What is Expanded Notation?

Expanded notation can be defined as a way of expressing numbers by showing the value of each digit. Writing a number in expanded notation is not like writing in expanded form.

Difference between Expanded notation and expanded form

In expanded notation, a number is represented as the summation of each digit multiplied by its place value, whereas in expanded form, addition is only utilized between place value numbers.

Expanded form and expanded notation is a useful way to rewrite numbers in order to show the place value of each digit in that number.

Example of expanded notation

569 in expanded form:

500 + 60 + 9

while 569 in expanded notation:


\fn_jvn \large (5 x 100) + (6 x 10) + (9 x 1)


The original number 569 is in the standard form.

How to convert the standard form into expanded notation?

To expand a specific number (from its standard form), we require to expand it into the sum of each digit multiplied by its matching place value (ones, tens, hundreds, and so on).

Further Reading:  Additive Identity and Additive Inverse

These techniques of writing a number in expanded notation and forms are explained in the examples below.

An Example


Convert 9586 into expanded notation.


The number 9586 can be written in expanded form as:

\fn_jvn \large 9586 = 9,000 + 500 + 80 + 6

In this way, every number that comes after a digit is replaced with 0’s. For instance, 9 and 5 in the number are represented as 9000 and 500 respectively.



Write 25,688 in expanded form?


25,688 in the expanded form is represented as:

\fn_jvn \large 25,688 = 20,000 + 5,000 + 600 + 80 + 8

Writing a number in expanded notation requires showing the place of a number in exponential powers of 10.

Expanded notation for decimals:

Decimal numbers can also be converted into expanded notation by using exponential powers of 10.



Write 45. 69 in expanded notation?


\fn_jvn \large 45.69 = 50 + 5 + 0.6 + 0.09


Write the decimal number 658.605 in expanded notation.


\fn_jvn \large 658.605 = 600 + 50 + 8 + 0.6 + 0.002