Expanded Notation

In these lessons, we will learn how to write whole numbers in expanded notation and how to write decimals in expanded notation.

The following examples show how to write the Expanded Notation for whole numbers and for decimals. Scroll down the page for examples and solutions.

Whole Numbers In Expanded Notation

The digits in the number 3,463,352 has the following place values and values of digit.

Place value	Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
Value of digit	3 000 000	400 000	60 000	3 000	300	50	2

We can add the values of the digits to get the number.
3,000,000 + 400,000 + 60,000 + 3,000 + 300 + 50 + 2 = 3,463,352

To show the place values of the digits in a number, we can write the number with expanded notation.

Example:
Write 62,502 in expanded notation.

Solution:
62,502 = 60,000 + 2,000 + 500 + 2

Write the ten thousands: 60,000 as 6 × 10,000
Write the thousands: 2,000 as 2 × 1,000
Write the hundreds: 500 as 5 × 100
Write the tens: 0 as 0 × 10
Write the ones: 2 as 2 × 1

So, 62,502 = (6 × 10,000) + (2 × 1,000) + (5 × 100) + (2 × 1)

Example:
Write 4,205,891 in expanded notation.

Solution:
4,205,891 = 4,000,000 + 200,000 + 5,000 + 800 + 90 + 1
= (4 × 1,000,000) + (2 × 100,000) + (5 × 1,000) + (8 × 100) + (9 × 10) + (1 × 1)

How To Write Numbers In Expanded Notation?

Example:
Write in expanded notation.
a) 416
b) 2414

Learn All About Writing Numbers In Expanded Notation

For example, you will learn how to write 278,502 as 200,000 + 70,000 + 8,000 + 500 + 2.

Decimals In Expanded Notation

How to write decimal numbers in expanded notation?

Examples:

1. Write 5.08 in expanded notation.
2. Write 0.604 in expanded notation.