Decimals
Decimals
A Decimal Number (based on the  number 10) contains a Decimal Point.
 
First, let's have an example:
Here is the number "forty-five and six-tenths" written as a decimal number:
 
The decimal point goes between Ones and Tenths.
 
45.6 has 4 Tens, 5 Ones and 6 Tenths, like this:
Now, let's discover how it all works ...
Place Value
It is all about Place Value !
When we write numbers, the position (or "place") of each digit
is important.
the "7" is in the Ones position, meaning 7 ones (which is 7),
the "2" is in the Tens position meaning 2 tens (which is twenty),
and the "3" is in the Hundreds position, meaning 3 hundreds.
"Three Hundred Twenty Seven"
As we move left, each position  is 10 times bigger!
 
Tens are 10 times bigger than Ones
Hundreds are 10 times bigger than Tens
... and ...
As we move right, each position  is 10 times smaller.
From Hundreds, to Tens, to Ones
 
But what if we continue past Ones?
What is 10 times smaller than Ones?
110ths (Tenths) are!
But we must first put a decimal point,
so we know exactly where the Ones position is:
 
"three hundred twenty seven and four tenths"
but we usually just say "three hundred twenty seven point four"
And that is a Decimal Number!
 
We can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:
Have a play with decimal numbers yourself:
Large and Small
So, our Decimal System lets us write numbers as large or as small as      we want, using the decimal point. Digits can be placed to the left      or right of a decimal point, to show values greater than one      or less than one.
The decimal point is the most important part of a Decimal Number.  Without it we are lost,  and don't know what each position means.
17
whole number (such as 17)
 
As we move further left,
every  place gets 10       times bigger.
 
The first digit on the right means
tenths (1/10).
As we move further right,
every  place       gets 10 times smaller
(one tenth as big).
See decimals on the Zoomable Number Line
Definition of Decimal
The word "Decimal" really means "based on 10" (From Latin decima: a tenth part).
We sometimes       say "decimal" when we mean anything to do with our numbering       system, but a "Decimal Number" usually means there is       a Decimal Point.
Ways to think about Decimal Numbers ...
... as a Whole Number Plus Tenths, Hundredths, etc
We can think of a decimal number as a whole number plus tenths, hundredths, etc:
Example 1: What is 2.3 ?
On the left side is "2", that is the whole number        part.
The 3 is in the "tenths" position, meaning "3        tenths", or 3/10
So, 2.3 is "2 and 3 tenths"
Example 2: What is 13.76 ?
On the left side is "13", that is the whole number        part.
There are two digits on the right side, the 7 is in the "tenths" position, and the 6 is the "hundredths" position
So, 13.76 is "13 and 7 tenths and 6 hundredths"
... as a  Decimal Fraction
Or we can think of a decimal number as a Decimal Fraction.
A Decimal Fraction is a fraction where the denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words a power of ten )
So "2.3" looks like: