# Types of numbers

## Audio-visual

# Understanding

Numbers

## Types of numbers

## Nominal Numbers

Nominal - is a word used to describe the name of the number. "Nominal" simply means"name"! In simplest terms it **is** the number! Knowing both the face and place values helps us read and say the names of numbers.

If numbers were people they could use **nominal numbers** to have a conversation, perhaps like this...

"Hi. My name is seven. What's yours?" "Hi. Nice to meet you. My name is ninety four."

## Cardinal Numbers

Cardinal numbers = counting numbers.

What do they do? They help us to describe **how many.**

What are they? Cardinal numbers only include whole numbers, not parts of numbers such as decimals and fractions.

**NOTE:** Knowing both the face and place values of numbers helps us read, say and count (cardinal) numbers.

**EXAMPLES OF CARDINAL NUMBERS**

1 = One

2 = Two

3 = Three

423 = Four hundred and twenty three

**This of course, can continue forever!**

PRACTICAL EXAMPLE OF USING CARDINAL NUMBERS

Eg. I have lost four iPhones this year!

If you would like more information on more nominal numbers, simply **click here!**

## Ordinal Numbers

Ordinal Numbers = ordered numbers.

**What are they?** An ordinal number refers to the numerical order, sequence or position of something.

It would be useful for us to understand this word better if it was spelled "Ordernal" - but it isn't!

It does mean exactly the same thing though. Order means **sequence** and **position**.

**How do ordinal numbers differ from Cardinal?**

As you learnt last slide, Cardinal numbers refer to howmany of something. Ordinal refer to the position of something when it is in a seguence.

**PRACTICAL EXAMPLES OF ORDINAL NUMBERS**

"Robert came **first** (1st) in the running race."

"I am the **second** (2nd) son in my family."

"Your ticket at the concert is for the (3rd) **third** row and the (11th) **eleventh** seat.

"The **seventh** (7th) Prime Minister of Australia was Billy Hughes."

## Cardinal And Ordinal Numbers

lf you would like more information by video, simply **click here.**

lf you would like more information, simply **click here.**

## Positive Numbers

Positive Numbers = these are any number greater than zero (0). Therefore any number which is greater or bigger than zero is called a positive number

Positive numbers **can** include fractions and decimal numbers.

**How do positive numbers appear on a number line?**

We often use a basic number line to understand the interaction between positive numbers and negative numbers. Below is a number line that will assist you to understand positive numbers in a graphical sense.

**Understanding number signs**- Positive numbers may have a sign (+) and can be shown as such **+4,or**+5 etc If there is **no symbol** then it is automatically a positive number e.g. 5 is the same as +5

## Negative Numbers

Negative Numbers = all numbers that are less than zero (0).

Another way to say this is: a negative number is any number smaller than zero(0).

Negative numbers can also include fractions and decimal numbers.

**How do negative numbers appear on a number line?**

Similar to the number line you saw in the last slide, below is a number line that will assist you to understand negative numbers in a graphical sense.

**Understanding number signs** Negative numbers are written with a negative sign before them. For example negative five is written as **-5**. The dash before the five indicates that it is negative.

*If you would like more information on NEGATIVE NUMBERS simply click on these resources: resource 1, resource 2.*

## Whole Numbers And Integers

Whole Numbers = A whole number is any complete (whole) number above zero such as 1,2,3,4,5 and so on.

Whole numbers **can only be positive**, and they cannot be a **fraction or decimal**...

lntegers = Complete numbers [not fraction or decimal] which **can be positive, negative, or zero!** This is the difference between whole numbers and integers, an integer is any complete number, whereas a whole number must be above zero.

**EXAMPLES OF INTEGERS**

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Negative IntegersPositive Integers

## Examples Of Integers

Integers

We see and use positive and negative integers in our environment all the time. Below are some examples.

The weather report

It was minus 5 degrees today in Japan!

A bank account

I have negative $125 in my bank account!

Sales report

Today we sold 25 more than usual.

## Rational Numbers

**A Rational Number is any number that can be written as a fraction and is finite (fixed and not on going). Possibilities include the following:**

1) Positive and negative integers. All integers can also be written as a fraction by placing the integer itself over (the number) one.

Examples: Positive integers written as fractions

7 = ^{7}/_{1}5 = ^{5}/_{1}9 = ^{9}/_{1}

**AND**

Negative integers written as fractions

-7 = - ^{7}/_{1}-5 = - ^{5}/_{1}-9 = - ^{9}/_{1}

2) Fixed quantity or an exact amount, even if a fraction or decimal.

e.g.

^{1}/_{3 } 0.142857142857^{3}/_{4 } 0.75^{6}/_{8 } 0.75

## Irrational Numbers

**Irrational Numbers include any number that is not Rational!**

Irrational numbers include numbers that are **not a fixed quantity/amount** and cannot be expressed exactly as a common fraction.

Irrational numbers cannot be represented as ratios or proportions (rational numbers can be) because this would be impossible.

