# The decimal number system and place value (decimal numbers)

## Audio-visual

# Understanding

Numbers

## The Decimal Number System and

Place Value (Whole Numbers)

For Whole Numbers

## The Place Value System

For Whole Numbers

The Decimal System for whole numbers is based on Place Values.

Place value **increase** 10 times as each place moves to the **left**.

Place value **decreases** by 1/10 each time a place moves to the **right**.

Numbers Less Than One

## Place Value System For Decimal

Numbers Less Than One

**What happens to place value for decimal numbers?**

Exactly the same system applies for numbers which are less than one (Decimal Numbers).

For Whole Numbers

## Place Value

Let's now look at how the numeral 8 can change its value by being in a different "PLACE" in our Decimal Place Value System.

Consider the last row in thet able above(highlighted in green).

This shows which will show the different values of an 8 in three different places (80,8/10 and 8/1 000)

• An 8 digit in the 2nd Place has a value of 80 ( 8 tens).

• However an 8 in the 1st Decimal Place gives a value of 8 tenths or 8/10

• And an 8 in the 3rd Decimal Place gives a value of 8 thousandths or alternatively 8/1000

• Together these three "8s" together give a number with a total value of 80.808 (eighty point eight zero eight)

Numbers Less Than One

To Create Numbers

**0**

**0**

## Using The Decimal System

To Create Numbers

The value (or size) of the number in the example in the bottom row of the table

is written as 9 573.842 (nine thousand, five hundred and seventy three point eight four two).

Decimal numbers that contain no whole numbers always start with a zero. Eg. 0.4 (zero point four) or 0.572 (zero point five seven two).

Now go to the **Activity 1** and have a go at creating some numbers yourself, remembering to separate the numbers into groups of three.

## Expanded Notation

"Expanded Notation" is simply a way of writing a number by adding

together the value of each digit

Example 1: 7 392 = 7 000 + 300 + 90 + 2

Example 2: 436.58 = 400 + 30 + 6 + 5/10 + 8/10

If we look at Example2 again, these values can then be further expanded to include the place value of each digit:

Example 2: 436.58= 400 + 30 + 6 + 5/10 + 8/100

= (4 x 100) + (3 x 10) + (6 x 1) + (5 x 1/10) + (8 x 1/100)

To Create Numbers

If we look at Example2 again, these values can then be further expanded to include the place value of each digit:

Example 2: 436.58= 400 + 30 + 6 + 5/10 + 8/100

= (4 x 100)

+ (3 x 10)

+ (6 x 1)

+ (5 x 1/10)

+ (8 x 1/100)

## Expanded Notation

**Summary of what we have learnt:**

- By analysing numbers this way we can get a good understanding of place value and an appreciation of how place value works using decimal numbers in our Decimal Number System.

**Video Explanation:**

- Now head to this video to consolidate your learning with this video:
**click here**.

Now have a go at **Activity 2** to practise analysing some bigger numbers according to their place value. Correct your answers using the **marking key**.

## Reading Decimal Numbers

Consider this number:

537 894 230.814 926

It may be difficult to read because the place values of the first numbers are not apparent by just looking at it.

It is easier to read if we identify each of the groups of three digits.

537 894 230.814 926

## Reading Decimal Numbers

**Summary of what we have learnt:**

- In the previous slide you have learnt how to break down a large number by looking at the place value of each figure.
- You also saw how the different groups can assist you in breaking down a figure. These groups were denoted by colour on the previous slide.

Now have a go at **Activity 3** to practise reading and writing some of these larger decimal numbers.

Use the **Marking Key** to check your answers.

Now that you have completed Topic One about how

our Decimal number system works, test your

understanding of the Topic by: completing the quiz.

*Lets get started - have a go at the quiz!* *After you have completed the quiz, check your answers.*

Follow the link to view the pdf version of topic 1.2.

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