Sets and Subsets of the Real Number System

​Additional Learning Resources

​https://youtu.be/vPA-kC-U1s4

Multiple Choice

Classify the subset of real numbers to which each number belongs.

12

• Integer, Natural

• Rational, Integer, Whole, Natural

• Integer

• Irrational, Whole

Multiple Choice

Classify the subset of real numbers to which each number belongs.

√2

• Integer, Natural

• Rational, Integer, Whole, Natural

• Integer

• Irrational

Multiple Choice

Classify the subset of real numbers to which each number belongs.

$$\frac{1}{3}$$  

• Rational

• Rational, Integer, Whole, Natural

• Integer

• Irrational, Whole

Multiple Choice

Which statement is NOT true?

• Every counting number is a whole number.

• Every integer is a rational number.

• Every decimal is an irrational number.

• Every natural number is a real number.

Multiple Choice

Which statement is true?

• The set of real numbers is a subset of rational numbers

• The set of decimal numbers are subset of irrational numbers.

• The set of whole numbers is subset of rational numbers.

• The set of irrational numbers are subset of rational numbers.

Multiple Choice

Which number is the smallest?

• 2.5

• 0.33…

• √9

• -3

Multiple Choice

Which number is the greatest?

• 2.5

• 0.33…

• √9

• -3

Multiple Choice

Which is in order from least to greatest?

• √25, 4.20, $$\frac{1}{3}$$   , -0.66…, -7

• -7, -0.66…, $$\frac{1}{3}$$ , 4.20, √25

• -0.66…, $$\frac{1}{3}$$  , -7, 4.20, √25

• √25, -0.66, 4.20, -7, $$\frac{1}{3}$$  

Multiple Choice

Which list shows the numbers in decreasing order?

• √25, 4.20, $$\frac{1}{3}$$   , -0.66…, -7

• -7, -0.66…, $$\frac{1}{3}$$ , 4.20, √25

• -0.66…, $$\frac{1}{3}$$  , -7, 4.20, √25

• √25, -0.66, 4.20, -7, $$\frac{1}{3}$$  

Multiple Choice

Which of the following best represents the arrangement of -2.25, -1,  $$\frac{1}{2}$$   , 1.75  on the number line?

​WHAT'S IN

​In this part of the lesson, your previous knowledge about Rational and Irrational numbers will be checked. Your learnings about these two concepts will equip you to the lesson, Subsets of Real Numbers.

Multiple Select

Classify the real numbers to which subset/s of real number belongs.

-3

• Whole Number

• Integer

• Rational

• Irrational

Multiple Select

Classify the real numbers to which subset/s of real number belongs.

0

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

Classify the real numbers to which subset/s of real number belongs.

$$\frac{4}{3}$$  

• Whole Number

• Integer

• Rational

• Irrational

Multiple Select

Classify the real numbers to which subset/s of real number belongs.

$$\sqrt[]{64}$$  

• Whole Number

• Integer

• Rational

• Irrational

Multiple Select

Classify the real numbers to which subset/s of real number belongs.

13

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

Classify the real numbers to which subset/s of real number belongs.

-0.125

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

Classify the real numbers to which subset/s of real number belongs.

$$\sqrt[]{2}$$  

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

Classify the real numbers to which subset/s of real number belongs.

$$\epsilon$$  

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

Classify the real numbers to which subset/s of real number belongs.

0.50 

• Whole Number

• Integer

• Rational

• Irrational

Multiple Choice

_____is a subset of real numbers that can be positive, negative or zero.

• Counting

• Integers

• Irrational

• Rational

• Whole

Multiple Choice

Counting numbers and zero are called _____ numbers.

• Counting

• Integers

• Irrational

• Rational

• Whole

Multiple Choice

The set of _____ numbers are numbers that cannot be expressed as a fraction.

• Counting

• Integers

• Irrational

• Rational

• Whole

Multiple Choice

Natural numbers are also called _____ numbers.

• Counting

• Integers

• Irrational

• Rational

• Whole

Multiple Choice

The subset of _____ numbers includes Integers, Whole and Counting Numbers.

• Counting

• Integers

• Irrational

• Rational

• Whole

Multiple Choice

All rational numbers are real numbers.

