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Worksheets

The Real Number System

Total questions: 20

Worksheet time: 1hrs 10mins

Name
Class
Date
1.
What is an example of an irrational number?
a)
-2/3
b)
.75575557654..
c)
23
d)
0
2.
What is an example of an integer?
a)
-9
b)
0.567
c)
1/2
d)
-0.957643...
3.

Natural numbers are:

a)

1.5, 2, 2.5, 3, . . .

b)

0,1,2,3,4,5...

c)

1, 2, 3, 4, . . .

d)

. . . , -2, -1, 0, 1, 2, . . .

4.
A repeating decimal (like 4.7777...) is what type of number?
a)
Rational 
b)
Irrational
5.
A decimal that stops (like 2.48) is which type of number? 
a)
Rational
b)
Irrational
6.
Point B could represent which of the following numbers?
a)
√24
b)
√30
c)
√35
d)
√42
7.
The square root of 5 is between what two integers?
a)
4 and 5
b)
2 and 3
c)
3 and 4
d)
9 and 10
8.

What category/categories does the following number fall into?  9 = 3\sqrt{9}\ =\ 3  

a)

Integer

b)

Whole, Integer, Rational, and Real

c)

Irrational and Real

d)

Natural, Whole, Integer, Rational, and Real

9.

Two numbers are shown on the number line.

Which value is NOT located between these two numbers on the number line?

a)
b)
c)
d)
10.
a)
b)
c)
d)
11.

List the following numbers from least to greatest:

-64 , 3.5 , √27 , 6.666...

a)

-64 , 3.5 , √27 , 6.666...

b)

3.5 , √27 , 6.666..., -64

c)

3.5, -64, √27, 6.666...

d)

6.666, √27, -64, 3.5

12.

Order 10.5, √105 , and 3π + 1 from greatest to least.

a)

√ 105 , 3π + 1, 10.5

b)

3π + 1,√ 105 , 10.5

c)

√ 105 , 10.5, 3π + 1

d)

10.5, √ 105 , 3π + 1

13.

Order the following numbers from least to greatest.

a)

-.8, -.63, -.6, -.72

b)

-.6, -.63, -.72, -.8

c)

-.8, -.72, -.63, -.6

14.

Order the following numbers from greatest to least.

a)

-1.25, -.8, -.4, .15

b)

.15, -.4, -.8, -1.25

c)

.15, -.8, -.4, -1.25

15.
a)
b)
c)
d)
16.
a)
b)
c)
d)
17.
Which of the following is NOT a perfect square?
a)
49
b)
100
c)
64
d)
80
18.
Which of the following is a perfect square?
a)
39
b)
50
c)
6
d)
81
19.
What do we call √ ?
a)
radicand
b)
radical symbol
c)
cube root
d)
index
20.
What is a square root
a)
A number to the second power
b)
A square that has roots on it
c)
A number divided by 2
d)
Square roots are numbers that produce a specified quantity when multiplied by itself