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.

Video Examples:Expanded Form


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

Solved Example on Expanded Form

Ques: 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, letís 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.