Free Printable Number Systems

1.

Which of the following is an irrational number?

a)

0.333

b)

$\sqrt{8}$

c)

$\sqrt{49}$

d)

$\frac{5}{22}$

2.

What type of number is a non-repeating, non-terminating decimal?

a)

irrational

b)

prime

c)

rational

d)

imaginary

3.

Which is the best rational approximation for $\sqrt{55}$ ?

a)

7.5

b)

27.5

c)

5.5

d)

11.0

4.

The number $-\sqrt{16}$ belongs to what number system(s)?

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

imaginary number

5.

Which statement about $\sqrt{15}$ and $\pi$ is true?

a)

Both numbers can be categorized as rational.

b)

Both numbers can be written as decimal numbers that neither terminate nor repeat.

c)

Both numbers can be written as fractions with integer numerators and denominators.

d)

Both numbers can be categorized as natural numbers because they are positive.

6.

Which decimal appears to be a rational number?

a)

2.14285714285714...

b)

3.14159265358979...

c)

4.79583152331272...

d)

5.56776436283002...

7.

The value of π cannot be written as the ratio of two integers. Which statement is true?

a)

π is a rational number.

b)

π is an irrational number.

c)

The decimal expansion of π terminates.

d)

The decimal expansion of π repeats.

8.

Which point best represents $\sqrt{10}$ on a number line?

a)

point A

b)

point B

c)

point C

d)

point D

9.

Between which two numbers does $\sqrt{11}$ lie on a number line?

a)

4 and 5

b)

5 and 6

c)

10 and 11

d)

3 and 4

10.

Which best represents the position of $\sqrt{8}$ on the number line below?

a)

Point P

b)

Point Q

c)

Point R

d)

Point S

11.

Read the question carefully:

a)

6.24

b)

7.68

c)

8.31

d)

9.43

12.

-7 is classified as...

a)

Rational

b)

Whole

c)

Natural

d)

Integers

13.

All whole numbers are natural numbers.

a)

True

b)

False

14.

Which is an integer but not a whole number?

a)

0

b)

91

c)

-91

d)

19

15.

All whole numbers are integers.

a)

True

b)

False

16.

Convert 11/20 from a fraction to a decimal

a)

5.5

b)

.55

c)

.11

d)

.1120

17.

How would you express .005 as a fraction?

a)

5/10

b)

5/100

c)

5/1,000

d)

5/10,000

18.

Which of the following can be classified as a whole number?

a)

-3.5

b)

$\frac{5}{4}$

c)

245

d)

0.66

19.

What set of numbers describes the following number?

-4

a)

Integer

b)

Natural

c)

Whole

20.

Change 125% to a decimal.

a)

1.25

b)

12.5

c)

125

d)

1250

21.

Write 6% as a decimal.

a)

6

b)

0.6

c)

0.06

d)

0.006

22.

Convert to a decimal:

$\frac{8}{25}$

a)

.22

b)

.34

c)

.32

d)

.5

23.

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}

24.

Write 4/100 as a decimal

a)

.40

b)

.04

c)

4.4

d)

4

25.

1/2

a)

Rational

b)

Irrational

26.

3.4567...

a)

Rational

b)

Irrational

27.

Convert 5/8 into a decimal.

a)

.58

b)

.75

c)

.625

d)

.852

28.

a)

1/2

b)

1/10

c)

1/100

d)

1/9

29.

The numbers -20 and 20 are

a)

Negative

b)

Positive

c)

Opposites

d)

Rational

30.

9 is what type of number?

a)

Negative

b)

Rational

c)

Opposite

d)

Positive

31.

9 is what type of number?

a)

Negative

b)

Rational

c)

Opposite

d)

Positive

32.

-15, -45, -60 Are what type of numbers?

a)

Negative

b)

Whole numbers

c)

Rational

d)

Opposites

33.

Peter hiked for 6 3/4 miles. After resting, Peter hiked back along the same route for 4 1/4 miles. How many more miles does Peter need to hike to return to the place where she started?

a)

2 1/2

b)

-2 1/2

c)

-11

d)

11

34.

