Download Pre Alegbra unit 1 review solutions

UNIT 1
Study Guide
MODULE
?
1
Review
EXAMPLE 4
_
Order 6, 2π, and √38 from least to greatest.
2π is approximately equal to 2 × 3.14, or 6.28.
Real Numbers
_
√ 38
Key Vocabulary
ESSENTIAL QUESTION
How can you use real numbers to solve real-world problems?
___
x = 0.81
___
100x = 81.81
___
-x -0.81
99x = 81
6
6.22 = 38.44
2π
6.2
6.3
6.4
6.5
_
EXERCISES
Find the two square roots of each number. If the number is not a
perfect square, approximate the values to the nearest 0.05.
real number (número real)
repeating decimal (decimal
periódico)
(Lesson 1.1)
4, -4
1. 16
square root (raíz cuadrada)
terminating decimal
(decimal finito)
9
x = __
11
6.1
6.12 = 37.21
From least to greatest, the numbers are 6, √38, and 2π.
rational number (número
racional)
81
x = __
99
_
6 < √38 < 7
√38
6
perfect cube (cubo perfecto)
perfect square (cuadrado
perfecto)
principal square root (raíz
cuadrada principal)
EXAMPLE 1
_
Write 0.81 as a fraction in simplest form.
is approximately 6.15 based on the following reasoning.
_
_
_
√ 36 < √ 38 < √ 49
cube root (raiz cúbica)
irrational number (número
irracional)
1 _
_
, - 71
7
1
4. __
49
2 _
_
, - 25
5
4
2. __
25
_
5.
√ 10
15, -15
3. 225
3.15, -3.15
6.
_
√ 18
4.25, -4.25
Write each decimal as a fraction in simplest form. (Lesson 1.1)
EXAMPLE 2
Solve each equation for x.
5
_
9
_
7. 0.5
A x2 = 289
B x3 = 1,000
x = 3√1,000
x = ±17
x = 10
The solutions are 17 and -17.
The solution is 10.
214
___
999
_
9. 0.214
Solve each equation for x. (Lesson 1.1)
_
_
x = ±√289
7
__
11
_
8. 0.63
10. x2 = 361
49
12. x2 = ___
121
11. x3 = 1,728
x = 19
7
x = __
11
x = 12
_
A 5.4
rational, real
B
8
_
4
whole, integer, rational, real
C
_
√ 13
irrational, real
_
13. _23
14. -√100
integer, rational, real
rational, real
_
5.4 is a repeating decimal.
15
15. __
5
16.
_
√ 21
irrational, real
whole, integer, rational, real
8
__
=2
4
Compare. Write <, >, or =. (Lesson 1.3)
13 is a whole number that
is not a perfect square.
17.
_
√7 +
5
<
7+
_
√5
18. 6 +
_
√8
<
_
√6
+8
Order the numbers from least_
to greatest. (Lesson 1.3)
72
_
_
8.9, √ 81 , __
72
20. √81, __
,
8.9
21. √ 7, 2.55, _37
7
7
Unit 1
59
60
19.
_
√4 -
2
<
4-
_
√2
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Write all names that apply to each number. (Lesson 1.2)
EXAMPLE 3
Write all names that apply to each number.
_
7
_
, 2.55, √7
3
Unit 1
Real Numbers, Exponents, and Scientific Notation
60
MODULE
?
2
Unit 1 Performance Tasks
Exponents and Scientific
Notation
Key Vocabulary
scientific notation
(notación científica)
1.
ESSENTIAL QUESTION
How can you use scientific notation to solve real-world problems?
CAREERS IN MATH Astronomer An astronomer is studying
Proxima Centauri, which is the closest star to our Sun. Proxima Centauri
is 39,900,000,000,000,000 meters away.
a. Write this distance in scientific notation.
3.99 × 1016 m
EXAMPLE 1
Write each measurement in scientific notation.
b. Light travels at a speed of 3.0 × 108 m/s (meters per second). How
can you use this information to calculate the time in seconds it takes
for light from Proxima Centauri to reach Earth? How many seconds
does it take? Write your answer in scientific notation.
A The diameter of Earth at the equator is approximately 12,700 kilometers.
Move the decimal point in 12,700 four places to the left: 1.2 7 0 0.
Divide the distance Proxima Centauri is from Earth by the speed of
12,700 = 1.27 × 104
light; 1.33 × 108 s
B The diameter of a human hair is approximately 0.00254 centimeters.
c. Knowing that 1 year = 3.1536 × 107 seconds, how many years does
it take for light to travel from Proxima Centauri to Earth? Write your
answer in standard notation. Round your answer to two decimal
places.
Move the decimal point in 0.00254 three places to the right: 0.0 0 2.5 4
0.00254 = 2.54 × 10-3
4.22 years
EXAMPLE 2
× 107
_________
Find the quotient: 2.4
9.6 × 103
2. Cory is making a poster of common geometric shapes. He draws a
3
square
_with a side of length 4 cm, an equilateral triangle with a height
of √200 cm, a circle with a circumference of 8π cm, a rectangle with
122
___
length 5 cm, and a parallelogram with base 3.14 cm.
Divide the multipliers: 2.4 ÷ 9.6 = 0.25
7
10
Divide the powers of ten: ___
= 107-3 = 104
103
a. Which of these numbers are irrational?
