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WorksheetsNumber Systems Unit Test Review
Total questions: 159
Worksheet time: 5hrs 30mins
Name
Class
Date
1.
-14 could NOT be which type of number?
a)
Integer
b)
Real
c)
Rational
d)
Natural
2.
Classify 17/10
a)
Whole
b)
Rational
c)
Natural
d)
None of the above
3.
What number below is a natural, whole, integer, rational, and real number ?
a)
-4
b)
5.1
c)
0.7
d)
3
4.
Classify √35.
a)
Rational, Integer
b)
Whole, Integer, Rational
c)
Irrational, Integer
d)
Irrational
5.
Classify 0
a)
Whole
b)
Integer
c)
Rational
d)
All of the above
6.
Which statement is NOT true?
a)
Every rational number is a real number.
b)
Every counting number is a whole number.
c)
Every integer is a rational number.
d)
Every decimal number is an irrational number.
7.
How would 0.333333 be classified?
a)
rational and real
b)
real and whole
c)
only integer
d)
only irrational
8.
Which of the following statements is always true?
a)
All integers are whole numbers
b)
all rational numbers are integers
c)
some whole numbers are not rational numbers
d)
all whole numbers are integers
9.
What is the square root of 81?
a)
40.5
b)
9
c)
6561
d)
162
10.
Which number is an irrational number?
a)
√9
b)
√49
c)
√100
d)
√120
11.
Which statement is NOT true?
a)
0.121212… is a rational number.
b)
0.34353637 is an irrational number.
c)
8.14 is a rational number.
d)
5.12345… is an irrational number.
12.
Which number is irrational?
a)
9.6
b)
√45
c)
3/8
d)
3.4 x 10 ⁵
13.
How is the number represented in Scientific Notation? 657,000,000,000,000
a)
6.57 X 10^12
b)
657 X 10^12
c)
6.57 X 10^14
14.
(9^4 )(9^12) = 9^8
a)
True
b)
False
15.
(34^8)^0
a)
34^8
b)
0
c)
1
16.
Write 0.0000000000004567 in scientific notation.
a)
4.567 x 10^13
b)
4.567 X 10^-13
c)
4.567 X 10^-12
17.
Write 1.89 X 10^-5 in standard form.
a)
189,000
b)
1.8900000
c)
0.0000189
18.
If the volume of a cube is represented by t, what would an edge length be?
a)
t cubed
b)
square root of t
c)
cube root of t
19.
A rational number is
a)
any number that CAN be written as a fraction or ratio.
b)
Perfect squares are rational
c)
both answers are correct
20.
An irrational number is
a)
repeating decimals with a pattern are irrational
b)
non-terminating and non-repeating decimals that can NOT be written as a fraction
c)
both answers are correct
21.
9.8 X 10^7 is ABOUT how many times 1.7 times 10^5?
a)
.5
b)
50
c)
500
22.
Classify the number.
a)
counting, whole, integer, rational
b)
Irrational
c)
integer, rational
23.
Classify the number
a)
Rational
b)
Irrational
24.
Classify the number.
a)
Rational
b)
Irrational
25.
Classify the number 12 times pi.
a)
Rational
b)
Irrational
26.
Classify the number.
a)
Rational
b)
Irrational
27.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
28.
According to exponent rules, when we divide powers we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
29.
According to exponent rules, when we multiply powers we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
30.
According to exponent rules, when we raise a power to a power we _______ the exponents.
a)
add
b)
subtract
c)
multiply
d)
divide
31.
How do you solve:
(2x5)(6x4)
(2x5)(6x4)
a)
MULTIPLY coefficients
MULTIPLY exponents
MULTIPLY exponents
b)
DIVIDE coefficients
SUBTRACT exponents
SUBTRACT exponents
c)
Combine like terms
d)
MULTIPLY coefficients
ADD exponents
ADD exponents
32.
How would you change this to a positive exponent:
1/x-3
1/x-3
a)
1/x3
b)
x3
c)
3x
d)
1/3x
33.
(2⁸)²
a)
2¹⁶
b)
2¹⁰
c)
2⁶
d)
2⁴
34.
x⁻⁶
a)
1 ⁄ x⁶
b)
x⁶
c)
-x⁶
d)
-1 ⁄ x⁶
35.
(-2)³⋅(-2)⁶
a)
(-2)⁹
b)
(-2)¹⁸
c)
(-2)⁻³
d)
(-2)
36.
