Number Sense – Practice Problems
Ratios, Proportions, & Percents
1. Calculate the percent decrease.
83,000
75,530
A. 1% decrease
B. 9% decrease
C. 99% decrease
D. 91% decrease
Exponents
2. Simplify the following expression.
(36)3
A. 318
B. 33
C. 39
D. 363
Compute Solutions
3. Which shows the expression below simplified?
(5.6 × 10-5) - (1.5 × 10-7)
A. 5.45 × 10-5
B. 5.585 × 10-5
C. 5.5985 × 10-5
D. 5.585 × 10-6
Compute Solutions
4. Simplify the following expression.
(-126) ÷ (-9)
A. 14
B. -14
C. -17
D. 17
Exponents
5. Simplify the following expression.
A.
B.
C.
D.
Estimate Solutions
6. Which of the following is approximately equal to the expression below?
A. 80
B. 40
C. 44
D. 50
Real Numbers
7.
To which subset of the real numbers does  belong?
I.
II.
III.
IV.
V.
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Rational Numbers
A. I, IV, and V only
B. I only
C. I and V only
D. V only
Real Numbers
8.
The numbers shown above belong to which of the following subsets of the real numbers?
I.
II.
III.
IV.
V.
Natural Numbers
Rational Numbers
Integers
Whole Numbers
Irrational Numbers
A. II only
B. V only
C. I, II and V only
D. All of the numbers do not belong to any one group.
Real World Problems
9. The table shows the atomic radii of four elements.
Element
Atomic Radii (m)
Potassium
2.2 × 10-7
Argon
7.1 × 10-8
Boron
8.5 × 10-8
Silver
1.6 × 10-7
Which list shows the atomic radii of the elements ordered from greatest to least?
A. Potassium, Silver, Boron, Argon
B. Potassium, Boron, Silver, Argon
C. Argon, Boron, Silver, Potassium
D. Boron, Argon, Potassium, Silver
Real Numbers
10.
{12, 13, 25, 33, 45, 57, 67}
The numbers shown above belong to which of the following subsets of the real numbers?
I.
II.
III.
IV.
V.
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Rational Numbers
A. II only
B. III and IV only
C. II, III, and IV only
D. II, III, IV, and V only
Exponents
11. Simplify the following expression.
85 ÷ 8-3
A. 8-8
B. 88
C. 82
D. 8-15
Square & Cube Roots
12. Simplify:
A. 2
B. 16
C. 1
D. 4
Real Numbers
13.
{0, 7, 10, 22, 24, 28, 31}
The numbers shown above belong to which of the following subsets of the real numbers?
I.
II.
III.
IV.
V.
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Rational Numbers
A. III only
B. II, III, and IV only
C. II, III, IV, and V only
D. II, III, and V only
Order of Operations
14. If N = 21 - 4 × 0.4 + 32, then the value of N is
A. 159.8
B. 15.8
C. 31.6
D. 28.4
Ratios, Proportions, & Percents
15. Starting at the same point, Jack and Jill go hiking in opposite directions. If Jack hikes at a
speed of 8 miles per hour, and Jill hikes at a speed of 8 miles per hour, how far apart will they be
in 2 hours?
A. 24 miles
B. 33 miles
C. 21 miles
D. 32 miles
Compute Solutions
16. Simplify the following expression.
24 × 17
A. 432
B. 408
C. -408
D. -432
Scientific Notation
17. Write the number 25,350 × 10-10 in scientific notation.
A. 2.535 × 10-5
B. 25.35 × 10-6
C. 2.535 × 10-14
D. 2.535 × 10-6
Scientific Notation
18. Write the number 2.045 × 103 in standard form.
A. 2,045
B. 20,450
C. 0.002045
D. 204.5
Real Numbers
19. To which real number subset do the following real numbers belong?
A. natural numbers
B. rational numbers
C. integers
D. irrational numbers
Real World Problems
20. Tim is making a race course. The race course is 6
9
miles long and is divided into 6
11
sections. How long is each section?
A.
B.
