# 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**.

**Note:**

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**.

**Table of Contents**

## 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**.

**Note:**

Read about **Whole Number** here.

**Let us show you here an example.**

**Example 1**

Convert 1278 in the expanded notation.

**Solution:**

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**.

**Note:**

You can read about **Standard Notation** here.

### FAQ's

**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.