8⁷ ⁄ 8²
a)
8⁵
b)
8⁹
c)
8¹⁴
d)
1⁵
37.
x⁵⁄x³
a)
x²
b)
x
c)
1
d)
x⁸
38.
Simplify the following expression:
xy-7
xy-7
a)
xy7
b)
x/y7
c)
x7/y
d)
x7y
39.
(2x3y)6
a)
2x18y6
b)
64x18y6
c)
64x3y6
d)
2x3y6
40.
-14x7/7x
a)
-2x6
b)
-2x
c)
-2x5
d)
-2x8
41.
(-4r3s5)0 (3b4c2d)
a)
1
b)
-12b4c2d
c)
3b4c2d
d)
0
42.
9n4 . 6n7
a)
15n11
b)
54n28
c)
3n3
d)
54n11
43.
-3xy3 . (4xy)2
a)
-12x3y5
b)
-48x2y4
c)
-48x3y5
d)
-12x2y6
44.
3³ ⋅ 3
a)
34
b)
33
c)
30
d)
1 ⁄ 34
45.
-82 ⋅ -84 ⋅ -83
a)
-89
b)
-824
c)
-249
d)
-2424
46.
a)
77/25
b)
77/250
c)
308/9
d)
308/999
47.
a)
3/10
b)
1/3
c)
1/9
d)
30/99
48.
a)
7/50
b)
14/9
c)
7/45
d)
14/99
49.
a)
1/2
b)
1/10
c)
1/100
d)
1/9
50.
a)
1 8/9
b)
17/90
c)
17/100
d)
1 18/99
51.
Repeating decimals belong to which of the following types of numbers? (There may be one or more answers... please select all answer choices that apply)
a)
Irrational
b)
Rational
c)
Integers
d)
Whole
e)
Natural
52.
The number 0 belongs to which of the following types of numbers? (There may be one or more answers... please select all answer choices that apply)
a)
Irrational
b)
Rational
c)
Integer
d)
Whole
e)
Natural
53.
The square root of 169 belongs to which of the following types of numbers? (There may be one or more answers... please select all answer choices that apply)
a)
Irrational
b)
Rational
c)
Integer
d)
Whole
e)
Natural
54.
7 belongs to which of the following types of numbers? (There may be one or more answers... please select all answer choices that apply)
a)
Irrational
b)
Rational
c)
Integer
d)
Whole
e)
Natural
55.
Convert 0.266666... to a fraction.
a)
26/99
b)
8/3
c)
4/15
d)
26/90
56.
Explain the error(s).
a)
-1.2 isn't an integer.
b)
-2 isn't a whole number and 3.4 isn't a rational number.
c)
-2 isn't a whole number and -1.2 isn't an integer.
d)
The numbers are graphed correctly.
57.
How would you write 0.0005 in scientific notation?
a)
50 x 105
b)
5 x 104
c)
5 x 103
d)
.5 x 103
58.
How would you write -5.6 x 10-3 in standard form?
a)
0.0056
b)
-5,600
c)
0.00056
d)
-0.0056
59.
Scientific Notation is made up of two number parts. The first part should be a number between 1 and 100.
a)
True
b)
False
60.
Scientific Notation is made up of two number parts. The second part is a power of base 10.
a)
True
b)
False
61.
When writing a number in scientific notation, the first number must be greater than 1, but less than 10.
a)
False
b)
True
62.
Which of the following is correct scientific notation?
a)
20.35 x 104
b)
.2035 x 104
c)
2035 4
d)
2.035 x104
63.
(2 x 109)(4 x 10-4)
a)
8 x 1013
b)
8 x 1036
c)
8 x 105
d)
8 x 10-36
64.
(5 x 106)(5 x 107)
a)
2.5 x 1012
b)
2.5 x 1014
c)
25 x 1012
d)
25 x 1013
65.
5 x 1012
------------
2 x 106
------------
2 x 106
a)
2.5 x 102
b)
2.5 x 106
c)
3 x 102
d)
2.5 x 1018
66.
(2.8 * 108) (2.2*103)
a)
6.16 * 1024
b)
5.0 * 1011
c)
6.16 * 1011
d)
61.6 * 1011
67.
What is the simplified version of
a)
3.9 x 106
b)
4 x 1020
c)
4 x 106
d)
3.9 x 1020
68.
