7th Grade Math: Expanded Notation

Tips for Reviewing Expanded Notation with Your 7th Grader

First, expanded notation can help your child do many math problems more quickly. Your son or daughter can also do left-to-right multiplication, which may be easier than the method your 7th grader has learned.

Additionally, learning expanded notation is one of the first steps in learning how to write computer programs. In order to point out a practical use of expanded notation, you might ask your child, 'Do you want to write a new computer game someday?' Once your 7th grader understands expanded notation, it'll be easy to learn scientific notation. Scientific notation plays a major role in computer languages and physical sciences.

What Is Expanded Notation?

There are many complicated or confusing definitions of expanded notation. One simple way of explaining it is to say it's separating a number into its digits and writing it as a sum of each digit's value. Or one may simply say that it's writing a number out by multiplying the digits by their columns. Like most math concepts, this is best learned by illustration.

One of the easiest ways to show this form is by writing a number, such as 7,495. Above each digit, beginning at the right, write the number of zeros that the digits in each column represent. So you'd write 0 above the 5, 1 above the 9, 2 above the 4 and 3 above the 7. Then verbalize what you're doing and write the number as 7 with 3 zeros behind it + 4 with 2 zeros behind it and so on.

Several Expanded Notation Formats

There's more than one way to write a number in expanded form; usually, base-ten numerals are used in the earlier grades, and other forms are added is your child progresses in school. Our previous example of 7,495 may be written three ways:

• 7,000 + 400 + 90 + 5 (as you did above)
• (7 x 1000) + (4 x 100) + (9 x 10) + (5 x 1)
• (7 x 10^3) + (4 x 10^2) + (9 x 10^1) + (5 x 10^0)

The last example is also the beginning step for scientific notation. If your child doesn't know this expanded notation format, you may have to explain that 10^3 = 10 X 10 X 10 and 10^0 (or any other number ^0) = 1.