C.
D.
Real World Problems
21. For Jeff's wedding, 7 of his friends shared the cost of his gift equally. The gift cost $459.41.
How much did each of his 7 friends contribute?
A. $65.63
B. $65.73
C. $3,215.87
D. $75.63
Absolute Value
22. Simplify the following expression.
-20|5 - 9|
A. 80
B. 280
C. -80
D. -280
Estimate Solutions
23. Betsy just drove across town to her new office, and she wants to calculate her average speed
during her commute. The distance from her house to her office is 15 miles. She estimates that the
drive took 30 minutes to complete. These are the values Betsy used to calculate her speed.
If the trip actually took 34 minutes, what is the error in her speed calculation? Round to the
nearest mph.
A. 8 mph
B. 7 mph
C. 6 mph
D. 4 mph
Ratios, Proportions, & Percents
24. Jethro is planting flowers in his garden. He wants the ratio of tulips to roses to be 3 to 2.
Jethro wants to plant a total of 35 flowers.
How many tulips should he plant?
A. 7
B. 53
C. 21
D. 19
Compute Solutions
25.
16 ÷ 0.8
A. 20
B. 128
C. 12.8
D. 2
Exponents
26. Simplify the following expression.
2-3 × 27
A. 2-10
B. 23
C. 24
D. 2-21
Order of Operations
27. Simplify the following expression.
17 - (5 + 1) - 6 ÷ 3
A. 11
B. 9
C. 15
D. 2
Order of Operations
28. Simplify: 11 + 4/8 × 0
A. 0
B. 1 3/8
C. 11
D. 11 1/2
Estimate Solutions
29. Nelly had a garage sale. In the first hour, she sold two old bikes for $45.00 each, 8 CDs for
$1.95 each, and 3 toys for $3.84 each.
About how much did Nelly make in the first hour of her garage sale?
A. Between $123.00 and $133.00
B. Between $113.00 and $123.00
C. Between $108.00 and $118.00
D. Between $118.00 and $128.00
Estimate Solutions
30. Jed lives on a busy street. Six to nine cars pass by Jed's house every five minutes.
Which of the following is a reasonable number of cars which pass by Jed's house in 45 minutes?
A. 72
B. 51
C. 84
D. 97
Scientific Notation
31. Write the standard number 78,020 in scientific notation.
A. 7.802 × 103
B. 7.802 × 10-4
C. 7.802 × 104
D. 78.02 × 104
Estimate Solutions
32. Caleb bought a dining room table at a garage sale. Compared to a similar table he had priced
at a furniture store, the garage sale table was about 50% less than the store price.
If the store price was $101.67, about what price did Caleb pay for the table from the garage sale?
A. $50.00
B. $40.00
C. $70.00
D. $60.00
Absolute Value
33. Simplify the following expression.
34 - |-1 - 10|
A. 25
B. 45
C. 43
D. 23
Estimate Solutions
34. James wants to measure the volume of a cube-shaped box. The ruler that he is using to
measure a side of the cube is marked at centimeters only, so he must estimate the tenths place.
He estimates the cube's side to be 6.7 cm long. The actual length of a side of the cube is 6.9 cm.
What is the error in the volume calculation that resulted from the estimation?
A. 30.246 cm3
B. 55.492 cm3
C. 27.521 cm3
D. 27.746 cm3
Exponents
35. Simplify the following expression.
A.
B.
C.
D.
Order of Operations
36. Simplify the following expression.
65 - 2 • (4 - 2)4
A. -191
B. 35
C. 33
D. 30
Absolute Value
37. Simplify:
|-5|
Ratios, Proportions, & Percents
38. If Janet traveled 3,200 miles in 8 hours on a flight to New York, how fast was the plane
traveling?
A. 405 miles per hour
B. 395 miles per hour
C. 390 miles per hour
D. 400 miles per hour
Compute Solutions
39. Simplify the following expression.
(-111) - 23
A. 88
B. 134
C. -134
D. -88
Absolute Value
40. Simplify:
-|-20|
Real World Problems
41.