A microgram is equal to 1 x 10 -6 grams. How many times greater than a microgram is 1 x 102 grams?
a)
1 x 10-8
b)
1 x 10-4
c)
1 x 104
d)
1 x 108
69.
What property of multiplication allows us to rearrange and multiply our factors in ANY order?
a)
Distributive Property
b)
Associative Property
c)
Identity Property
d)
Commutative Property
70.
Solve:
(6 x 106) / (2 x 103)
(6 x 106) / (2 x 103)
a)
12 x 103
b)
3 x 109
c)
1.2 x 104
d)
3 x 103
71.
Solve:
(9 x 10-6) divided by (3 x 10-3)
(9 x 10-6) divided by (3 x 10-3)
a)
27 x 10-9
b)
3 x 10-3
c)
3 x 10-9
d)
27 x 10-3
72.
Solve:
(2.2 x 10 4) x (7.1x 10 5)
(2.2 x 10 4) x (7.1x 10 5)
a)
1.562 x 1010
b)
15.62 x 109
c)
15.62 x 1020
d)
1.562 x 1020
73.
Subtract the within the scientific notation.
(2 x 10³) - (1.9 x 10²)
(2 x 10³) - (1.9 x 10²)
a)
1.81 x 10⁵
b)
1.81 x 10³
c)
1.81 x 10⁶
d)
1.81 x 10⁴
74.
Add withing scientific notation
(5.2 x 10⁷) + (3.01 x 10⁴)
(5.2 x 10⁷) + (3.01 x 10⁴)
a)
5.20301 x 10¹¹
b)
.520301 x 10⁷
c)
5.20301 x 10⁷
d)
5.20301 x 10⁸
75.
Subtract withing scientific notation
(7.32 x 10⁶) - (4.01 x 10⁸)
(7.32 x 10⁶) - (4.01 x 10⁸)
a)
-3.937 x 10⁸
b)
3.937 x 10⁸
c)
3.937 x 10⁷
d)
3.937 x ⁻²
76.
Solve:
(8.0 x 1013) - (7.5 x 1012)
(8.0 x 1013) - (7.5 x 1012)
a)
1.55 x 1013
b)
0.5 x 100
c)
5.0 x 1011
d)
5.0 x 1013
77.
UNDERSTANDING
If the exponent is a positive number...
If the exponent is a positive number...
a)
you will get a large number
b)
you will get a smaller number
78.
UNDERSTANDING
If the exponent is a negative number...
If the exponent is a negative number...
a)
you will get a large number
b)
you will get a small number
79.
(7.1 X 108) + (1.4 X 108)=
a)
8.5 X 108
b)
6.8 X 108
c)
5.7 X 108
d)
8.9 X 108
80.
(7.9 X 102) - (2.3 X 102)=
a)
4.32 X 102
b)
5.6 X 102
c)
1.02 X 103
d)
5.72 X 102
81.
When multiplying numbers in scientific notation, what do you do to the leading numbers?
For example:
(4×10⁵)(3×10⁻²)
For example:
(4×10⁵)(3×10⁻²)
a)
Keep them the same
b)
Divide them
c)
Add them
d)
Multiply them
82.
When dividing numbers in scientific notation, what do you do to the exponents?
For example:
(4×10⁵) ∕ (3×10²)
For example:
(4×10⁵) ∕ (3×10²)
a)
Add them
b)
Subtract them
c)
Keep them the same
d)
Divide them
83.
When adding or subtracting numbers in scientific notation, what do you do to the exponents once you have converted them to be the same number?
For example:
(4×10⁵) + (3×10⁵)
For example:
(4×10⁵) + (3×10⁵)
a)
Keep them the same
b)
Subtract them
c)
Add them
d)
Multiply them
84.
Order from least to greatest.
a) 4×10³
b) 3×10⁵
c) 2.5×10³
d) 5.6×10⁻⁵
a) 4×10³
b) 3×10⁵
c) 2.5×10³
d) 5.6×10⁻⁵
a)
C, A, B, D
b)
A, B , C, D
c)
B, A, D, C
d)
D , C , A , B
85.
