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The decimal number system and place value (whole numbers)


Audio-visual version  Audio-visual

Understanding Numbers
Topic: The Decimal Number System and
Place Value (Whole Numbers)
1
Number/ Numeral Systems
Throughout history there have been many number/numeral system used, from the early Babylonian numeral system (3100 BC) through to the modern Binary system used in computing.
The Number System most countries in the modern world use today for counting, calculating and reading and writing numbers is called the “Decimal” system because its based on the number 10 (”Dec” in Latin means ten).
1
Number/ Numeral Systems
Throughout history there have been many number/numeral system used, from the early Babylonian numeral system (3100 BC) through to the modern Binary system used in computing.
The Number System most countries in the modern world use today for counting, calculating and reading and writing numbers is called the “Decimal” system because its based on the number 10 (”Dec” in Latin means ten).
Next:
Comparing Number Systems
1
Number/ Numeral Systems
Throughout history there have been many number/numeral system used, from the early Babylonian numeral system (3100 BC) through to the modern Binary system used in computing.
The Number System most countries in the modern world use today for counting, calculating and reading and writing numbers is called the “Decimal” system because its based on the number 10 (”Dec” in Latin means ten).
1
The Decimal System
This system comes from and uses the ten Hindu-Arabic digits which are:
0
1
2
3
4
5
6
7
8
9
These numeral digits can be used very easily to represent quantities (e.g. five apples) or it can be used to show computations from 0 to 9 (e.g. 6+2=8). See below.
The next screen will consider what happens when numbers are greater than 9.
1
Place Value for Whole Numbers
Each“PLACE” (or column) that the digits 0 to 9 occupy have a different value. This gives the digits different values depending on the place they have.
The following table shows an example of how Place Value looks using just the first seven “PLACES” for whole numbers in the Decimal System.
1
Place Value
Let’s 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 the following table, which will show the different value of an 8 in three different places (80 000, 80 and 8).
7th Place
6th Place
5th Place
4th Place
3rd Place
2nd Place
1st Place
Value of Place (Words)
Million
Hundred Thousand
Ten Thousand
Thousand
Hundred
Ten
One
Value of Place (Digits)
1 000 000
100 000
10 000
1 000
100
10
1
Example of
80 088
8
8
8
a) An 8 in the 5th Place gives a value of 80 000 (8 ten thousands).
b) However an 8 in the 2nd Place gives a value of 80 (8 tens)
c) And finally an 8 digit in the 1st Place has a value of just 8 (8 ones).
Together these three “8s” give a number with a total value of 80 088 or eighty thousand and eighty eight.
1
Place Value
Let’s 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 the following table, which will show the different value of an 8 in three different places (80 000, 80 and 8).
7th Place
6th Place
5th Place
4th Place
3rd Place
2nd Place
1st Place
Value of Place (Words)
Million
Hundred Thousand
Ten Thousand
Thousand
Hundred
Ten
One
Value of Place (Digits)
1 000 000
100 000
10 000
1 000
100
10
1
Example of
80 088
8
8
8
a) An 8 in the 5th Place gives a value of 80 000 (8 ten thousand).
b) However an 8 in the 2nd Place gives a value of 80 (8 tens)
c) And finally an 8 digit in the 1st Place has a value of just 8 (8 ones).
Together these three “8s” give a number with a total value of 80 088 or eighty thousand and eighty eight.
1
Using Decimal System to Create Numbers
7th Place
6th Place
5th Place
4th Place
3rd Place
2nd Place
1st Place
Value of Place (Words)
Million
Hundred Thousand
Ten Thousand
Thousand
Hundred
Ten
One
Value of Place (Digits)
1 000 000
100 000
10 000
1 000
100
10
1
Example of
9 573 842
The value of the number in the example in the bottom row of the table is written as:
9 573 842 (nine million, five hundred and seventy three thousand, eight hundred and forty two).
Go to Activity One (in the right-hand side of this screen), and have a go at creating some numbers yourself, remembering to separate the numbers into groups of three.
2
4
8
8 4 2
5 7 3
9
1
Expanded Notation
“Expanded Notation” is simply a way of writing numbers by adding together the value of each digit:
e.g. , 7 392 = 7000 + 300 + 90 + 2
These values can then be further expanded to include the place value of each digit:
7 392 = 7000 + 300 + 90 + 2
By analysing numbers this way we can get a good understanding of place value and an appreciation of how place value works in our Decimal Number System.
Have a go at Activity Two to practise analysing some bigger numbers according to their place value.
7 392 = ( 7 x 1 000 ) + ( 3 x 100 ) + ( 9 x 10 ) + ( 2 x 1 )
7 392 =
( 7 x 1 000 )
+ ( 3 x 100 )
+ ( 9 x 10 )
+ ( 2 x 1 )
1
Expanded Notation
“Expanded Notation” is simply a way of writing numbers by adding together the value of each digit:
e.g. , 7 392 = 7000 + 300 + 90 + 2
These values can then be further expanded to include the place value of each digit:
7 392 = 7000 + 300 + 90 + 2
By analysing numbers this way we can get a good understanding of place value and an appreciation of how place value works in our Decimal Number System.
Have a go at Activity Two to practise analysing some bigger numbers according to their place value.
7 392 = ( 7 x 1 000 ) + ( 3 x 100 ) + ( 9 x 10 ) + ( 2 x 1 )
1
Bigger Numbers
Writing numbers to show positive value of tens of millions, hundreds of millions, billions, tens of billions, and so on, follows the same system of “Place Value” as was explained in the previous slides, and shown in the table below.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen thousand, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Reading Big Numbers
Consider this number:
367 894 230 814 926
It’s difficult to read because the place values of the first three numbers is not apparent by just looking at it.
It is easy to read if we name each of the groups of three digits:
(Three hundred and sixty seven trillion, eight hundred and ninety four million, two hundred and thirty million, eight hundred and fourteen, nine hundred and twenty six)
Have a go at Activity Three to practise some of these bigger numbers.
1
Quiz
Congratulations, you have completed the Topic One about how our decimal number system works.
Test your understanding of the Topic by completing the quiz.
Have a go at the Quiz.

Are you satisfied with your understanding of the topic? If not, we suggest that you go through this topic again and then have another go at the Quiz.

If you are satisfied, then move onto Topic 1.2, which is still about Place Value in our decimal number system, but will include decimal or fractional numbers (numbers less than one but greater than zero).

PDF Version PDF

 

Follow the link to view the pdf version of Topic 1.1.

 


Please note: If you find some of the concepts in this topic challenging, you may wish to go to Topic 1.3, which covers more fundamental concepts of mathamatics.

 

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