Free Printable Real Number System Review

1.

Define whole numbers:

a)

Whole numbers start from 1 and up (counting numbers).

b)

A whole number has no decimal or fractional part and starts with zero.

c)

All positive and negative integers, fractions and decimal numbers.

d)

Positive or negative, large or small, whole numbers, fractions or decimal numbers.

2.

Natural Numbers:

a)

Whole numbers from 1 and up (counting numbers)

b)

a number that cannot be expressed as a fraction (because the decimal goes on forever without repeating)

c)

Positive or negative, large or small, whole numbers, fractions or decimal numbers

d)

A number with no fractional or decimal part and starts with zero

3.

Integers are the set of (a) and their (b)

Choose from the below words

whole numbers

opposites

fractions

irrational

rational

4.

The number 1 is a:

a)

Whole number

b)

All of the above

c)

Integer

d)

Rational number

5.

.33333 is a: (a)

Choose from the below words

rational number

irrational number

integer

6.

$\frac{5}{7}$ is a/an:

a)

integer

b)

rational number

c)

whole number

d)

irrational number

7.

Match the following

a)

A number with no fractional or decimal part and starting with zero.

1.

Whole number

b)

Whole numbers from 1 and up (counting numbers)

2.

Natural number

c)

All whole numbers and their negative counterparts (opposites)

3.

Integer

d)

Positive or negative, large or small, whole numbers, fractions or decimal numbers/rational and irrational numbers

4.

Real number

e)

All positive and negative integers, fractions and decimal numbers.

5.

Rational number

8.

The square root of 5, represented as $\sqrt{5}=2.23606799775...$ , is an

(a) .

Choose from the below words

irrational number

rational number

imaginary number

Integer

9.

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

Choose from the below words

integer

rational

irrational

whole number

10.

Where does the number 45 go? (a)

Choose from the below words

All categories

whole number

rational number

integer

natural number

11.

Which of the following is an irrational number?

a)

0.333

b)

$\sqrt{8}$

c)

$\sqrt{49}$

d)

$\frac{5}{22}$

12.

Identify the rational numbers.

a)

$\sqrt{4}$

b)

$\pi$

c)

$3.5$

d)

$\sqrt{2}$

e)

$\frac{2}{3}$

13.

A rational number can be written as a fraction.

a)

true

b)

false

14.

A terminating decimal is a decimal that ______.

a)

never ends.

b)

repeats numbers in a pattern.

c)

ends.

d)

never ends and never repeats.

15.

0.181818181818181818......is

a)

Rational

b)

Irrational

c)

Terminating Decimal

d)

Repeating Decimal

16.

Is 3.74 a rational number?

a)

yes

b)

no

17.

A repeating decimal is what type of number?

a)

Rational

b)

Irrational

18.

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 and never repeats

c)

two is an even number

d)

the decimal never repeats

e)

the decimal never stops

19.

Which expressions represent irrational numbers?

a)

$\sqrt{50}$

b)

$\left(\sqrt{36}\right)\ \left(\frac{1}{2}\right)^4$

c)

$\left(\sqrt{169}\right)+\left(\sqrt{16}\right)$

d)

$\left(\sqrt{225}\right)^3$

e)

$\left(4\right)\ \left(\sqrt{0.25}\right)^2$

20.

Which of the following is an irrational number?

a)

$\sqrt{0}$

b)

$\sqrt{3}$

c)

$1\overline{.36}$

d)

$-0.19$

21.

Is $\frac{77}{3}$ rational or irrational?

a)

Rational

b)

Irrational

22.

Is $.\overline{11}$ rational or irrational?

a)

Rational

b)

Irrational

23.

Is $-\sqrt{64}$ rational or irrational?

a)

Rational

b)

Irrational

24.

Is $\sqrt{40}$ rational or irrational?

a)

Rational

b)

Irrational

25.

Is $17.33$ rational or irrational?

a)

Rational

b)

Irrational

26.

Is $-7341.2$ rational or irrational?

a)

Rational

b)

Irrational

27.

Select the only RATIONAL number:

a)

$\sqrt{2}$

b)

$\frac{\pi}{4}$

c)

$\pi$

d)

$\sqrt{49}$

28.

Select the ONLY irrational number:

a)

$\frac{152}{6}$

b)

$.149203827...$

c)

$3\times\sqrt{4}$

d)

$-.747474747474...$

29.

Is $-2\pi$ rational or irrational?

a)

Rational

b)

Irrational

30.

$\frac{1}{3}\ \cdot\ \sqrt{2}$

a)

rational number

b)

Irrational Number

31.

Is $\left(\sqrt{2}\right)^2$ rational or irrational? (Hint: Simplify before choosing!)

a)

Rational

b)

Irrational

32.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

33.

A fraction is which type of number?

a)

Rational

b)

Irrational

34.

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

35.

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

36.

The √40 is between which two integers?

a)

7 & 8

b)

6 & 7

c)

5 & 6

d)

4 & 5

37.

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

a)

irrational

b)

prime

c)

rational

d)

imaginary

38.

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

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

imaginary number

39.

Which statement about the square root of 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.

40.

Which decimal appears to be a rational number?

a)

2.14285714285714...

b)

3.14159265358979...

c)

4.79583152331272...

d)

5.56776436283002...

41.

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

a)

point A

b)

point B

c)

point C

d)

point D

42.