Order from least to greatest...
a) 4.5×10⁻³
b) 0.000045
c) 3.1×10⁻³
d) -45
a) 4.5×10⁻³
b) 0.000045
c) 3.1×10⁻³
d) -45
a)
D , B , C, A
b)
B , C , D , A
c)
C , A , D , B
d)
A , C , D , B
86.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
4.3×10⁶ ? 5.4×10²
4.3×10⁶ ? 5.4×10²
a)
<
b)
>
c)
=
87.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
5.6×10⁻⁵ ? 5.4×10⁻³
5.6×10⁻⁵ ? 5.4×10⁻³
a)
<
b)
>
c)
=
88.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
6.7×10³ ? 6,700
6.7×10³ ? 6,700
a)
<
b)
>
c)
=
89.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
7.6×10⁴ ? 0.00076
7.6×10⁴ ? 0.00076
a)
<
b)
>
c)
=
90.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
6.5×10³ ? 7.8×10³
6.5×10³ ? 7.8×10³
a)
<
b)
>
c)
=
91.
Which inequality sign should be placed between these numbers to make it a true/correct statement?
5.4×10⁻³ ? 0.0000054
5.4×10⁻³ ? 0.0000054
a)
<
b)
>
c)
=
92.
Determine the missing value.
(5.4×10?) - (3.2×10³) = 2.2×10³
(5.4×10?) - (3.2×10³) = 2.2×10³
a)
4
b)
2
c)
3
d)
9
93.
(6 × 106) - (9.9 × 104)
a)
59 × 106
b)
5.901 × 106
c)
-4 × 102
d)
None of these
94.
The population of Cherokee County is 5.6 x 103. The population of Cedar Bluff is 1.3 x 102. How many more people are there in Cherokee County than Cedar Bluff?
a)
57.4 x 103
b)
5047
c)
5,470
d)
5.47
95.
IWhat is the correct scientific version of the following answer to an addition problem:
792.9 x 10-3
792.9 x 10-3
a)
79.29 x 100
b)
7.929 x 101
c)
7.929 x 10-3
d)
7.929 x 10-1
96.
The following answer to a subtraction problems would be written as ________________________ in standard form.
.15 x 105
.15 x 105
a)
150
b)
1,500,000
c)
1,500
d)
None of these
97.
√ 4
a)
2
b)
7
c)
16
d)
1
98.
√ 1
a)
1
b)
100
c)
10
d)
0
99.
√ 64
a)
4
b)
6
c)
9
d)
8
100.
√ 36
a)
4
b)
6
c)
12
101.
√ 144
a)
4
b)
12
c)
16
d)
32
102.
52
a)
16
b)
25
c)
20
d)
10
103.
22
a)
2
b)
4
c)
5
d)
6
104.
72
a)
50
b)
49
c)
14
d)
48
105.
112
a)
132
b)
144
c)
121
d)
22
106.
√ 9
a)
8
b)
9
c)
3
d)
81
107.
√ 16
a)
132
b)
4
c)
2
d)
8
108.
√ 25
a)
5
b)
100
c)
4
d)
21
109.
Solve for x when x = (3/4)2
a)
x = 4/3
b)
x = 9/4
c)
x = 9/16
d)
x = 3/16
110.
A square with side length s has an area of 0.81 square units. What is the length of the side of the square?
a)
0.9 units
b)
0.6561 units
c)
0.405 units
d)
0.3 units
111.
Select the answer with all perfect squares.
a)
-144, 9, 50, 75, 81, 100
b)
9, 50, 75, 81, 100
c)
9, 50, 81, 100
d)
9, 81,100
112.
The number 16 is a
a)
perfect square
b)
perfect cube
113.
The number 25/9 is a
a)
perfect square
b)
perfect cube
114.
The number -27/64 is a
a)
perfect square
b)
perfect cube
115.
The number 1000 is
a)
perfect square
b)
perfect cube
116.
CHALLENGE.
a)
3
b)
62
c)
6
d)
2
117.
a)
1/2
b)
2/3
c)
10/16
d)
9/11
118.
a)
7/14
b)
1/49
c)
4/9
d)
12/19
119.
a)
x = 16
b)
x = 64
c)
x = 512
d)
x = 2
120.
a)
z = 1/7
b)
z = 5/7
c)
z = 5/49
d)
z = 1/2
121.
What is the inverse of "squaring" a number?
a)
Division
b)
Cube Root
c)
Square Root
d)
Multiplication
122.
The following numbers are displayed below.
√81 and 9
Which value is greater?
