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Worksheets

The Real Number System

Total questions: 72

Worksheet time: 5hrs 28mins

Name
Class
Date
1.

Organize these options into the right categories

Categorize the following

RED FORD F150

BLUE RAM 1500

BLUE SHIRT

SILVER JEANS

RED SHORTS

SILVER UHAUL TRUCK

Trucks
Clothing
2.

Organize these options into the right categories

Categorize the following

RED FORD F150

YELLOW RAM 1500

BANANA

LEMON

YELLOW SHIRT

APPLE

CARROTS

PUMPKIN

ORANGE SPORTS CAR

RED
YELLOW
ORANGE
3.

The numbers 0,1,2,3...are called?

a)

whole numbers

b)

integers

c)

rational numbers

d)

whole, integer, rational

4.

What is the best classification for this number? -4

a)

rational

b)

whole

c)

integer

d)

whole, integer, rational

5.

Which of the following are rational numbers?

a)

64

b)

15

c)

74\frac{7}{4}  

d)

7.452

6.

Is 74.8‾74.\overline{8}  a natural number?

a)

Yes, because this value can be placed on a number line.

b)

No, do to the repeating 8 it is not a natural number.

c)

It can be depending on how it is used. If it used to measure height then it can be but if used to measure money it is not a natural number.

7.

Which of the following categories describes the value of 91?

Select all that apply.

a)

irrational number

b)

rational number

c)

natural number

d)

whole number

e)

integer

8.

Which categories cannot be applied to describe 5?

a)

Whole

b)

Integer

c)

Rational

d)

Irrational

9.

Is π\pi  a natural number?

π\pi (Pi)

a)

Yes

b)

No

10.

Select ALL classifications that apply to this number:

10

a)

Real Number

b)

Rational Number

c)

Integer

d)

Whole Number

e)

Natural Number

11.

What is the best classification for this number?   0.35

a)
whole
b)
rational
c)
irrational
d)
real
12.

Fill in the blank. An integer is ____________ rational.

a)

sometimes

b)

always

c)

never

d)

only on Mondays

13.
An example of an integer is...
a)
9.1
b)
8/9
c)
-9
d)
-2.3
14.

A whole number is an integer

a)

Always

b)

Sometimes

c)

Never

15.

An example of a whole number is:

a)

4/9

b)

-9

c)

5.2

d)

17

16.

Which of the following is not an integer?

a)

0

b)

1.57

c)

-6

d)

10

17.

Select all: Natural Numbers

a)

4.5

b)

5

c)

-2

d)

0

e)

7,652

18.

Select all: Integers

a)

4.2

b)

4

c)

-4.2

d)

4/3

e)

-2

19.

Which of the following is NOT a natural number?

a)

12

b)

3,000

c)

5

d)

0

20.

Pi is an example of which type of number?

a)

Irrational number

b)

Natural number

c)

Unnatural number

d)

Fraction

21.
Classify the following:
√13?
a)
Rational
b)
Irrational
22.

What type of number is 3.5‾3.\overline{5}  ?

a)

Integer

b)

Rational Number

c)

Irrational Number

d)

Natural Number

23.

Which number is an irrational number?

a)

2.33333 . . .

b)

5.72314.....

c)

5.72

d)

52

24.
Classify 17/10
a)
Whole
b)
Rational
c)
Natural
d)
None of the above
25.
Classify 3
a)
Natural, Whole, Integer, Rational
b)
Whole, Rational
c)
Integer
d)
Rational
26.

π or PI is classified as which?

a)

Rational only

b)

Irrational only

c)

Rational, Real

d)

Irrational, Real

27.
1,378,472,706 and best be classified as what?
a)
natural, whole, integer, rational
b)
whole, integer, rational
c)
rational
d)
natural, whole, integer, rational, real
28.
Which statement is NOT true?
a)
Every rational number is a real number.
b)
Every counting number is a whole number.
c)
Every integer is a rational number.
d)
Every decimal number is an irrational number.
29.

Select all that apply that will classify the following number: 4

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

30.

Select all that apply that will classify the following number: 12\frac{1}{2}  

a)

NATURAL

b)

WHOLE

c)

INTEGER

d)

RATIONAL

31.
The set of rational numbers includes all the following except...
a)
-42
b)
5/0
c)
0
d)
14.7
32.
What is an example of an irrational number?
a)
-2/3
b)

0.75575557654...

c)
23
d)
0
33.
Which of the following statements is always true?
a)
All integers are whole numbers
b)
all rational numbers are integers
c)
some whole numbers are not rational numbers
d)
all whole numbers are integers
34.
What are your counting numbers (1,2,3..)?
a)
Rational Numbers
b)
Whole Numbers
c)
Natural Numbers
d)
Irrational Numbers
35.

We can classify π or PI as _____________.

a)

Rational only

b)

Irrational only

c)

Rational, Real

d)

Irrational, Real

36.
What is a rational number ?
a)
A rational number  is a number that cannot be written as a fraction.
b)
A rational number is a number that can be written as a fraction.
c)
A rational number cannot be a repeating  decimal.
37.
What type of number is π ?
a)
Rational
b)
Irrational
38.

Perfect Squares are irrational

a)

True

b)

False

39.