_
√ 200 and 8π
Combine the answers and write the product in scientific notation.
b. Write the numbers in this problem in order from least to greatest.
Approximate
_π as 3.14.
122
3.14, √200 , ___
, 8π, 43
5
EXERCISES
Write each number in scientific notation. (Lessons 2.2, 2.3)
1. 25,500,000
2.55 × 107
c. Explain why 3.14 is rational, but π is not.
314
3.14 is a terminating decimal that can be written in the form __ba: ____
1000
7.34 × 10−3
2. 0.00734
157
. π is a nonrepeating, nonterminating decimal that cannot be
or ___
500
Write each number in standard notation. (Lessons 2.2, 2.3)
3. 5.23 × 104
52,300
4. 1.33 × 10-5
0.0000133
Simplify each expression. (Lessons 2.1, 2.4)
5. (9 - 7)3 · 50 + (8 + 3)2
129
7. 3.2 × 105 + 1.25 × 104 + 2.9 × 105
6.225 × 105
1
____
1,296
(4 + 2)2
6. _______
[(9 - 3)3]2
8.
written in the form __ba .
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
0.25 × 104 = 0.25 × (10 × 103) = (0.25 × 10) × 103 = 2.5 × 103
(2,600)(3.24 × 104)
8.424 × 107
Unit 1
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Unit 1
Real Numbers, Exponents, and Scientific Notation
62
UNIT 1 MIXED REVIEW
Personal
Math Trainer
Assessment
Readiness
my.hrw.com
Online
Assessment and
Intervention
_
A between 20 and 21 millimeters
B between 64 and 65 millimeters
C between 204 and 205 millimeters
D between 649 and 650 millimeters
2. Which of the following numbers is rational
but not an integer?
A -9
C 0
B -4.3
D 3
3. Which statement is false?
D π+3
7
7.2
7.4
B
8
14. The total land area on Earth is about
6 × 107 square miles. The land area of
Australia is about 3 × 106 square miles.
About how many times larger is the
land area on Earth than the land area of
Australia?
_
D 7.8
8. Which of the following is the number
5.03 × 10-5 written in standard form?
A 503,000
A 2
B
B 658,600 people
C 6,586,000 people
D 65,860,000 people
5. Which of the following is not true?
_
A √ 16 + 4 > √ 4 + 5
_
A 2
B
4
C 8
D 16
Mini-Task
18. Amanda says that a human fingernail has a
thickness of about 4.2 ×10-4 meter. Justin
says that a human fingernail has a thickness
of about 0.42 millimeter.
0.00042 m
b. Do Justin’s and Amanda’s
measurements agree? Explain.
Yes; 0.00042 m × 1,000 mm/m
= 0.42 mm
10
C 20
D 0.0000503
D 60
9. In a recent year, about 20,700,000
passengers traveled by train in the United
States. What is this number written in
scientific notation?
15. What is the value of the expression
8.3 × 104 - 2.5 × 103 - 1.9 × 104 written in
scientific notation?
B
B 2.07 × 10 passengers
A 2.5 × 10-2 pounds
B 2.5 × 101 pounds
C 2.5 × 10
-1
appropriate to measure the
16. What is the value of the expression
( 2.3 × 107 )( 1.4 × 10-2 ) written in scientific
notation?
10. A quarter weighs about 0.025 pounds.
What is this weight written in scientific
notation?
Sample answer: Since the
very small number, it is more
D 6.15 × 104
D 2.07 × 108 passengers
B 4π > 12
3.9 × 104
C 6.15 × 103
C 2.07 × 107 passengers
c. Explain why Justin’s estimate of the
thickness of a human fingernail is more
appropriate than Amanda’s estimate.
thickness of a fingernail is a
A 3.9 × 103
4
C
_
15
√ 18 + 2 < __
2
_
D 6 - √ 35 < 0
3
17. What is the value of √64 ?
a. What is the width in meters written in
standard notation?
D 343
A 2.07 × 101 passengers
A 6,586 people
21
C 49
C 0.00503
_
7.8
A π+4
152
B ___
20_
C √ 14 + 4
B All whole numbers are integers.
4. In 2011, the population of Laos was about
6.586 × 106 people. What is this number
written in standard notation?
7.6
4
C _
9
4
D ±_
9
[ ( 9 - 2 )2 ]4
13. What is _________
written in simplest form?
( 4 + 3 )5
A 7
7. Which number is indicated on the
number line?
B 50,300,000
D All integers are whole numbers.
2
A _
3
2
B ±_
3
C 6
A No integers are irrational numbers.
C All rational numbers are real numbers.
© Houghton Mifflin Harcourt Publishing Company
22
A __
3 _
B 2 √8
4
C _
5
5
D __
11
thickness in millimeters than
in meters.
© Houghton Mifflin Harcourt Publishing Company
1. A square on a large calendar has an area of
4,220 square millimeters. Between which
two integers is the length of one side of the
square?
4
A _
9
5
B _
9
36
12. What is the value of x if x2 = __
?
81
5π
6. Which number is between √50 and __
?
2
Selected Response
___
11. Which fraction is equivalent to 0.45?
A 3.7 × 10–14
B
3.7 × 105
C 0.322 × 106
pounds
D 3.22 × 105
D 2.5 × 102 pounds
Unit 1
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Unit 1
Real Numbers, Exponents, and Scientific Notation
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