√81 and 9
Which value is greater?
a)
they are equivalent
b)
√81
c)
9
d)
can't be determine
123.
What is the square root symbol called?
a)
Radicand
b)
Radical
c)
The house
d)
It doesn't have a name
124.
Which of the following is NOT a perfect square?
a)
9
b)
10
c)
25
d)
16
125.
If x2 = 144, then x = ?
a)
ONLY -12
b)
ONLY 72
c)
ONLY 12
d)
12 AND -12
126.
a)
not a perfect square
b)
2/6
c)
8/6
d)
1/4
127.
Which are not a perfect squares? Choose all that apply
a)
36
b)
1
c)
48
d)
9
e)
112
128.
In between what two integers is the square root of 77?
a)
5 and 6
b)
6 and 7
c)
7 and 8
d)
8 and 9
129.
Find the best estimate for √18 .
Look at the number line.
a)
4.2
b)
4
c)
4.5
d)
5
130.
Estimate the square root.
a)
9
b)
10
c)
11
d)
12
131.
Estimate the square root.
a)
3
b)
4
c)
5
d)
6
132.
x*x*x*x
a)
4x
b)
3x
c)
x4
d)
x3
133.
12*m*n*n
a)
12mn2
b)
12m2n
c)
122m2n2
d)
2mn
134.
3ab3
a)
3*a*b*b*b
b)
3*3*3*a*a*a*b*b*b
c)
ab*ab*ab
d)
ab3*ab3*ab3
135.
m5
a)
m five
b)
five m
c)
five raised to the m power
d)
m raised to the fifth power
136.
The √20 is between which two consecutive integers?
a)
19 and 21
b)
2 and 3
c)
5 and 6
d)
4 and 5
137.
The following numbers are displayed below.
√8 and 2.9
Which number is greater?
√8 and 2.9
Which number is greater?
a)
same
b)
2.9
c)
√8
d)
can't be determined
138.
What is the length of a side of a square with and area of 25 square feet?
a)
12.5 feet
b)
10 feet
c)
5 feet
d)
6 feet
139.
In between what two integers is the square root of 44?
a)
3 and 4
b)
4 and 5
c)
5 and 6
d)
6 and 7
140.
Point B could represent which of the following numbers?
a)
√24
b)
√30
c)
√35
d)
√42
141.
∛125
a)
5
b)
4
c)
6
d)
7
142.
∛216
a)
6
b)
7
c)
5
d)
8
143.
∛343
a)
7
b)
6
c)
8
d)
9
144.
103
a)
30
b)
100
c)
1000
d)
3000
145.
Evaluate √92
(The square root of nine squared)
(The square root of nine squared)
a)
9
b)
81
c)
3
d)
√18
146.
What is the value of
(-2)3
(-2)3
a)
8
b)
-8
c)
±8
d)
6
147.
1/3 as a decimal
a)
.33333...
b)
.3
c)
.36
d)
.32
148.
2/3 as a decimal
a)
.66666...
b)
.6
c)
.23
d)
.14
149.
What is the square root of 169?
a)
12
b)
13
c)
14
d)
15
150.
What is the square root of 36?
a)
3
b)
4
c)
5
d)
6
151.
Which of the following would result in a repeating decimal? (Choose all that apply)
a)
1/3
b)
3/4
c)
1/5
d)
4/6
e)
6/12
152.
Which of the following would result in a repeating decimal?
a)
55/99
b)
5/12
c)
6/9
d)
2/3
e)
10/15
153.
How can you classify the number: -6.5
(Select all that apply)
a)
Whole
b)
Integer
c)
Rational
d)
Irrational
e)
Real
154.
How can you classify the number:
a)
Real
b)
Integer
c)
Rational
d)
Irrational
e)
Natural
155.
How can you classify the number:
(Select all that apply)
a)
Natural
b)
Whole
c)
Integer
d)
Rational
e)
Irrational
156.
Which equations are true? (Select all that apply)
a)
b)
c)
d)
e)
157.
Will's kitchen is shaped like a square. The room has an area of 225 ft^2. What is the length of one side of Will's kitchen?
a)
25
b)
112.5
c)
5
d)
22.5
158.
A cubed shape paperweight has a volume of 64 cm^3. What is the length of the paperweight?
a)
4
b)
8
c)
21.3
d)
32
159.
Which of the following is irrational? (Select all that apply)
a)
b)
c)
d)
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