### Converting Between Standard and Expanded Form – Quiz

Numbers can be written in many different ways, and one of the most important is **expanded form**. Expanded form shows a number broken down into each of its place values. On the other hand, **standard form** is how we usually see numbers written, using just digits. In this post, we’ll learn how to convert between the two forms and practice doing it with some examples and a quiz.

### What is Standard Form?

Standard form is the regular way of writing numbers using digits. For example, the number **73,241** is written in standard form. The digits (7, 3, 2, 4, and 1) each represent a certain value based on their place in the number.

- 7 is in the
**ten thousands**place, so it means 70,000. - 3 is in the
**thousands**place, so it means 3,000. - 2 is in the
**hundreds**place, so it means 200. - 4 is in the
**tens**place, so it means 40. - 1 is in the
**ones**place, so it means 1.

When we put them all together, we get **73,241**.

### What is Expanded Form?

Expanded form is when you break down a number to show the value of each digit based on its place value. You write it as a sum of each digit’s value.

For example, the number **73,241** in expanded form is:

**70,000**(because the 7 is in the ten thousands place)**+ 3,000**(because the 3 is in the thousands place)**+ 200**(because the 2 is in the hundreds place)**+ 40**(because the 4 is in the tens place)**+ 1**(because the 1 is in the ones place)

So, in expanded form, we write the number like this:

**70,000 + 3,000 + 200 + 40 + 1**

### Why Do We Use Expanded Form?

Expanded form helps us understand what each digit in a number means. It breaks the number into smaller parts, which makes it easier to see how big a number is. This can be very useful when you’re working with large numbers.

Let’s take a big number like **90,731,319**. When we break it down into expanded form, we can clearly see the value of each digit:

**90,000,000 + 7,000,000 + 400,000 + 70,000 + 1,000 + 300 + 10 + 9**

### How to Convert Between Standard and Expanded Form

Now that we know what standard and expanded form are, let’s look at how to switch between them.

#### 1. Converting from Expanded Form to Standard Form

To convert from expanded form to standard form, all you have to do is add the numbers together. Let’s use the example:

**90,000,000 + 7,000,000 + 400,000 + 70,000 + 1,000 + 300 + 10 + 9**

When you add these together, you get the number **97,471,319** in standard form.

#### 2. Converting from Standard Form to Expanded Form

To convert a number from standard form to expanded form, you break it down by each digit’s place value. Let’s take **542,389** as an example:

- The 5 is in the hundred thousands place, so it means
**500,000**. - The 4 is in the ten thousands place, so it means
**40,000**. - The 2 is in the thousands place, so it means
**2,000**. - The 3 is in the hundreds place, so it means
**300**. - The 8 is in the tens place, so it means
**80**. - The 9 is in the ones place, so it means
**9**.

So, **542,389** in expanded form would be written as:

**500,000 + 40,000 + 2,000 + 300 + 80 + 9**

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