### Converting Between Standard and Expanded Form (Find the Missing Number) – Quiz

Understanding **place value** and how to break down numbers into **expanded form** is an important skill in math. But what happens when a number is missing in expanded form? This quiz will challenge you to use your knowledge of place value to find the missing part of a number. Before we dive into the quiz, let’s go over what expanded form is and how we can use it to figure out missing numbers.

### What is Expanded Form?

Expanded form is a way to break down a number so we can see the value of each digit based on its place in the number. Each digit gets multiplied by its place value, and we add them all together to get the full number.

For example, let’s look at the number **47,321**:

- The 4 is in the
**ten thousands**place, so it means**40,000**. - The 7 is in the
**thousands**place, so it means**7,000**. - The 3 is in the
**hundreds**place, so it means**300**. - The 2 is in the
**tens**place, so it means**20**. - The 1 is in the
**ones**place, so it means**1**.

So, in expanded form, **47,321** would be written as:

**40,000 + 7,000 + 300 + 20 + 1**.

Expanded form helps us understand the value of each digit in the number.

### Finding a Missing Number in Expanded Form

Now that you know how to write numbers in expanded form, let’s see what happens when part of the number is missing. Imagine you have this expanded form:

**30,000,000 + ____ + 600,000 + 80,000 + 5,000 + 900 + 40 + 7 = 36,685,947**

We need to figure out what number is missing in the expanded form so that when we add everything together, we get **36,685,947**. Here’s how we can do it step by step:

- First, add up the parts of the expanded form that you already know:
**30,000,000 + 600,000 + 80,000 + 5,000 + 900 + 40 + 7**.

- Next, subtract that total from the final number
**36,685,947**. - The difference will tell you what the missing number is.

### Example: Solving for the Missing Number

Let’s solve the example step by step.

We have:

**30,000,000 + ____ + 600,000 + 80,000 + 5,000 + 900 + 40 + 7 = 36,685,947**

First, we add the known parts of the expanded form:

**30,000,000 + 600,000 + 80,000 + 5,000 + 900 + 40 + 7** = **30,685,947**

Now, subtract this total from the full number **36,685,947**:

**36,685,947 – 30,685,947 = 6,000,000**

So, the missing number is **6,000,000**.

In expanded form, the complete number is:

**30,000,000 + 6,000,000 + 600,000 + 80,000 + 5,000 + 900 + 40 + 7 = 36,685,947**.