Tue is diving 8 1/2 feet below sea level. He decides to descend 5 1/2 more feet. How many feet below sea level is he?

a)

13 2/2

b)

14

c)

-14

d)

-13 2/2

35.

- 12 + - 8

a)

- 20

b)

20

c)

4

d)

-4

36.

Peter hiked for 6 3/4 miles. After resting, Peter hiked back along the same route for 4 1/4 miles. How many more miles does Peter need to hike to return to the place where she started?

a)

2 1/2

b)

-2 1/2

c)

-11

d)

11

37.

A __________ is any number that can be written as a ratio of two integers.

a)

Absolute Value

b)

Venn Diagram

c)

Rational Number

d)

Integer

38.

- 12 + - 8

a)

- 20

b)

20

c)

4

d)

-4

39.

5 + 9

a)

59

b)

14

c)

-14

d)

-4

40.

- 62 + - 17 + - 2

a)

81

b)

-81

c)

43

d)

-43

41.

Which decimal is equivalent to $\frac{1}{3}$ ?

a)

0.13

b)

0.3

c)

1.3

d)

3.3

42.

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.

43.

What type of number is π ?

a)

Rational

b)

Irrational

44.

The √98 falls between what two numbers on a number line?

a)

10 and 11

b)

11 and 12

c)

9 and 10

d)

90 and 100

45.

Which statement is true?

a)

The number ⅚ is irrational

b)

The number 0.345345345 is irrational

c)

The number (4π/16π) is irrational

d)

The number (√11)² is rational

46.

Which number is rational below?

a)

√20

b)

√64

c)

6π

d)

√7

47.

In between what two integers is the square root of 77?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

48.

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

49.

Irrational numbers...

a)

reduce to π

b)

never end and never repeat

c)

can sometimes be perfect squares

d)

must be negative

50.

Which of the following is irrational?

a)

0.444444444

b)

-4/5

c)

π

d)

0.2

51.

√4

a)

irrational

b)

rational

52.

4π

a)

rational

b)

irrational

53.

√7

a)

Rational

b)

Irrational

c)

real

d)

fake

54.

.141414141414...

a)

Rational

b)

Irrational

c)

real

d)

fake

55.

-17.5

a)

Rational

b)

Irrational

c)

real

d)

fake

56.

Approximate the following irrational number to the nearest hundredth without using a calculator.
The square root of 32

a)

5.33

b)

4.5

c)

8

d)

5.66

57.

What does this number belong to:
a terminating decimal

a)

Rational Number

b)

Irrational Number

58.

The √40 is between which two integers?

a)

7 & 8

b)

6 & 7

c)

5 & 6

d)

4 & 5

59.

169

a)

Is a perfect square.

b)

Is not a perfect square.

60.

A perfect square is which type of number?

a)

Rational

b)

Irrational

61.

5/2

a)

Rational

b)

Irrational

62.

4.032

a)

Rational

b)

Irrational

63.

Which number is irrational?

a)

9.6

b)

√45

c)

3/8

d)

3.4 x 10 ⁵

64.

Pi

a)

Rational

b)

Irrational

65.

Which number is rational?

a)

∛51

b)

√94

c)

∛12

d)

√64

66.

Which number is irrational?

a)

0.416

b)

-8/5

c)

∛64

d)

√27

67.

√81

a)

Rational

b)

Irrational

68.

-13

a)

Rational

b)

Irrational

69.

√121

a)

12

b)

10

c)

11

d)

3

70.

√256

a)

14

b)

16

c)

13

d)

17

71.

√289

a)

15

b)

17

c)

14

d)

13

72.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

73.

The area of a square painting is 81 cm². What is the side length of the painting?

a)

40.5 cm

b)

162 cm

c)

6,561 cm

d)

9 cm

74.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

75.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

76.

Choose <, >, or = to create a true statement.

$\frac{18}{24}$ ____ 55%

a)

<

b)

>

c)

=

77.

Use $<,\ >,\ or\ =$ to compare.
$\frac{1}{4}$ _____ $0.06$

a)

$<$

b)

$>$

c)

$=$

78.

