expanded form


Definition of Expanded Form

Expanded Form is a way to break up a number to show how much each digit in the number represents. In other words, expanded form is the method of pulling a number apart and expressing it as a sum of the values of each digit.

The best way to identify the expanded form of a number is to simply write the number in words.



 
Examples of Expanded Form
 
Expanded form of whole numbers

In order to understand expanded form better, one needs to be good at place value.

Consider the number 543. Arrange the digits in a place value chart as shown below.


From the chart above, we see that:

            the value of 5 is 5 × 100 =          500

the value of 4 is 4 × 10   =           40

            the value of 3 is 3 × 1     =            3

          
Therefore, the expanded form of the number 543 is 500 + 40 + 3.

 
Expanded form of decimal numbers
 
Consider the decimal 892.15. Arrange the digits in a place value chart as shown below.
 

From the chart above, we see that:


the value of 8 is 8 × 100 =          800

the value of 9 is 9 × 10   =           90

            the value of 2 is 2 × 1    =              2

           

Therefore, the expanded form of the number 892.15 is 800 + 90 + 2 + 0.1 + 0.05.


Solved Example on Expanded Form

Choose the expanded form of the number 14,793.


Solution:

 

The expanded form of the number 14,793 can be found using a place value

chart. We leave it to you for practice as this method has already been

discussed in the examples above.

 

Now, let’s try to write the number in words and see how it helps us identify the

expanded form.

 

The number 14,793 is read as: 14 thousands 7 hundreds 93 which is the

 

same as 1 ten thousand  4 thousands 7 hundreds 9 tens and 3 ones.

 

So, the expanded form of 14,793 is 10,000 + 4,000 + 700 + 90 + 3.

 

Related Terms for Expanded Form

  • Place value
  • Sum
  • Digit