What is Expanded Notation?

As children progress through their schooling, the maths they learn becomes more advanced and challenging. When the numbers become too large or complicated for children to work within their heads, they can use expanded notation to make sums simpler and help them understand the value of the numbers they’re working with. They do this by partitioning the numbers.

Separate large numbers into smaller units before attempting to add, subtract, multiply or divide them; this helps students understand the value of the numbers more clearly and give them a step-by-step process to make mental maths easier.

What’s the difference between Expanded Notation and Expanded Form?

To write a number in expanded form, you’d break it down to show the value of its digits. For example, this would mean 144 would become 100 + 40 + 4 = 144.

You can also use it to calculate sums. If a student were given this equation, they would use expanded form by breaking the numbers into more manageable chunks. It would look like this:

Step 1. 46 + 73 =?

Step 2. 40 + 70 + 6 + 3 = 119

When you break the numbers down, you show each digit’s value. You can also use Base 10 Blocks as a visual aid to help illustrate this.

Expanded Notation includes another step, where each digit is multiplied by the appropriate place value. For example, 144 in expanded notation would be written as (1 x 100) + (4 x 10) + (4 x 1) = 144.

Because expanded notation includes this extra step, it emphasizes the value of each digit and requires students to consider each one individually and how it contributes to the whole number.

How to use Expanded Notation with Decimals

When using decimal numbers, expanded notation works in a very similar way. The difference is that each decimal number will be divided by its place value, depending on whether it is in the tenths or the hundredths place.

For example, if our number were 236.82, the expanded form and notation would look like this:

200 + 30 + 6 + 0.8 + 0.02 = 236.82

(2 x 100) + (3 x 10) + (6 x 1) + (8 x 1/10) + (2 x 1/100) = 236.82

When working with a decimal number, remember that the number of 0’s in the denominator for the decimals is equivalent to how many places it sits after the decimal point. So, looking at the above example, this would mean that the eight sits in the space after the decimal point, and the two would sit two spaces behind the decimal point.