What number system does √7 belong to?

a)

Rational

b)

Irrational

c)

Whole

d)

Integer

43.

Includes integers, fractions, terminating, and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

44.

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

a)

Fake

b)

Non Real

c)

Real

d)

Cool

45.

A non-perfect square is which type of number?

a)

Rational

b)

Irrational

46.

The square root of 57 is ...

a)

rational

b)

irrational

47.

Which numbers below are rational?

a)

6.3589

b)

$\sqrt{26}$

c)

$\sqrt{81}$

d)

$\frac{11}{2}$

e)

7

48.

Which numbers below are irrational? (dots in this case do not mean repeating)

a)

$\pi$

b)

6 + $\sqrt{30}$

c)

$0.123456.......$

d)

$\sqrt{32}$

e)

- $\sqrt{121}$

49.

Ms. Finn wants to find the side length of a square that has an area of 150 feet. Should her answer be rational or irrational?

a)

Rational because $150\ \div\ 2$ is 75, and 75 can be written as a decimal

b)

Rational because 150 is a whole number so it can be written as a decimal.

c)

Irrational because $\sqrt{150}$ is not a perfect square

d)

Irrational because $150\ \div4$ is 37.5 which can't be written as a fraction.

50.

Which of the following is an example of an irrational number between 6 and 7?

a)

$2\pi$

b)

6.875

c)

6.12345....

51.

The square roots of perfect squares will never be irrational numbers.

(a)

52.

Repeating decimals will (sometimes, always, never) be rational numbers

(a)

53.

Irrational Numbers will (always, sometimes, never) be able to be written as fractions

(a)

54.

Repeating decimals will (sometimes, always, never) be rational numbers

(a)

55.

Irrational Numbers will (always, sometimes, never) be able to be written as fractions

(a)

56.

Which number is a rational number?

a)

1/4

b)

π

c)

√3

57.

Is the following number rational or irrational?

77/3

a)

Rational

b)

Irrational

58.

Order from least to greatest.

a)

$\sqrt[]{2}$

b)

$\pi$

c)

$3\frac{7}{8}$

d)

$\frac{32}{8}$

1)

2)

3)

4)

59.

The decimal, 0.12568934... is:

a)

Rational

b)

Irrational

60.

$\frac{15}{3}$

a)

irrational

b)

rational

c)

integer

d)

whole number

e)

natural number

61.

6.313131313

a)

irrational

b)

rational

c)

integer

d)

whole number

e)

natural number

62.

$\frac{1}{3}$

a)

irrational

b)

rational

c)

integer

d)

whole number

e)

natural number

63.

Square roots of perfect squares are always _____ numbers.

a)

irrational

b)

rational

64.

Square roots of non - perfect squares are always _____ numbers.

a)

irrational

b)

rational

65.

includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

66.

Irrational Numbers....

a)

cannot be represented as a simple fraction

b)

can be represented as a fraction

c)

can be a repeating decimal

67.

A perfect square is which type of number?

a)

Rational

b)

Irrational

68.

Which number has a square root that is between 7 and 8?

a)

48

b)

81

c)

60

d)

36

69.

Between which two whole numbers does the √115 fall?

a)

9 and 10

b)

10 and 11

c)

9 and 11

d)

11 and 12

70.

Classify $-3.254$

a)

Rational

b)

Irrational

71.

A fraction is which type of number?

a)

Rational

b)

Irrational

72.

√31

a)

Rational

b)

Irrational

73.

4.032

a)

Rational

b)

Irrational

74.

Which number is a rational number?

a)

2.25

b)

-8.78654684598.....

c)

Square root of 99

d)

3.14...

75.

A never ending decimal is which type of number?

a)

Rational

b)

Irrational

76.

$\frac{19}{21335}$ is

a)

Rational

b)

Irrational

77.

$3.567567567567567567567...$ is

a)

Rational

b)

Irrational

78.

$-14.3467498884384575993874...$ is

a)

Rational

b)

Irrational

79.

0.8 is a rational number

a)

True

b)

False

80.

A perfect square is which type of number?

a)

Rational

b)

Irrational

81.

A whole number is which type of number?

a)

Rational

b)

Irrational

82.

What number is a whole number but not at natural number?

a)

-1

b)

0

c)

1

d)

1.1

e)

$\sqrt[]{-1}$

83.

Convert 0.25 to a fraction in simplest form.

a)

$\frac{1}{4}$

b)

$\frac{25}{100}$

c)

$\frac{5}{20}$

d)

$\frac{2}{5}$

84.

Which number is between 7 and 8?

a)

√7

b)

√42

c)

√59

d)

√68

85.

$\sqrt{\frac{2}{3}}$

a)

Rational

b)

Irrational

86.

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

a)

Rational

b)

Irrational

87.

$-6,\ 0.\overline{5}\ ,\ and\ 3.75$ are ALL examples of rational numbers

a)

True

b)

False

88.

What is the answer to the problem in the picture?

a)

3/4

b)

4/5

c)

5/6

d)

6/7

89.

What is the fractional equivalent to 0.33333333333333...?

a)

2/3

b)

1/6

c)

1/3

d)

1/2

90.

What is the decimal equivalent to 2/3

a)

0.33333...

b)

2.333333333...

c)

2.3

d)

0.66666...

Real Number System Review

Total questions: 90

Worksheet time: 2hrs 11mins

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