Expanded Notation

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

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.

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