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Chapter 1 Real Numbers
Name_______________________
Study Guide
Date________________________
3
1.
Write the fraction
2.
Evaluate (−3)3 .
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3.
Write . 5̅ as a fraction in simplest form.
__________
11
as a decimal.
510
4.
Using exponents, simplify
5.
Using exponents, simplify 24 ∙ 27 .
6.
Simplify.
3 3
55
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.
__________
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15𝑥 6
a. (4𝑥 )
b.
c. [(𝑢3 )2]4
d. −4𝑥 2 𝑦(−3𝑥𝑦 3 )
e.
42𝑐 4
−6𝑐 12
f.
3𝑥 2
𝑛7
𝑛3
7.
Write 4−2 using a positive exponent.
8.
Write
9.
Write each number in standard form.
1
52
using a negative exponent.
a. 2.1 × 104
10.
11.
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b. 3.07 × 10−4
In one week there are 10,080 minutes. What is this number
in scientific notation?
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Evaluate.
a. (1.2 × 102 )(2 × 103 )
c.
(5×103)
(10 ×10−4 )
b. (3.2 × 10−6 )(4.5 × 107 )
d.
(12 × 105 )
(4 × 106 )
12.
The top speed of a cheetah is approximately 1.2 × 102 kilometers per hour,
while the speed of the fastest human is approximately 4 × 101 kilometers
per hour. How many times faster is the top speed of a cheetah than the speed
of a human?
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13.
Evaluate.
a. −√
196
3
b. √−27
81
14.
Solve the equation 𝑡 2 = 121.
15.
To which set of numbers does -5.2 belong?
A. rational
B. integer
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C. irrational
D. whole
16.
Find the missing exponent in the equation 3𝑦 5 ∙ 𝑦 ? = 3𝑦10 .
17.
Evaluate the given expression if a = 4 and b = -3.
𝑎2 − 𝑏 3
18.
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The area of a square carpet tile is 900 square centimeters. What is the length
of one edge of the tile? What is the perimeter of the tile?
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3
19.
Without using a calculator, which is greater, 5 or √121 ?
20.
Order the set of numbers from least to greatest.
{4.509,
229
50
, 4.09, √21}
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