Name:
Date:
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 COVERED ON “NUMBER SENSE” TEST:
Converting among Fractions, Decimals, and Percents
Scientific Notation (both large AND small #’s– positive exponent and negative exponent)
Comparing Rational #’s (“greater than” or “less than”)
Ordering Rational #’s (mixture of fractions, decimals, %’s, scientific notation)
General Fraction, Decimal, % Word Problems
Exponents
Perfect Square #’s and Square Roots
NOTES SPACE/HELPFUL TIPS (to be filled out in class):
Converting fractions, decimals, and percents
Converting between Percents and Decimals:
“To the left, to the left!”
ABCDEFGHIJKLMNOPQRSTUVWXYZ
“To the right, to the right!”
Converting a Fraction to a Decimal:
“Take the top #,
Divide by the
bottom #!”
Converting a Decimal to a Fraction: READ IT, ______________ IT, REDUCE IT!!!
Fraction
1.
Decimal
7/
8
2.
0.05
3.
4.
45%
1/
3
5.
0.4
6.
7.
25 %
3/
5
8.
6.2
9.
10.
Percent
9.5%
5/
11
2
Scientific notation
Convert between scientific notation and standard form. A few examples are done for you.
Standard
Form
1.
6,230,000
2.
8,200
3.
.00015
4.
.000027
5.
61,000
0.0092
10.
1.5 x 10-4
6.1 x 10 4
9.2 x 10 -3
5.26 x 10 -5
8.
9.
6.23 x 106
7.02 x 10 3
6.
7.
Scientific
Notation
2,680,000
.000025
11.
1.2 x 10 4
12.
2.789 x 10 3
13.
93,000
14.
.017
15.
8.3 x 10 0
16.
7.7 x 10 -4
17.
9,240,000,000
18.
.00019
19.
3.6 x 10 1
20.
8.4 x 10 -4
3
COMPARING DECIMAL NUMBERS
Directions: Look at the below examples. Then, complete #’s 1 – 10:
Arrange the following decimals in order of size, from smallest to largest. You may
wish to attach zeros at the end in order to compare.
4
Ordering rational NUMBERS
Order the following #’s in the order indicated:
#
Fraction
Decimal
%
Scientific
Notation
1.
2/
3
0.6
59%
6.6 x 10-2
2.
11/8
1.2
1.12%
1.125 x 103
Answer
(List in Original Form):
Least to Great:
Greatest to Least:
Multiple Choice:
3. Which of the following is equivalent to 5/8 ?
A. 62.5
B. 62.5%
C. 6.25 x 10-3
D. 5.8
4. 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
5. Which of the following is equivalent to 0.75?
A. 75%
B. 75/10
C. 7.5 x 10-2
D. 75
6. Jerry got a 41/50 on his math test. What is his grade as a percentage?
A. 41%
B. 78%
C. 82%
D. 80%
5
Exponents
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
2.
1012
100
3.
Evaluate the following powers of 10 with negative exponents. You must give both
the fraction and decimal form:
4.
10-2
5.
10-4
10-5
6.
Evaluate the following powers with positive exponents:
7.
10.
73
8.
60
11.
34
26
9. 182
12.
83
Evaluate the following powers with negative exponents:
13.
7-2
14.
3-3
15. 15-2
16.
4-3
17.
2-4
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 = _____
169
Find the square root of the following numbers :
1.
9
= __________
2.
121 = __________
3.
4.
361 = __________
5.
64
= __________
6.
= __________
196 = __________
7.
81
= __________
10 .
225 = __________
8.
100 = __________
9.
11.
400 = __________
12.
324 = __________
9
= __________
Between which two consecutive WHOLE numbers do the following #’s fall between?:
13.
40 lies between __________ and __________.
14.
15.
10 lies between __________ and __________.
16. 215 lies between __________ and __________.
95 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? __________
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
1
9