The number 1 is a:

a)

Whole number

b)

All of the above

c)

Integer

d)

Rational number

40.

-10 is an ​ (a)   and a ​ (b)   number.

Choose from the below words
integer
rational
irrational
whole number
41.

Where does the number 45 go? ​ (a)  

Choose from the below words
All categories
whole number
rational number
integer
natural number
42.

What letter usually represents an imaginary number?

a)

a

b)

i

c)

j

d)

x

43.
A decimal that stops is which type of number? Example: 2.75
a)
Rational
b)
Irrational
c)
None of these
44.
A repeating decimal is what type of number?
a)
Rational 
b)
Irrational
c)
None of these
45.

Which answer includes ALL of the classifications of the following number:

0

a)

Rational, Integer

b)

Rational

c)

Rational, Integer, Whole

d)

Rational, Integer, Whole, Natural

46.
Which statement is true?
a)
Every rational number is an integer
b)
Every whole number is a natural number
c)
Every integer is a whole number
d)
Every whole number is a rational number
47.
Which word does NOT describe 5?
a)
Whole
b)
Integer
c)
Rational
d)
Irrational
48.
Which statement is FALSE?
a)
Every rational number is a real number.
b)
Every decimal number is an irrational number.
c)
Every integer is a rational number.
49.
Explain the error(s).
a)
-1.2 isn't an integer.
b)
-2 isn't a whole number and 3.4 isn't a rational number.
c)
-2 isn't a whole number and -1.2 isn't an integer.
d)
The numbers are graphed correctly.
50.

The numbers 1, 2, 3, and 4 are which type of rational number?

a)

Natural

b)

Whole

c)

Integer

d)

Rational

e)

All of the above

51.

225\sqrt{225}  is what type of number?

a)

Fraction

b)

Imaginary

c)

Irrational

d)

Rational

e)

Non-repeating decimal

52.

Which symbol makes the statement true?

3.14 ___________  π\pi  

a)

>

b)

<

c)

=

53.

Some fractions are irrational numbers.

a)

True

b)

False

54.

Repeating decimals are examples of rational numbers.

a)

True

b)

False

55.

All square roots are irrational numbers.

a)

True

b)

False

56.

Gabby and Olivia are working on math homework. They are asked to determine if −3.2‾-3.\overline{2} is rational or irrational. Gabby says the number is rational, whereas Olivia says the number is irrational. Who is correct and why?

a)

Olivia is correct because the number cannot be written as a fraction, thereby making it irrational.

b)

Olivia is correct because the number is a repeating, non-terminating decimal, thereby making it irrational.

c)

Gabby is correct because the number is an integer, thereby making it rational. 

d)

Gabby is correct because the number can be written as the fraction  −3 29-3\ \frac{2}{9}  , thereby making it rational.

57.

What is 1/2 as a decimal?

a)

.5

b)

.2

c)

5

d)

2

58.
Classify the following:
 -78
a)
integer
b)
integer, real
c)
integer, whole, rational
d)
integer, rational, real
59.
-14 could NOT be which type of number?
a)
Integer
b)
Real
c)
Rational
d)
Natural
60.
Classify the number 0
a)
Whole
b)
Integer
c)
Rational
d)
All of the above
61.
A repeating decimal is what type of number?
a)
Rational 
b)
Integer
c)
Natural 
62.
Order from least to greatest:
[-8, 7, -6, 5, -4, 3, -2]
a)
-2, 3, -4, 5, -6, 7, -8
b)
-2, -4, -6, -8, 3, 5, 7
c)
-6, -8, -4, -2, 7, 5, 3
d)
-8, -6, -4, -2, 3, 5, 7
63.
Put the rational numbers in order from least to greatest.
-4.2, -4 1/2, -4, 0, 4 
a)
0, -4 1/2, -4.2, 4, -4
b)
-4 1/2, -4.2, -4, 0, 4
c)
-4 1/2, -4.2, -4, 4, 0
64.

Order these numbers from least to greatest.

a)

b)

c)

d)

1)
2)
3)
4)
65.
List in order from greatest to least
12, -9, -6, 10
a)
12, 9, 6, 10
b)
-6, -9, 10, 12
c)
5, 4, 3, 21
d)
12, 10, -6, -9
66.

Which point on the number line best represents -1.2?

a)

A

b)

B

c)

C

d)

D

e)

E

67.

Click on the image - Write the number positioned at point A.

a)

−4.25 -4.25\

b)

−3.75-3.75

c)

4.254.25

d)

−4.5-4.5

68.

Which child is shorter than Ellis? (Hint: turn all fractions into decimals)

(a)  

69.
Which is the least:  0.06 or 0.060
a)
0.06
b)
They are equal.
c)
0.060
d)
Depends on the time of day.
70.

Which is the smallest number?

a)

0.54

b)

0.45

c)

0.5

d)

0.55

71.

Which of these is the largest number?

a)

0.76

b)

0.7

c)

0.67

d)

0.6

72.
Order from Greatest to Least

1.876, 1.77, 1.80
a)
1.876, 1.80, 1.77
b)
1.80, 1.77, 1.876
c)
1.876, 1.77, 1.80
d)
1.80, 1.77, 1.876

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