What is expanded form?

Learn what expanded form is and have a go at some questions!

Author
Katie Wickliff

Published
October 25, 2023

What is expanded form?

Learn what expanded form is and have a go at some questions!

Author
Katie Wickliff

Published
Oct 25, 2023

What is expanded form?

Learn what expanded form is and have a go at some questions!

Author
Katie Wickliff

Published
Oct 25, 2023

Key takeaways

Expanded form is a way to write numbers by adding the value of its digits
Using expanded form helps us to determine place value and add up large numbers without using a calculator!

Table of contents

As kids learn about the place value of numbers, they’ll also be introduced to expanded form.

If you don’t know what expanded form means, don’t worry! This guide provides a comprehensive overview of expanded form and explains how to write numbers in expanded form.

We’ve also included plenty of examples and practice questions to build your child or pupils’ confidence. Let’s get started!

What is expanded form in maths?

Expressing a number in expanded form stretches out the number to show the value of each digit.

While we’re used to seeing numbers in their standard form, expanded form helps us to determine place value and is also a great way to add large numbers without a calculator. Finally, understanding expanded form helps kids develop a stronger number sense!

Examples of expanded form

Standard form: 834

8 hundreds

3 tens

4 ones

Expanded form: 800+30+4

In this expanded form example, we see that the digit in the hundreds place (8) is represented by writing 800, the digit in the tens place (3) is represented by writing 30, and the digit in the ones place (4) is represented by writing 4.

Let’s try another expanded form example with a larger number:

Standard form: 23,791

2 ten thousands

3 thousands

7 hundreds

9 tens

1 ones

Expanded form: 20,000 + 3,000 + 700 + 90 + 1

To find out more about standard form, be sure to take a look at our handy guide!

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How to write numbers in expanded form

Understanding place value is essential to writing numbers in their expanded form.

Using a place value chart or another table can help kids accurately express the expanded form of both whole numbers and decimal numbers, like the example below.

Writing whole numbers in expanded form

Start from the left with the first digit (6). We know that the digit is in the thousands place, so write “6” in the blank space under thousands. Then we do the same for the digit in the hundreds place, in the tens, and in the ones.

Inserting digits into the chart helps students write the whole number in expanded form:

6,000 + 100 + 60 + 1

Writing decimals in expanded form

Decimal numbers consist of a whole number and a fractional part, separated by a dot called a decimal point.

In a decimal number, the digits to the left of the decimal point are whole numbers, and the digits to the right of the decimal point are fractional parts of the number.

Writing expanded form with decimals is similar to writing whole numbers in expanded form. Children can use a place value chart or table to write the expanded form of decimals, like the example below:

Standard form: 83.74