A.
B.
C.
D.
Compute Solutions
42.
50 × 0.06
A. 0.03
B. 0.3
C. 3
D. 300
Square & Cube Roots
43. Simplify: 3 1
A.
B.
C.
3
1
9
1
D. 3
Real World Problems
44. Lance is sealing envelopes for his father. He can seal 10 envelopes a minute. How many
1
envelopes can he seal in 4 hours?
2
A. 2,800
B. 2,700
C. 2,900
D. 3,000
Real Numbers
45. Which is the most specific subset of the real numbers that contains the number below?
-5
A. integers
B. rational numbers
C. irrational numbers
D. natural numbers
Square & Cube Roots
46. Which of the following statements is correct about
A.
is an integer
?
B.
C.
D.
is an irrational integer
is a rational number between 10 and 11
is an irrational number between 10 and 11
Ratios, Proportions, & Percents
47. The librarian counted 1,600 books in the library stacks before school started. The third week
of school, 30% of the school library books were checked out.
How many books were in the library after 10% of the checked out books were returned?
A. 1,168
B. 1,280
C. 1,120
D. 480
Estimate Solutions
48. Which of the following is approximately equal to the product of the multiplication problem
below?
3.868 × 21.65
A. 63
B. 88
C. 84
D. 42
Exponents
49. Simplify the following expression.
(54)3 × 57
A. 514
B. 549
C. 55
D. 519
Order of Operations
50. Simplify the following expression.
32 - 22(4 - 2) ÷ 4
A. -2
B. 20
C. -8.75
D. 5
Square & Cube Roots
51. Which of the following is equal to 5?
A.
B.
C.
D.
Real Numbers
52. To which real number subset do the following real numbers belong?
A. irrational numbers
B. rational numbers
C. natural numbers
D. whole numbers
Ratios, Proportions, & Percents
53. Martha is driving to Miami for Spring Break, and she averages 60 miles per hour for 2 hours
while she's driving on the highway. While she's driving on side streets for 1 hour, she only
averages 45 miles per hour. What is the total distance that she covers on her road trip?
A. 69 miles
B. 105 miles
C. 210 miles
D. 165 miles
Order of Operations
54. Simplify the following expression.
19 - (2 + 2) - 10 ÷ 2
A. 10
B. 14
C. 3
D. 24
Scientific Notation
55. Visible blue light has a wavelength of about 0.0000475 centimeters.
What is this measurement written in scientific notation?
A. 4.75 × 10-4 centimeters
B. 4.75 × 10-5 centimeters
C. 4.75 × 104 centimeters
D. 4.75 × 105 centimeters
Scientific Notation
56. Write the standard number 0.00121 in scientific notation.
A. 12.1 × 10-3
B. 1.21 × 103
C. 1.21 × 10-3
D. 1.21 × 10-2
Compute Solutions
57. Simplify the following expression.
170 ÷ 10
A. 20
B. -17
C. -20
D. 17
Square & Cube Roots
58. Determine which two values the following number is between.
A. 13 and 14
B. 14 and 15
C. 12 and 13
D. 15 and 16
Absolute Value
59. Simplify the following expression.
14|2 - 8| + 21
A. 105
B. -119
C. -63
D. 161
Real World Problems
60. Jim borrowed $12,530.05 interest-free. He has already made 12 equal payments of $628.02,
but he would like to finish paying off his debt with only 6 more equal payments. How much will
he need to increase his payments by to pay off his loan in six more payments?
A. $832.30
B. $2,088.34
C. $204.28
D. $2,042.82
Order of Operations
61. Simplify the following expression.
14 ÷ 7 + 42 • 3 - 9
A. 45
B. -94
C. 41
D. 59
Ratios, Proportions, & Percents
62. Turner can read
4
of a chapter in 11 minutes? How many chapters can Turner read in 32
5
minutes?
A.
B.
C.
D.
Square & Cube Roots
63. Which of the following is equal to 12?
A.
B.
C.
D.