Which of the following can be classified as a whole number?

a)

-3.5

b)

$\frac{5}{4}$

c)

245

d)

0.66

79.

What set of numbers describes the following number?

-4

a)

Integer

b)

Natural

c)

Whole

80.

In what category does $\frac{6}{11}$ belong ?

a)

Integer

b)

Natural Number

c)

Rational Number

81.

What is the decimal equivalent of $\frac{4}{25}$ ?

a)

16%

b)

0.16

c)

1.6

d)

0.08

82.

TRUE OR FALSE?

A rational number can be written as a fraction.

a)

True

b)

False

83.

Which is the symbol for: Less Than ?

a)

<

b)

>

c)

=

d)

∞

84.

Change 125% to a decimal.

a)

1.25

b)

12.5

c)

125

d)

1250

85.

Write 6% as a decimal.

a)

6

b)

0.6

c)

0.06

d)

0.006

86.

Convert to a decimal:

$\frac{8}{25}$

a)

.22

b)

.34

c)

.32

d)

.5

87.

Which symbol would make this statement true?

$\frac{4}{9}\$ _____ 48%

a)

<

b)

>

c)

-

88.

Convert this to a decimal: $\frac{4}{7}$

a)

57.14%

b)

47%

c)

0.47

d)

0.5714

89.

If you wanted to convert $\frac{8}{9}$

to a decimal, what would be the first step?

a)

Place an 8 on the right side of the decimal point

b)

Divide 8 by 9

c)

Divide 9 by 8

d)

Place a 9 on the right side of the decimal point

90.

Irrational numbers...

a)

are non-repeating

b)

are non-terminating and non-repeating decimals

c)

can sometimes be perfect squares

d)

are non-terminating

91.

What number system does √7 belong to?

a)

Rational

b)

Irrational

c)

Whole

d)

Integer

92.

What number system does -17.5 belong to?

a)

Rational

b)

Irrational

c)

Integer

d)

Whole

93.

What does this type of number belong to:

a terminating decimal

a)

Rational Number

b)

Irrational Number

94.

A perfect square is which type of number?

a)

Rational

b)

Irrational

95.

A decimal that terminates is which type of number? Example: 2.75

a)

Rational

b)

Irrational

96.

includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

97.

All ______ numbers, which include rational and irrational numbers, can be plotted on a number line.

a)

Fake

b)

Non Real

c)

Real

d)

Cool

98.

The square root of 57 is ...

a)

rational

b)

irrational

99.

Once simplified, is this number rational or irrational? 10√2

a)

Rational

b)

Irrational

100.

The sum of two irrational numbers will ________________be irrational.

a)

Always

b)

Sometimes

c)

Never

101.

Once simplified, is this number rational or irrational? (√2) * (√2)

a)

Rational

b)

Irrational

102.

The product of two Rational numbers is ________________ Rational.

a)

Always

b)

Sometimes

c)

Never

103.

The product of two Irrational numbers is _________________ Rational.

a)

Always

b)

Sometimes

c)

Never

104.

True or False?
¼ < ½

a)

True

b)

False

105.

Round √5 to the nearest hundredth.

a)

2.24

b)

2.23

c)

2.2360

106.

Which number is irrational?

a)

5.499

b)

$\sqrt{17}$

c)

- $\sqrt{9}$

d)

-10

107.

Which point best represents $\sqrt{10}$ on a number line?

a)

point A

b)

point B

c)

point C

d)

point D

108.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

109.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

110.

Which of the following numbers is rational?

a)

√8

b)

√16

c)

√50

d)

√75

111.

A fraction is which type of number?

a)

Rational

b)

Irrational

112.

Which number is a rational number?

a)

2.25

b)

-8.78654684598.....

c)

Square root of 99

d)

3.14...

113.

Which number is an irrational number?

a)

2.5

b)

5.72314.....

c)

-17

d)

1/2

114.

Mr. Cleaves wrote four irrational numbers on the SMART board and asked Saul to choose the number closest to 4. Which irrational number should Saul choose?

a)

√8

b)

√17

c)

√12

d)

√10

115.

