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Study Guide
MODULE
?
1
Review
Real Numbers
EXAMPLE 4
_
Order 6, 2π, and √38 from least to greatest.
2π is approximately equal to 2 × 3.14, or 6.28.
_
√ 38
Key Vocabulary
cube root (raiz cúbica)
ESSENTIAL QUESTION
How can you use real numbers to solve real-world problems?
EXAMPLE 1
_
Write 0.81 as a fraction in simplest form.
___
x = 0.81
___
100x = 81.81
___
-x -0.81
99x = 81
irrational number (número
irracional)
6
(Lesson 1.1)
1. 16
square root (raíz cuadrada)
terminating decimal
(decimal finito)
© Houghton Mifflin Harcourt Publishing Company
C
B x3 = 1,000
The solutions are 17 and -17.
The solution is 10.
irrational, real
6.5
2 _
_
, - 25
5
5.
_
√ 10
3.15, -3.15
6.
7
__
11
_
8. 0.63
4.25, -4.25
_
√ 18
214
___
999
_
9. 0.214
10. x2 = 361
49
12. x2 = ___
121
11. x3 = 1,728
x = 19
7
x = __
11
x = 12
Write all names that apply to each number. (Lesson 1.2)
_
13. _23
14. -√100
rational, real
_
5.4 is a repeating decimal.
15
15. __
5
16.
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
<
integer, rational, real
_
√ 21
_
√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, _73
7
7
Unit 1
8_MFLESE056718_U1SG.indd 59
15, -15
3. 225
Solve each equation for x. (Lesson 1.1)
_
x = 3√ 1,000
x = 10
_
√ 13
6.4
4
2. __
25
5
_
9
_
7. 0.5
x = ±17
whole, integer, rational, real
4, -4
1 _
_
, - 17
7
1
4. __
49
EXAMPLE 3
Write all names that apply to each number.
B
6.3
Write each decimal as a fraction in simplest form. (Lesson 1.1)
_
x = ±√289
8
_
4
2π
6.2
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.
repeating decimal (decimal
periódico)
A x2 = 289
_
6.22 = 38.44
_
EXAMPLE 2
Solve each equation for x.
A 5.4
rational, real
6.1
6.12 = 37.21
From least to greatest, the numbers are 6, √38, and 2π.
real number (número real)
9
x = __
11
_
6 < √38 < 7
√38
6
perfect cube (cubo perfecto)
perfect square (cuadrado
perfecto)
principal square root (raíz
cuadrada principal)
rational number (número
racional)
81
x = __
99
is approximately 6.15 based on the following reasoning.
_
_
_
√ 36 < √ 38 < √ 49
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irrational, real
19.
_
√4 -
2
<
4-
_
√2
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UNIT 1
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_
7
_
, 2.55, √7
3
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Real Numbers, Exponents, and Scientific Notation
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2
Exponents and Scientific
Notation
Unit 1 Performance Tasks
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
10
Divide the powers of ten: ___
= 107-3 = 104
103
7
a. Which of these numbers are irrational?
_
√ 200 and 8π
Combine the answers and write the product in scientific notation.
© Houghton Mifflin Harcourt Publishing Company
0.25 × 104 = 0.25 × (10 × 103) = (0.25 × 10) × 103 = 2.5 × 103
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
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 .
0.0000133
(2,600)(3.24 × 104)
8.424 × 107
Unit 1
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