Estimate Solutions
64. Which of the following is approximately equal to the expression below?
A. 7
B. 5
C. 8
D. 6
Absolute Value
65. Simplify the following expression.
-|22| + 36
A. -14
B. 14
C. 17
D. -53
Real Numbers
66. Which statement is correct?
A. Zero is not part of the whole numbers.
B. Zero is not part of the rational numbers.
C. Zero is not part of the natural numbers.
D. Zero is not part of the integers.
Real World Problems
67. Mary bought 4 ½ yards of suide fabric for $15.50 per yard. She also bought 4 ½ yards of silk
fabric for $21 per yard. How much did Mary spend on fabric altogether?
A. $166.50
B. $162.00
C. $139.50
D. $164.25
Order of Operations
68. Evaluate the expression below.
A. 3
B. 1
C. 26
D. 22
Ratios, Proportions, & Percents
69. Last week, a total of 4,300 fans attended the Baytown College football game. This week, a
total of 3,225 fans attended the Baytown College football game. What is the percent decrease in
attendance from last week to this week?
A. 85% decrease
B. 25% decrease
C. 90% decrease
D. 75% decrease
Real World Problems
70. Courtney's dog sleeps in a crate that is 40 inches wide, 26 inches tall, and 44 inches deep.
What is the volume of the dog crate?
A. 44,760 inches3
B. 45,760 inches3
C. 1,972 inches3
D. 110 inches3
Compute Solutions
71. Simplify the following expression.
23 + (-177)
A. 200
B. -164
C. -154
D. 154
Absolute Value
72. Why is it that |-4| = |4|?
A. When the numbers are squared, they give the same answer.
B. The absolute value of a number gives its distance from zero on the number line.
The absolute value of a number always gives the opposite of a negative number and the
C.
square of a positive number.
D. When you multiply either number by -1, you get the other.
Compute Solutions
73. Which shows the expression below simplified?
(6 × 104) × (6 × 10-2)
A. 12 × 102
B. 3.6 × 103
C. 3.6 × 101
D. 3.6 × 102
Compute Solutions
-12 × 1/7
74.
A. -2 2/7
B. -1 2/7
C. -1 5/7
D. 5/7
Order of Operations
75. Simplify the following expression.
A. 17
B. 11
C. 2
D. 13
Scientific Notation
76. Write the number 0.000397 × 1024 in scientific notation.
A. 3.97 × 1028
B. 3.97 × 1020
C. 3.97 × 1021
D. 39.7 × 1020
Exponents
77. Simplify the following expression.
A.
32
B.
C.
1.024
D.
Square & Cube Roots
78. Determine which two values the following number is between.
A. 10.06 and 10.07
B. 10.04 and 10.05
C. 10.05 and 10.06
D. 10.07 and 10.08
Absolute Value
79. Simplify the following expression.
23 + |-8| + 20
A. 51
B. 35
C. -51
D. -5
Real World Problems
80. The population of Oklahoma City was approximately 560,000 in 2009. The population of
Oklahoma City was approximately 445,000 in 1990. What is the difference between the
approximated populations of Oklahoma City?
A. 1.005 × 106
B. 2.492 × 1012
C. 1.15 × 105
D. 1.15 × 106
Real World Problems
81. Candra had a gift card for $130. She spent $20.83 on Friday and $56.51 on Saturday using
her gift card. Then, on Sunday she returned an item she bought on Saturday, and $13.76 was
credited back to her gift card. How much money is left on Candra's gift card on Monday?
A. $52.66
B. $122.93
C. $66.42
D. $38.90
Exponents
82. Simplify the following expression.
(24)6 ÷ 224
A. 2
B. 24
C. 1
D. 2-14
Real Numbers
83. Which of the following is a rational number?
A.
B.
C.
D.
Scientific Notation
84. How do you write the standard number 73,900 in scientific notation?
A. 7.39 × 105
B. 73.9 × 103
C. 7.39 × 104
D. 7.39 × 103
Ratios, Proportions, & Percents
85. Sarah runs at a speed of 4 miles per hour for 4 miles. She then hops on her bicycle and rides
for 24 miles at a speed of 12 miles per hour. How long does Sarah run and ride her bicycle?