**How to identify irrational numbers?** lrrational Numbers never end such as: **non recurring decimal numbers.** For example:

**Pi** = 3.141592... (the numbers in the decimal places keep going forever, in ever increasing accuracy). Click to see how **pie goes on indefinitely.**

**MORE INFORMATION & ACTIVITIES**

## Factors & Multiples

Factors are numbers that "go into" (can be divided into) a number exactly. This means they have no part remaining or left over when shared into a number.

Example: The integer 5 divides exactly into the larger integer 15, so we can say that:

5 is a factor of 15.

First Way: one way we can check this is to **count up** by 5. If we count by "lots of" 5 then we will land on 15, exactly. (3 lots of 5 = 15)

5plus 5 more10plus 5 more15

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Second Way: another way to find factors of a number is to share the larger number by lots of a smaller numbers (**divideit**). If the answer is a whole number with no left over, remainder or decimal, then you have found another factor!

**For example: 15 + 5 = 3 **-> you can see here there is no decimal left over. The answer is a whole 3.

Second Way: another way to find factors of a number is to share the larger number by lots of a smaller numbers (**divide it**). If the answer is a whole number with no left over, remainder or decimal, then you have found another factor!

**For example: 15 + 5 = 3 **-> you can see here there is no decimal left over. The answer is a whole 3.

## Factors (cont)

**Example: what are the factors of 6?**

Try this activity.

a) Can 6 be divided by one? Count along line by 1 **YES!**

b) Can 6 be divided by two? Count along line by 2 **YES!**

c) Can 6 be divided by three? Count along line by 3 **YES!**

d) Can 6 be divided by six? Count along line by 6 **YES!**

The numbers **1, 2, 3, 6** all 'land on' 6 so **are all factors** of 6.

**Question** - "Is the integer 4 a factor of 6?" WHY?

**NO!**

*Because 6 is not divisible by 4 exactly.*

## Factors (cont)

So, the "factors of the number 12 are (**1,2,3,4,6,and 12**)."

The number **one will always be a factor** of ALL whole numbers.

The number itself (in this case 12) will always go into itself so will always be a factor.

Therefore any number will always have at least one and the number itself as factors!

## Multiples

A **multiple** is the number any factor will "go into".

**Example:**

**The factors of 15 are 1,3,5, and 15.**

**Therefore we can say that: 15 is a multiple of 1, 3, 5, and 15.**

**Q. Is 28 a multiple of 7?**

When we multiply a factor of any number by another factor of the same number and we get a multiple, **i.e. factor x factor = multiple.**

**Example:** e.g. 7 and 4 are factors of 28. ** Yes, 28 is a multiple of 7.**

So, factor x factor 7 x 4 = 28 (the multiple)

**Q. Is 28 a multiple of 4?**** Yes, 28 is a multiple of 4.**

**Q. What are the multiples of 7?**** The multiples of 7 are 7,14,21,28.35...**

## Prime Numbers

Prime Number : A prime number has only two factors, the number one (1) and the number itself....and no more.

**Example:**

1. The integer 7 is a prime number as it only has the two factors, 1 and 7.

2. The only factors of 5 = 1 and 5, **is 5 a prime number?**

3. **Is 11 a prime number? What factors does 11 have?**

## Composite Numbers

Composite numbers:These numbers are called **COMPOSITE numbers = have more than two factors**. These are the opposite to prime numbers from the last slide.

**Example:**

1. The integer 9. Is 9 a composite number? What are its factors?

**Factor of 9:**

2. The only factors of 5 = 1 and 5, **is 5 a prime number?**

**Factor of 12:**

Nine is NOT a prime number because it has factor(s) other than one (1) and itself (9), It also has integer three (3) as a factor.**Therefore 9 is a composite number. **

Twelve has more than 1 and 12 as factors. It also has 3,4, and 6 as factors. This makes 12 a composite number.**Therefore 12 is a composite number. **

## Square Numbers

Square numbers: If represented as objects e.g. dots on a page, can be placed into a square shape, with equal sides (x4) and equal number of rows and columns.

The integer nine **(9)** as shown above **IS a square number** because we can represent it as a square shape.

Here are many square numbers. Can you think of some other square numbers?

Here are some....

4 , 9, 16 , 25

TIP: when we multiply a number by it self, we get a square number.

Lets take a look on the next slide.

4 , 9, 16 , 25

## Square Numbers (cont)

Multiply a number by itself to get a **square number.**

a) 2 x 2 = 4b) 3 x 3 = 9c) 4 x 4 = 16d) 10 x 10 = 100

What are the square numbers up to 100?

## Triangular Numbers

Triangular numbers: These can be represented in the shape of a triangle.

**Example:**

1. Is three (3) a triangular number?

le. Will three dots fit triangularly here?

2. Is six (6) a triangular number?

le. Will six dots fit triangularly here?

## Triangular Numbers (cont)

Triangular numbers can be explored a little further.

Count the numbers of smiles on each row below and **see if you can find a pattern**, [tip: be sure to try to figure it out before clicking to reveal].

Now try to use what you know about the pattern to predict the next triangular number! Can you predict it?

## End Topic

CONGRATULATIONS ON COMPLETING THE TYPES OF

NUMBERS TOPIC.

This topic has covered the following items:

follow the link to view the pdf version of topic 1.3.

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