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Name: __________________________________________
Date: _____________
Lesson 1-8: Number Systems

_________________________: one of two equal factors of a number

_______________________________: a number with a square root that is a rational number
Name the set or sets of numbers to which each real number belongs. Circle the appropriate
response(s).
84
12
1.
N W
Z Q
I
5. 3.145
N W
N W
6.
Z Q
I
9. 0
N W
6
7
2. 
3.
Z Q
I
Z Q
I
I
N W
Z Q
I
N W
Z Q
Z Q
I
N W
N W
8.
I
11. 
10. -7
Z Q
N W
54
4.
7. 0.62626262…
25
N W
2
3
Z Q
I
Z Q
I
Z Q
I
22.51
N W
12. 9
Z Q
I
N W

Closure Property – when you perform an operation on a set of numbers, that set is said to be
closed under that operation if when you perform the operation on any numbers within that set, the
result is a number within that set of numbers.
o The set of whole numbers is said to be closed under addition because when you add any
two whole numbers, the result will always be a whole number.
o The set of whole numbers is not closed under subtraction because when you subtract any
two whole numbers, the result is not always a whole number. For example, 4 – 5 = -1,
which is not a whole number.
Determine whether each set of number is closed under the indicated operation.
13. whole numbers, multiplication
14. integers, division
15. integers, addition
16. natural numbers, subtraction
17. irrational, addition
18. rational, multiplication
Find each of the following square roots. Try to do each of these without using a calculator.
19.
64  _______
20.  81  _______
21.  100  _______
24. 
22. 
4
 _______
25
23.  121  _______
25. 
25
 _______
16
26. 
28.  6.25  _______
121
 _______
100
29.  1.69  _______
Graph each set of numbers on the number line provided.
 4 1 2 5
31.  , , , 
 3 3 3 3
32. a  2
25
 _______
144
27.  3600  _______
30.
1.44  _______
33. b  4.5
Replace each blank with <. >, or = to make a true statement. Try to do these without a calculator.
34.
37.
19 ______ 3.8
8
______ 0.8
9
35. 7.2 ______ 50
2
36. 2 ______ 5
3
38. 6.23 ______ 48
39.
1
1
______
8
8
Order each of the following sets of numbers from least to greatest. Try to do these without a
calculator.
3
7
40.  ,  5, 25 ,
4
4
42.
44.
5
,  2, 124 ,  3.11
4
1
41.  1.25, 0.05,  , 5
4
1
9
43. 0.35, 2 , 5 ,
3
5
45. The Pythagorean Theorem is used to
find the length of an unknown side of a
right triangle when two side lengths are
known. The length of side c (the
hypotenuse) can be found with the
formula c  a 2  b 2 . Should this
formula have a  symbol in front of
it? Why or why not?