Expanded Notation Definition

When a number is written by showing the value of all digits multiplied by ones, tens, and hundreds according to their respective place value, it will be termed an Expanded Notation. In simple words, the actual number will be shown as the sum of all digits multiplied by their place value.


Read about Place Value here.

For example, we can write 2564 in expanded notation as:

= 2 x 1000 + 5 x 100 + 6 x 10 + 4 x 1

Similarly, we can write any number in expanded notation just by adding the digits and multiplying them according to their place value.

How to convert a number in expanded notation?

In Mathematics, it is pretty simple to convert a whole number in expanded notation. You only have to separate the digits with a “+” sign and then multiply them with thousands, hundreds, tens, and ones, according to their place value.


Read about Whole Number here.

Let us show you here an example.

Example 1

Convert 1278 in the expanded notation.


For this conversion, we have to write the numbers in a separate format first.

= 1 + 2 + 7 + 8

Now, we can easily identify the place value of all the digits. So, we will multiply them with thousands, hundreds, tens, and ones as per their place.

= 1 x 1000 + 2 x 100 + 7 x 10 + 8 x 1

Quick Tip: You can find the number with which the digit is multiplied by counting the digits placed on the right side of the concerned number.

To whom expanded notation is useful?

The expanded notation may not have huge significance at high levels. But Mathematical students need to learn about it as it will help them in understanding the basic rules of Mathematics. Also, students will be able to understand the difference between standard notation and expanded notation.


You can read about Standard Notation here.


How do you define expanded notation?

Expanded notation is the representation of a whole number as its digits addition after their multiplication with thousands, hundreds, and tens as per their place value.

Can we write 7.18 in an expanded notation?

Yes, we can also convert a decimal into an expanded notation.

What is the importance of expanded notation?

Expanded notation helps the students in understanding how a standard number is written.

Are expanded form and expanded notation the same?

No, expanded notation is different from expanded form. In expanded form, we won’t multiply the digits with thousands, hundreds, and tens. We just write the complete number as the addition of its digits.