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 units and tenths.

 

45.6 has 4 tens, 5 units 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.

In the number 327:

  • the "7" is in the Units position, meaning just 7 (or 7 "1"s),
  • the "2" is in the Tens position meaning 2 tens (or twenty),
  • and the "3" is in the Hundreds position, meaning 3 hundreds.
Place Value
"Three Hundred Twenty Seven"
keft As we move left, each position is 10 times bigger!
  Example: Hundreds are 10 times bigger than Tens

... and ...

As we move right, each position is 10 times smaller. right
From Hundreds, to Tens, to Units  

decimals-tenths  

But what if we continue past Units?

What is 10 times smaller than Units?

1/10 ths (Tenths) are!

 

But we must first write a decimal point,
so we know exactly where the Units position is:
  tenths

"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:


View Larger

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 indicate values greater than one or less than one.

The decimal point is the most important part of a Decimal Number. Without it, we would be lost ... and not know what each position meant.

17 . 591
         
On the left of the decimal point is a
whole number (17 for example)
   
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).

Zoom into decimals ...

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

You could 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, you could 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" would look like this:
23
10
   
And "13.76" would look like this:
1376
100

 

... as a Whole Number and Decimal Fraction

Or, you could think of a decimal number as a Whole Number plus a Decimal Fraction.

So "2.3" would look like this:
2  and 
3
10
   
And "13.76" would look like this:
13  and 
76
100

Those are all good ways to think of decimal numbers.