Free Printable Real Number System

1.

Integers can be negative, but whole numbers must be positive.

a)

True

b)

False

2.

Which subset contains decimals that can repeat?

a)

Irrational

b)

Rational

c)

Integer

d)

Natural

3.

Integers do not contain decimals or fractions, but rational numbers do.

a)

True

b)

False

4.

Natural numbers and whole numbers are the same set of numbers, except zero which is a whole number.

a)

True

b)

False

5.

$-\frac{48}{3}$ Identify all the subsets to which this value belongs.

a)

Rational, Integer, Whole

b)

Real, Irrational

c)

Real, Rational, Integer

d)

Real, Rational, Integer, Natural

6.

Which of the following values are members of the integer subset of real numbers:

15\ \ \ \ \ \ \ 0\ \ \ \ \ -4.86\ \ \ \frac{\ 27}{-3}\ \ \ \ \ \frac{12}{\sqrt{64}}\ \ \ -\sqrt{361}

a)

Only 15 and 0

b)

All except $\frac{12}{\sqrt{64}}\ and\ -4.86$

c)

All of them

d)

None of them

7.

From top to bottom, find the list with the subsets listed in the correct order. It must also list the correct subgroup for the circle on the right.

a)

Left (T to B): Irrational, Integer, Whole, Natural Right: Rational

b)

Left (T to B): Irrational, Integer, Natural, Whole Right: Rational

c)

Left ()T to B: Rational, Integer, Natural, Whole Right: Irrational

d)

Left (T to B): Rational, Integer, Whole, Natural Right: Irrational

8.

$0.33\overline{3}\ or\ \frac{1}{3}$

Which statement is true about this number?

a)

It is a repeating decimal, so it is a rational number.

b)

It is a terminating decimal, so it is a rational number.

c)

It is a repeating decimal, so it is an irrational number.

d)

It is a terminating decimal, so it is an irrational number.

9.

Choose the set of rational numbers.

a)

$\sqrt{12},\ -\sqrt{87},\ \pi,\ 4.285....$

b)

$.21953,\ 0,\ -4\ \frac{2}{3},\ 4.1313\overline{13}$

c)

$0,\ .21953,\ -4\ \frac{2}{3},\ \sqrt{10}$

d)

$0,\ \sqrt{12},\ -\sqrt{87}$

10.

Choose the set of irrational numbers.

a)

$\sqrt{12},\ -\sqrt{87},\ \pi,\ 4.285....$

b)

$.21953,\ 0,\ -4\ \frac{2}{3},\ 4.1313\overline{13}$

c)

$0,\ .21953,\ -4\ \frac{2}{3}$

d)

$\pi,\ \sqrt{12},\ -\sqrt{87}$

11.

Choose the definition for the subgroup Natural Numbers.

a)

The set of whole numbers and their opposites.

b)

The set of counting numbers and zero.

c)

The set of all non-repeating and non-terminating decimals.

d)

The set of counting numbers.

12.

Choose the definition for the subgroup Whole Numbers.

a)

The set of whole numbers and their opposites.

b)

The set of counting numbers and zero.

c)

The set of all non-repeating and non-terminating decimals.

d)

The set of counting numbers.

13.

Choose the definition for the subgroup Integers.

a)

The set of whole numbers and their opposites.

b)

The set of counting numbers and zero.

c)

The set of all non-repeating and non-terminating decimals.

d)

The set of counting numbers.

14.

Choose the definition for the subgroup Rational Numbers.

a)

The set of whole numbers and their opposites.

b)

The set of counting numbers and zero.

c)

The set of all non-repeating and non-terminating decimals.

d)

The set of all numbers that can be expressed as fractions.

15.

Choose the definition for the subgroup Irrational Numbers.

a)

The set of whole numbers and their opposites.

b)

The set of counting numbers and zero.

c)

The set of all non-repeating and non-terminating decimals.

d)

The set of all numbers that can be expressed as fractions.

16.

Identify which statement is false.

a)

The product of two rational numbers is rational.

b)

The sum of a rational number and an irrational number is irrational.

c)

The sum of a rational number and an irrational number is rational.

d)

The product of non-zero rational number and an irrational number is irrational.

17.

$\sqrt{81},\ 27,\ 4.\overline{6},\ \sqrt{11}$

Which Venn diagram best represents this set of numbers?

a)

b)

c)

d)

18.

Which of the following can be defined as an integer, but not a whole number?

a)

A. $-\ \frac{1}{3}$

b)

B. $-\sqrt{20}$

c)

C. $-\ \frac{20}{5}$

d)

D. $-13.1$

19.

The number 3.7 is best described as -

a)

A. a rational number

b)

B. an integer

c)

C. a whole number

d)

D. an irrational number

20.

Which of these is a rational number?

a)

$\sqrt{2}$

b)

$0.414114...$

c)

$\sqrt{5}$

d)

$-6.060606$

Real Number System

Total questions: 20

Worksheet time: 3hrs 0mins

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