• True

• False

Multiple Choice

An irrational number is always a real number.

• True

• False

Multiple Choice

Every whole number is an integer.

• True

• False

Multiple Choice

Every decimal number is a rational number.

• True

• False

Multiple Choice

All real numbers are integers.

• True

• False

Multiple Choice

$$\frac{1}{5}$$   is an irrational number.

• True

• False

Multiple Choice

Zero is an integer.

• True

• False

Multiple Choice

All natural numbers are sometimes positive.

• True

• False

Multiple Choice

All repeating decimals are irrational numbers.

• True

• False

Multiple Choice

There are no natural numbers between -5 and 0.

• True

• False

Fill in the Blank

Compare the following real numbers. Write >, < or = in the blanks.

$$\frac{7}{3}$$  _____ $$\frac{9}{2}$$  

Fill in the Blank

Compare the following real numbers. Write >, < or = in the blanks.

$$-1.54$$  _____ $$-\frac{5}{2}$$  

Fill in the Blank

Compare the following real numbers. Write >, < or = in the blanks.

$$-1.54$$  _____ $$-\frac{5}{2}$$  

Fill in the Blank

Compare the following real numbers. Write >, < or = in the blanks.

$$0.33...$$  _____ $$\frac{3}{9}$$  

Fill in the Blank

Compare the following real numbers. Write >, < or = in the blanks.

$$-\frac{11}{5}$$  _____ $$2.2$$  

Multiple Choice

Name the subset(s) of numbers to which each number belongs.

$$\sqrt[]{7}$$  

• Irrational

• Rattional

• Whole

• Integer

Multiple Choice

Name the subset(s) of numbers to which each number belongs.

-16.28

• Irrational

• Rattional

• Whole

• Integer

Multiple Select

Name the subset(s) of numbers to which each number belongs.

$$\sqrt[]{81}$$  

• Irrational

• Rattional

• Whole

• Integer

• Counting

Multiple Select

Name the subset(s) of numbers to which each number belongs.

$$-9$$  

• Irrational

• Rattional

• Whole

• Integer

Multiple Choice

Name the subset(s) of numbers to which each number belongs.

$$\frac{6}{17}$$  

• Irrational

• Rational

• Whole

• Integer

Multiple Choice

All whole numbers are integers.

• TRUE

• FALSE

Multiple Choice

Some fractions are irrational numbers.

• TRUE

• FALSE

Multiple Choice

Every rational number is a decimal.

• TRUE

• FALSE

Multiple Choice

Zero is a counting number.

• TRUE

• FALSE

Multiple Choice

Set A = {0, 1, 2, 3, 4, …} is the set of whole numbers.

• TRUE

• FALSE

Multiple Choice

Which number is the smallest?

• $$\frac{25}{6}$$  

• $$-5$$

• $$\sqrt[]{25}$$

• $$4.16$$

Multiple Choice

Which number is the greatest?

• $$\frac{25}{6}$$  

• $$-5$$

• $$\sqrt[]{25}$$

• $$4.16$$

Multiple Choice

Which is in order from least to greatest?

• $$\sqrt[]{4},\ 2.33...,\ 0,\ -2,\ \frac{7}{4}$$  

• $$2.33...,\sqrt[]{4},\ \frac{7}{4},\ 0,\ -2,\ \frac{7}{4}\$$  

• $$-2,\ 0,\ \frac{7}{4},\ \sqrt[]{4},\ 2.33...$$

• $$\sqrt[]{4},\ 0,\ 2.33...,\ -2$$

Multiple Choice

Which list shows the numbers in decreasing order?

• $$2.33...,\ \sqrt[]{4},\ \frac{7}{4},\ 0,\ -2$$  

• $$\sqrt[]{4},\ 2.33...,\ 0,\ -2,\ \frac{7}{4}$$  

• $$-2,\ 0,\ \frac{7}{4},\ \sqrt[]{4},\ 2.33...$$

• $$\sqrt[]{4},\ 0,\ 2.33...,\ -2$$

Multiple Choice

Which of the following best represents the arrangement of -2.5, √9, -1, $$\frac{1}{2}$$  on the number line?