Common Core Math Vocabulary

Expanded Form - Definition with Examples

What is Expanded Form?

In the expanded form. we break up a number according to their place value and expand it to show the value of each digit. For example, the expanded form of 943 is given. 

expanded form example 1

9 blocks of hundreds

expanded form example 2

4 blocks of tens

expanded form example 3

3 blocks of ones

9 hundreds 4 tens 3 ones

Expanded Form:    900  +   40   +   3
 

Each number has a place value. It determines the value of that digit according to its position in the number. The value of a digit in a number increases as we move from left to right. The digits on the left have lower place value than the digits on the right.

value of the digit in expanded form
 

To write the number 7286 in expanded form we follow the given steps: 

Step 1: Use place value diagram to express the number 

place value diagram to express number
 

Step 2: Write the number in expanded form. 

7286 = 7000 + 200 + 80 + 6
 

Expanded form of decimal numbers 

The decimal digits also have place values. A decimal number can be expanded as 

Expanded form of decimal numbers
 

  Fun Facts

  • Expanded form is not same as expanded notation.  The expanded notation a number is represented as the sum of each digit in a number multiplied by its place value. 

    Expanded form: 234 = 200 + 30 + 4

    Expanded notation: 234 = (2  100) + (3  10) + (4  1)

    In the expanded forms, we use only addition between the place value numbers and in the expanded notation we use addition and multiplication. 

 

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