Math 8 SOL 8.1b, 8.2, 8.5 STUDY GUIDE
Broadfoot/Allen/Hannam/Clark
Name: _______________________________ Date: _____________ Block: _______
This Summative Assessment covers SOL 8.1b, 8.2, and 8.5 learning targets.


Know how to:
o Compare and order decimals, fractions, percents, and numbers written in scientific
notation.
o Understand and be able to describe the relationship between the subsets of the real
number system.
o Determine whether a given number is a perfect square.
o Find the two consecutive whole numbers between which a square root lies.
Make sure you answer every question on this study guide. Practice showing all work on a
piece of scratch paper, since you must show all work on tests to receive full credit.
8.2 Real Number System
1. Label the real number system Venn diagram. (Irrational, Rational, Natural, Integers, Whole
Numbers)
Real Numbers
2. Place the following numbers in the appropriate circle in the Venn diagram above:
4
19
-7
π
0
21
-6.45
131
2.31
121
3
3
9
3
2.5743…
2
0.2
11
1
-5.2
-0.58
-12
5
1
Math 8 SOL 8.1b, 8.2, 8.5 STUDY GUIDE
Broadfoot/Allen/Hannam/Clark
3. Answer the following questions. Give an example if possible. Justify your answer in complete
sentence(s).
A. Can a number be both irrational and rational?
B. Can a number be both an integer and rational number?
C. Can a number be both a natural and an integer number?
D. Can a terminating decimal be an irrational number?
E. Can a number be an integer and a whole number?
4. Which of the following real numbers is not a rational number?
3
A. -19
B. 2
C. 4.313131
5
D.
13
5. List ALL the subsets to which the following numbers belong. Circle most specific subset.
A. 0
B. -4.353535
C. 13
D. 34
E. -3.136234…
F. -83
G. 2
3
5
8.5 Perfect Squares, Square Roots, Estimating Square Roots
6. Simplify.
A. 169
E.  16
B. - 100
C.
400
F.
G.
9
1
2
D.
81
Math 8 SOL 8.1b, 8.2, 8.5 STUDY GUIDE
Broadfoot/Allen/Hannam/Clark
7. Find two consecutive whole numbers between which the square root lies. Circle the number
that is closest to the square root.
A.
12
B.
123
C.
388
E.
73
F.
44
G.
97
D.
11
8. Find the side length of each square given the area of square.
A.
Area =
4 mm²
Area =
144 m²
Area =
81 in²
9. List the perfect squares.
Sq Root
0
1
2
4
of the
Perfect
Square
9
Perfect
Square
Sq Root
of the
Perfect
Square
9
Perfect
Square
11
18
7
8
16
17
36
12
13
100
Perfect
Square
Sq Root
of the
Perfect
Square
5
14
225
20
361
3
Math 8 SOL 8.1b, 8.2, 8.5 STUDY GUIDE
Broadfoot/Allen/Hannam/Clark
8.1b Ordering Rational Numbers
10. Order the set of rational numbers in ascending order (from least to greatest). (8.1b)
1
A. 2, 8, -9, -21, 5, -6, 0
B. 0.3, 2 , 11%, 2.2 x 10 2
5
3
C. 2.2 x 10 3 , 123 , 0.36, 165%
4
D. 2.2 x 10 1 ,
3
, 0.47, 15%
4
11. The following numbers have been ordered from least to greatest. Choose the number from
the box below that has been left out of this sequence. Write it in the space provided.
0.4, _________, 4.4 x 10-1,
9
, 46%
20
4.2 x 10-2
0.041
21
50
50%
12. For each fraction, find the decimal and percentage that is equivalent.
A.
B.
C.
D.
Fraction
2
5
7
10
1
2
2
3
3
8
Decimal
Percentage
4