Name:____________________________________________________________________________________Date:_____/_____/__________
Study Guide/ Practice
Unit 1 Test, “Number Sense”
Note: Many problems in this packet will be completed together in class during
review time. Students are not expected to complete every single problem in the
packet. They should complete several problems from each page-- in addition to
studying the notes and past quizzes– in order to be fully prepared for test.
Topics:
Converting among Fractions, Decimals, and Percentages
Comparing Rational #’s (“greater than” or “less than”)
Ordering Rational #’s (mixture of fractions, decimals, %’s, scientific notation)
Exponents
Perfect Square #’s and Square Roots
Scientific Notation (positive exponents and negative exponents)
On the back of this cover page is the Unit 1 “Quick Guide” – for your
reference.
Unit 1, “Number Sense,” Quick Guide
Fraction  Decimal
“Take the top #, divide
by the bottom #!”
1 = 8I1
8
(turn the fraction clockwise)
Negative exponents do
NOT make the answer
negative!!
Exponents:
10 3 = 10 x 10 x 10 = 1,000
1
1
1
1
10 -3 = 10 x 10x 10 = 1000 = 0.001
Square Root Examples:
𝟐𝟓 = 5 x 5 = 5
𝟑𝟔 = 6 x 6 = 6
𝟒𝟗 = 7 x 7 = 7
Converting fractions, decimals, and percentages
Converting between Percents and Decimals:
“To the _______, to the left!”
ABCDEFGHIJKLMNOPQRSTUVWXYZ
“To the ________, to the right!”
Converting a Fraction to a Decimal:
“Take the ______ #,
Divide by the __________ #!”
Converting a Decimal to a Fraction: READ IT, ______________ IT, REDUCE IT!!!
SHOW YOUR WORK!
Fraction
1.
Decimal
7/
8
2.
0.05
3.
4.
45%
1/
3
5.
6.2
6.
7.
8. 75% =
3
4
75
100
75
1000
0.75
7.5
7,500
Percent
9.5%
3/
5
9. 0.6 =
60%
6%
3
5
6
100
60
100
6
10
3
COMPARING & Ordering rational NUMBERS
Order the following #’s in the order indicated:
#
Fraction
Decimal
%
Answer
(List in Original Form):
1)
2/
3
0.6
59%
2.
11/8
1.2
1.12%
ASCENDING (Least to Greatest):
DESCENDING (Greatest to Least):
Place a > sign, a < sign, or an = sign in the following blanks:
3)
0.8 ________ 55%
5)
40% ________ 0.04
4)
3/
6)
20% ________ 1/5
4
________ 0.7
Circle the answer that makes the following true:
7)
25% < ________ < 0.7
A. 70%
B. 0.035
C. 0.3
8)
0.05 < ________ < 1/2
A. 0.5
B. 0.25
C. 0.025
Multiple Choice. Circle the correct answer. SHOW YOUR WORK!
9) Which of the following is equivalent
to 5/8 ?
A. 62.5
B. 62.5%
C. 6.25 x 10-3
D. 5.8
11) Which of the following is equivalent
to 0.75?
A. 75%
B. 75/10
C. 7.5 x 10-2
D. 75
10) Four students recorded their scores on a
quiz in different ways. Which score is the
highest?
A. 80%
B. 0.09
C. 9/100
D. 9/10
12) Jerry got a 41/50 on his math test. What is
his grade as a percentage?
A. 41%
B. 78%
C. 82%
D. 80%
4
Exponents & Powers of 10
Fill in the following powers of 10 chart :
1010= 10,000,000,000
105= __________________
100= __________________
109= _________________
104= __________________
10-1= __________________
108= _________________
103= __________________
10-2= __________________
107= __________________
102= __________________
10-3= __________________
106= __________________
101= __________________
10-4= _________________
Evaluate the following powers of 10 (use the pattern . . .):
1.
1014
1012
2.
3.
100
Evaluate the following powers of 10 with negative exponents. You must give both
the fraction and decimal form:
4.
10-2
10-4
5.
6.
10-5
Evaluate the following powers with positive exponents:
7.
53
60
10.
34
8.
11.
9. 150
26
12.
43
15.
4-3
Evaluate the following powers with negative exponents:
13.
7-2
16. 10-5 =
14.
1
10
1
1
1
1
x 10 x 10 x 10 x 10
3-3
1
10,000
17. 102 =
1
10
1
x 10
20
0.000001
0.00001
10 x 10
100
10 x 10 x 10 x 10 x 10
-10,000
-100
0.01
5
Perfect square #’s and square roots
Fill in the missing information in the below “perfect square” table:
12 = _____
62 = _____
112 = _____
162 = _____
22 = _____
72 = _____
122 = _____
172 = _____
32 = _____
82 = _____
132 = 169
182 = 324
42 = 16
92 = 81
142 = _____
192 = _____
52 = _____
102 = _____
152 = _____
202 = _____
Find the square root of the following numbers :
1.
36 = __________
2.
121 = __________
3.
324 = __________
4.
361 = __________
5.
64
= __________
6.
169 = __________
196 = __________
7.
81
= __________
10 .
225 = __________
8.
100 = __________
9.
11.
400 = __________
12.
9
= __________
c
Between which two consecutive WHOLE numbers do the following #’s fall between?:
13.
40 lies between __________ and __________.
15. 10 lies between __________ and __________.
14.
95 lies between __________ and __________.
16. 215 lies between __________ and __________.
17.
Bob wants to plant a square garden. The area of the garden will be 86 sq. ft. About how
long will each side be? __________
18.
What perfect square # does the square to the right represent? __________
What is its square root? __________
6
Scientific notation
Convert between scientific notation and standard form. A few examples are done for you.
Standard Form
Scientific Notation
1.
6,230,000
6.23 x 106
2.
8,200
3.
0.00015
4.
0.000027
5.
61,000
1.5 x 10-4
6.1 x 10 4
7.02 x 10 3
6.
9.2 x 10 -3
0.0092
7.
5.26 x 10 -5
8.
9.
2,680,000
10.
0.000025
11.
1.2 x 10 4
12.
2.789 x 10 3
13.
93,000
14.
0.017
15.
8.3 x 10 0
16.
7.7 x 10 -4
17.
9,240,000,000
18.
0.00019
19.
3.6 x 10 1
20.
8.4 x 10 -4
Order the following from least to greatest:
21)
3.05 x 105
9.845 x 102
6.1 x 109
5.7 x 105
1.68 x 107
2.25 x 104
4 x 104
Answer:
22)
8.3 x 10-5
Answer:
7
Miscellaneous
Multiple Choice:
8
Place the following numbers in the correct spot on the below number line:
0.75
40%
0.01
1/
10
80%
1/
4
9