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The decimal number system and place value (decimal numbers)


Audio-visual version Audio-visual

 

Understanding
Numbers

The Decimal Number System and
Place Value (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.


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).

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)

00

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).

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)

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.

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 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.

If you are satisfied, then move onto Topic 1.3, which is still about the various types of numbers such as Cardinal, Prime and Composite numbers.

 


PDF Version PDF

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

 

 

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