A. 6 hours
B. 4 hours
C. 8 hours
D. 3 hours
Scientific Notation
86. The speed of light is 3 × 108 meters per second. What is this speed in standard form?
A. 30,000,000 meters per second
B. 300,000,000 meters per second
C. 300,000 meters per second
D. 3,000,000,000 meters per second
Absolute Value
87. Simplify the following expression.
33 - |5 - 6| - 13
A. 21
B. 31
C. 19
D. 9
Estimate Solutions
88. Ellie has $40 to spend at a drugstore. She also has a coupon for $3.50 off of a $10 purchase.
She wants to buy four items priced as shown below.
• nail polish
• shampoo
• conditioner
• lotion
$6.36
$7.80
$7.80
$7.34
When is an exact amount necessary?
A.
B.
C.
D.
when Ellie is deciding if she will have enough left over to buy lunch
when Ellie is deciding if she will spend enough to use her coupon
when Ellie is told how much money is due
when Ellie is deciding if $40 is enough to buy all four items
Square & Cube Roots
89. Brody is experimenting with numbers. First, he took the square root of 16. Then, he squared
his result. After these steps, which number was Brody's final solution?
A. 64
B. 8
C. 4
D. 16
Absolute Value
90. Simplify the following expression.
39 - |-2 + 10|
A. 51
B. 31
C. 47
D. 27
Ratios, Proportions, & Percents
91. The value of Jamie's baseball card collection rose 30% in the last year. It is now worth $143.
What was it worth a year ago?
A. $107
B. $110
C. $80
D. $140
Scientific Notation
92. How do you write the number 2.24 × 103 in standard form?
A. 22,400
B. 2,240
C. 224,000
D. 224
Exponents
93. Simplify the following expression.
A.
B.
C.
D.
Scientific Notation
94. How do you write the number 4.094 × 107 in standard form?
A. 4,094,000
B. 40,940,000
C. 4,094,000,000
D. 409,400
Estimate Solutions
95. Don gets off of work at 5:45 and is planning on meeting some friends to watch the football
game. On the way to the game he plans to stop at a fast food restaurant to get a quick bite to eat.
At what time should he tell his friends he will arrive at the game?
In the question above, does Don need to give his friends an exact time or an estimated time that
he will arrive at the game?
A. an estimated time
B. an exact time
Order of Operations
96. Simplify the following expression.
A. 15
B. 21
C. 52
D. 35
Exponents
97. Which of the following is an equivalent representation of 2-2 ?
A.
B.
C.
D.
Square & Cube Roots
98. Simplify:
A. 5
B. 6
C. 7
D. 9
Square & Cube Roots
99. Simplify:
A. 11
B. 12
C. 10
D. 9
Real Numbers
100. To which real number subset do the following real numbers not belong?
A. natural numbers
B. integers
C. whole numbers
D. irrational numbers
Answers
1. B
2. A
3. B
4. A
5. C
6. B
7. B
8. A
9. A
10. D
11. B
12. A
13. D
14. D
15. D
16. B
17. D
18. A
19. B
20. D
21. A
22. C
23. D
24. C
25. A
26. C
27. B
28. C
29. B
30. A
31. C
32. A
33. D
34. D
35. C
36. C
37. 5
38. D
39. C
40. -20
41. A
42. C
43. B
44. B
45. A
46. D
47. A
48. B
49. D
50. A
51. B
52. A
53. D
54. A
55. B
56. C
57. D
58. A
59. A
60. C
61. C
62. B
63. A
64. D
65. B
66. C
67. D
68. D
69. B
70. B
71. C
72. B
73. B
74. C
75. B
76. B
77. D
78. B
79. A
80. C
81. C
82. C
83. C
84. C
85. D
86. B
87. C
88. C
89. D
90. B
91. B
92. B
93. C
94. B
95. A
96. A
97. D
98. C
99. B
100. D