
17. A square sandbox has an area of 25 ft2. What is the length of each of
its sides? (Hint: side = 25 )
_________________________________________________________________________________________
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3
UNIT 1: Real Numbers, Exponents, and Scientific Notation
Practice and Problem Solving: C
MODULE 1 Real Numbers
1. 1.17 in.
LESSON 1-1
2. 7.64 in.
Practice and Problem Solving: A/B
41
9
= 0.82, = 0.81, and
50
11
10
41
9
= 0.90 , 0.81
is closer to
.
50
11
11
3. Since
1. 0.125
2. 0.5625
3. 0.55
4. 5.32
4. ±
1
2
5. ±
1
4
5. 0.93
6. 2.583
7. 0.03
6. ≈ ±
8. 3.2
9. 5, −5
7. ≈ 1.73
10. 1, −1
8. ≈ 4.24
5
5
11. , −
2
2
12.
2
3
11 11
,−
7
7
9. When you find a square root, you find
two factors that are the same. They can
be positive or negative. When you find a
cube root, you find three factors that are
the same. They are positive.
13. 2
14. 5
15. 1
10. The length of one photo album page is
25 cm. The width of the page is 32 cm.
16. 13
17. 5.66
Practice and Problem Solving: D
18. 10.86
19. 4.24
1. 0.1
20. 17.86
2. 0.55
21. 2.83
3. 0.5625
4.
22. 8.66
129
500
5. 4
23. 1.4 lb
6.
24. 288 in2
4
5
333
1000
7. 4, −4
8. 7, −7
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322
9.
Success for English Learners
5
5
,−
2
2
1.
10. 7
2. Possible answer: If you have a square
with a side length of 5, then 52 is how
you find the area of that square.
11. 1
12.
1
= 0.25
4
2
3
3. Because the answer is an
approximation.
13. 5.66
14. 7.68
LESSON 1-2
15. 10.86
Practice and Problem Solving: A/B
16. 0.17 mi2
1. real, rational
17. 5 ft
2. real
Reteach
3. real, rational, integer
1. 3.75
4. real, rational, integer
2. 0.83
5. real, rational
3. 3.6
6. real, rational, integer, whole
4. 9, −9
7. false; irrational real numbers include
nonterminating decimals
5. 7, −7
6.
8. true
5 5
,−
6 6
9. rational; all money amounts can be
written as fractions
7. 3
8. 5
10. real numbers; the temperature can be
any number between 0 and 100 degrees
Celsius
9. 9
11. rational
6<
39 < 7
12. integers
Reading Strategies
13. irrational
1. Yes, because it can be written as a
fraction: 0.62 = 62 = 31 .
100
50
14. whole numbers
Practice and Problem Solving: C
2. No, because it cannot be written as a
decimal that terminates or repeats.
1. real
2. real, rational, integer
3. Yes, as long as the decimal is infinite
and nonrepeating, such as
0.31311311131111….
3. real, rational
4. real, rational, integer, whole
4. Yes, for example, 0.6 .
5. real, rational
5. A decimal that is an irrational number is
infinite and nonrepeating, such as the
value for π.
6. real, rational, integer, whole
7. integers; possible points are positive
and negative numbers
6. Both are real numbers and both can be
written as decimals.
8. real; elevation can be any number
above or below zero
9. no; there are an infinite number of
rational numbers between any two
integers
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