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Expanded Notation

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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.

Expanded Notation

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 use the place value chart to write a number in expanded form? Whole numbers, place value, expanded form, and writing whole numbers How to write numbers in expanded notation?
Examples:
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. How to Write a Decimal in Expanded Form with Negative Powers of Ten?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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