Which number falls between 4.5 and 4.6?

a)

4.05

b)

4.61

c)

4.58

d)

4.50

116.

A whole number is which type of number?

a)

Rational

b)

Irrational

117.

A non-perfect square is which type of number?

a)

Rational

b)

Irrational

118.

A perfect square is which type of number?

a)

Rational

b)

Irrational

119.

A never ending decimal is which type of number?

a)

Rational

b)

Irrational

120.

A repeating decimal is what type of number?

a)

Rational

b)

Irrational

121.

0.8 is a rational number

a)

True

b)

False

122.

What is 15 × ___ = 45

a)

3

b)

30

c)

4

d)

40

123.

Marcia read 2 books. Each book was 44 pages long. How many pages did she read total?

a)

46 pages

b)

42 pages

c)

88 pages

d)

22 pages

124.

Each pack of pencils contains 8 pencils. Sara bough 3 packs and divided them equally among 6 people. How many pencils did each person get?

a)

24

b)

4

c)

17

d)

5

125.

_____________ is a whole number that is not a fraction.

a)

An integer

b)

A rational number

c)

An irrational number

d)

A repeating number

126.

_______ number can be written as a ratio where the numerator and denominator are integers.

a)

An integer

b)

A rational

c)

An irrational

d)

A repeating

127.

_____________ number is a number that cannot be written as a ratio of two integers.

a)

An integer

b)

A rational

c)

An irrational

d)

A repeating

128.

_________ number is a number which a figure or group of figures is repeated indefinitely.

a)

An integer

b)

A rational

c)

An irrational

d)

A repeating

129.

__________ decimal is a decimal with a finite number of digits.

a)

A terminating

b)

A rational

c)

An irrational

d)

A repeating

130.

Which of these is an example of an integer?

a)

33

b)

3.3

c)

√3

d)

1∕3

131.

Which of these is an example of a rational number?

a)

√4

b)

√5

c)

√3

d)

√2

132.

Which of these is an example of an irrational number?

a)

√2

b)

√1

c)

√9

d)

√25

133.

Which of these is an example of a repeating number?

a)

1⁄3

b)

1⁄4

c)

1⁄5

d)

1⁄10

134.

Identify the rational numbers.

a)

$\sqrt{4}$

b)

$\pi$

c)

$3.5$

d)

$\sqrt{2}$

e)

$\frac{2}{3}$

135.

A rational number can be written as a fraction.

a)

true

b)

false

136.

A terminating decimal is a decimal that...

a)

Never ends

b)

repeats a pattern

c)

ends

d)

never ends and never repeats

137.

Perfect Squares are irrational

a)

True

b)

False

138.

Select the irrational numbers

a)

$\sqrt{50}$

b)

2

c)

$\pi$

d)

2.3454128904

139.

All whole numbers are rational numbers.

a)

True

b)

False

140.

0.66666666666......is

a)

Rational

b)

Irrational

c)

Terminating Decimal

d)

Repeating Decimal

141.

-6 is

a)

Rational

b)

Irrational

142.

$\sqrt{\frac{4}{9}}$

a)

Rational

b)

Irrational

143.

Irrational numbers can be written in the form of a fraction

a)

False

b)

True

144.

includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

145.

can be expressed as a fraction in an infinite number of ways

a)

Rational Numbers

b)

Irrational Numbers

146.

All ______ numbers, which include rational and irrational numbers, can be plotted on a number line.

a)

Fake

b)

Non Real

c)

Real

d)

Cool

147.

Irrational Numbers....

a)

cannot be represented as a simple fraction

b)

can be represented as a fraction

c)

can be a repeating decimal

148.

.141414141414...

a)

Rational

b)

Irrational

149.

pi - 3.141592....

a)

Rational

b)

Irrational

150.

√2

a)

Rational

b)

Irrational

151.

5

a)

Rational

b)

Irrational

152.

-17.5

a)

Rational

b)

Irrational

153.

