Expanded Notation



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

Related Topics:
Place Value Games


Place Value Worksheets

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)



The following video gives another example of using the place value chart to write a number in expanded form.



This video introduces whole numbers, place value, expanded form, and writing whole numbers.





How to write numbers in expanded notation.



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



How to Write a Decimal in Expanded Form with Negative Powers of Ten







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