LESSON - Classification of Numbers

The Real Number System

A Full Online Class

Why classification of numbers?

Classification of Numbers

By Mar Syazana

Multiple Choice

Is 36 a natural number?

• Yes

• No

Multiple Choice

True or false.

The number 7 is a natural number.

• True

• False

Multiple Choice

What is the difference between the whole number group and the natural number group

• Whole numbers are more organized

• Whole numbers start with 1 and Natural numbers start with 0

• Whole numbers start with 0 and Natural numbers start with 1

• They are both the same

Multiple Choice

How would you classify the number 0?

• Whole Number

• Natural Number

• Irrational Number

Natural & Whole Numbers Review

​The numbers we use for counting are the natural numbers: 1, 2, 3, 4, 5, and so on

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​The set of whole numbers is the set of natural numbers plus zero: {0, 1, 2, 3,…}

Open Ended

Explain the difference between a Whole Number and a Natural Number.

​Integers Review

​The integers include all whole numbers together with the “negatives” of the natural numbers.

Multiple Choice

Integers include _____.

• Only negative numbers

• Only positive numbers

• Fractions and decimals

• Both negative/ positive numbers and 0

Multiple Choice

How would you classify -4?

• Whole Number

• Integer

• Natural Number

Multiple Choice

which statement is true?

• all natural numbers are whole numbers

• all whole numbers are integers

• all natural and whole numbers are integer

• all natural numbers are integers

• ALL of the above

Let's summarize

Natural Numbers: Also called the counting numbers, this set includes all of the whole numbers except zero (1,

2, 3, ....)

Whole Numbers: Zero and the positive integers are the whole numbers.

Integers: The counting numbers (1, 2, 3, ...), their opposites ( 1, 2, 3, ...), and zero are integers.
A common error for students is to assume that the integers account for all (or only) negative numbers.

DMA5101

Multiple Choice

Is the fraction 4/5 a natural number?

• Yes

• No

Multiple Choice

$$\frac{2}{3}$$  is an integer.

• True

• False

Multiple Choice

How would you classify  $$\frac{5}{9}$$  ?

• Integer

• Rational Number

• Whole Number

• Irrational Number

Multiple Choice

Natural numbers, Whole numbers, and Integers are RATIONAL numbers because they can be written in fraction form. True or False?

• True

• False

Multiple Choice

What is the best classification for this number? (how far down can you push this into the Venn Diagram)

1/4

• integer

• rational

• none of these

• whole

Multiple Choice

$$0.463$$  is an irrational number.

• True

• False

Multiple Choice

A terminating decimal is a decimal that...

• never ends.

• repeats numbers in a pattern.

• ends.

• never ends and never repeats.

Multiple Choice

What is the best classification for this number? (how far down can you push this into the Venn Diagram)

10

• none of these

• whole

• integer

• rational

Multiple Choice

Is 8.27 rational or irrational?

• Rational

• Irrational

• Both

• None of the above

Multiple Choice

A repeating decimal is what type of number?

• Rational

• Irrational

Multiple Choice

$$0.\overline{3}$$ is what type of number

• rational

• irrational

• integer

Multiple Choice

Explain the error

• -1.2 isn't an integer.
• -2 isn't a whole number and 3.4 isn't a rational number.
• -2 isn't a whole number and -1.2 isn't an integer.
• The numbers are graphed correctly.

​What do you notice about rational vs irrational?

Multiple Choice

How would you classify $$\sqrt[]{8}$$  ?

• Whole Number

• Rational Number

• Integer

• Irrational Number

Multiple Choice

Which of the following numbers is an Irrational Number?

• 7.24

• -10

• 435,530

• 3.1415926535897932384...

• $$\frac{4}{9}$$

Multiple Choice

$$\pi$$ is what type of number

• rational

• irrational

• integer

Real Number System Intervention

Multiple Choice

Which diagram correctly displays the relationship between set of numbers?

Multiple Choice

The letter "A" can be replaced with with subset?

• Rational

• Irrational

• Integer

• Whole

• Natural

Multiple Choice

Which lists the correct labels for the diagram shown?

Fill in the Blanks

Draw

Place the following numbers in the Venn Diagram: $$4,0,-2,\frac{2}{3},\ 0.23,\ 0.\overline{67},\ \sqrt[]{3}$$

Poll

How comfortable are you with classifying real numbers?

• Very comfortable

• Comfortable

• I'm okay, but not really sure

• I have no idea how to classify

End of lesson

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