√25

a)

Rational

b)

Irrational

154.

√7

a)

Rational

b)

Irrational

155.

What kind of number is -3?

a)

rational

b)

irrational

c)

whole

d)

natural

156.

What kind of number is π ?

a)

rational

b)

irrational

c)

whole

d)

integer

157.

Is 3.74 a rational number?

a)

yes

b)

no

158.

A REPEATING decimal is what type of number?

a)

Rational

b)

Irrational

159.

Is -5/8 a rational number?

a)

yes

b)

no

160.

The square root of 2 is an irrational number because...

a)

All square roots are irrational

b)

The answer is a decimal that never stops

c)

Two is an even number

d)

The answer is 1

161.

Pi

a)

Rational

b)

Irrational

162.

Irrational numbers...

a)

reduce to π

b)

never end and never repeat

c)

can sometimes be perfect squares

d)

must be negative

163.

-17.5

a)

Rational

b)

Irrational

164.

A repeating decimal is what type of number?

a)

Rational

b)

Irrational

165.

4.032

a)

Rational

b)

Irrational

166.

A decimal that stops is which type of number? Example: 2.75

a)

Rational

b)

Irrational

167.

$\frac{18}{3}$

a)

Rational

b)

Irrational

168.

$\frac{7}{13}$

a)

Rational

b)

Irrational

169.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

170.

includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

171.

.141414141414...

a)

Rational

b)

Irrational

172.

pi - 3.141592....

a)

Rational

b)

Irrational

173.

√2

a)

Rational

b)

Irrational

174.

√25

a)

Rational

b)

Irrational

175.

4π

a)

rational

b)

irrational

176.

√25

a)

Rational

b)

Irrational

177.

4π

a)

rational

b)

irrational

178.

-√4

a)

rational
irrational

b)

rational

179.

a)

D, C, A, B

b)

D, A, B, C

c)

D, B, C, A

d)

A, C, B, D

180.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

181.

a)

7 and 8

b)

8 and 9

c)

17 and 18

d)

35 and 36

182.

a)

M

b)

N

c)

O

d)

P

183.

a)

F

b)

G

c)

H

d)

J

184.

A fraction is which type of number?

a)

Rational

b)

Irrational

185.

A perfect square is which type of number?

a)

Rational

b)

Irrational

186.

A non-perfect square is which type of number?

a)

Rational

b)

Irrational

187.

Zero

a)

Rational, Integer

b)

Rational

c)

Rational, Integer, Whole

d)

Rational, Integer, Whole, Natural

188.

Choose the best definition of the term INTEGERS...

a)

Whole numbers

b)

Negative numbers

c)

Negative Numbers and Positive Numbers

d)

Positive whole #s and their opposites and zero

189.

Choose the best definition of the term WHOLE NUMBERS...

a)

Numbers that have holes in them (like 0, 4, 8, etc.)

b)

Any positive #s

c)

1 and then +1 after that (1, 2, 3, 4, 5, 6...)

d)

Zero and the positive numbers with decimals of with .0

190.

put √7 in the right blank

a)

__, 2.5, 2.63, 2.65

b)

2.5, __, 2.63, 2.65

c)

2.5, 2.63, __, 2.65

d)

2.5, 2.63, 2.65, __

191.

-17.5

a)

Rational

b)

Irrational

192.

√25

a)

Rational

b)

Irrational

193.

Is the following number rational or irrational? (π / 2)

a)

Rational

b)

Irrational

194.

Is the following number rational or irrational? 0.333...

a)

Rational

b)

Irrational

195.

Is the following number rational or irrational? -7341.2

a)

Rational

b)

Irrational

196.

4.032

a)

Rational

b)

Irrational

197.

5/2

a)

Rational

b)

Irrational

198.

√31

a)

Rational

b)

Irrational

199.

Which number is irrational?

a)

0.416

b)

-8/5

c)

∛64

d)

√27

200.

√81

a)

Rational

b)

Irrational

201.

√81

a)

Rational

b)

Irrational

Number Systems

Total questions: 201

Worksheet time: 5hrs 20mins

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