### Converting Between Standard and Expanded Form (Expanded Form up to Billions) – Quiz

Understanding **place value** is crucial, especially when working with large numbers. One way to break down large numbers and understand them better is by writing them in **expanded form**. Expanded form helps us see the value of each digit based on its place value. In this post, we’ll explore how to convert numbers into expanded form, even for numbers as big as billions!

### What is Expanded Form?

Expanded form shows us the value of each digit in a number by separating it into parts based on place value. Instead of writing the number in its standard form, we write it as a sum of the values of its digits.

For example, let’s look at the number **1,205,347**.

In expanded form, it would be written as:

**1,000,000**(the 1 is in the millions place)**+ 200,000**(the 2 is in the hundred thousands place)**+ 5,000**(the 5 is in the thousands place)**+ 300**(the 3 is in the hundreds place)**+ 40**(the 4 is in the tens place)**+ 7**(the 7 is in the ones place)

So, in expanded form, **1,205,347** becomes:

**1,000,000 + 200,000 + 5,000 + 300 + 40 + 7**.

### How to Convert to Expanded Form for Big Numbers (Up to Billions!)

When dealing with really big numbers, like those in the millions and billions, expanded form becomes even more important because it helps us understand just how big each part of the number is. Let’s take a large number, like **10,200,540**, and convert it into expanded form step by step.

#### Step-by-Step Breakdown

**Look at each digit and identify its place value**:**1**is in the**ten millions**place, so it represents**10,000,000**.**0**is in the**millions**place, so it represents**0**(we don’t need to write it in expanded form).**2**is in the**hundred thousands**place, so it represents**200,000**.**0**is in the**ten thousands**place, so it represents**0**(we don’t need to include this either).**5**is in the**hundreds**place, so it represents**500**.**4**is in the**tens**place, so it represents**40**.**0**is in the**ones**place, so it represents**0**.

**Put the place values together**to create the expanded form:

**10,200,540**becomes:

**10,000,000 + 200,000 + 500 + 40**.

Now we’ve broken down the number into its place values!