# Week 2 – Lesson 2 – Expanded Notation

# Expanded Notation

Expanded form or expanded notation is a helpful way to rewrite numbers in order to show the place value of each digit.

There are basically two acceptable ways to show numbers in expanded notation. Here are some examples.

**Example:** 4,981

**Method #1:** 4,000 + 900 + 80 + 1

**Example:** 15,807 can be written as 10,000 + 5,000 + 800 + 7

Again, we can see the place value of each digit in the number. Notice that there were no tens in this number.

**Method 2:** (4 x 1,000) + (9 x 100) + (8 x 10) + (1 x 1)

This method shows the place value as a power of ten. We can also use exponents to show the powers of ten.

The answer would now be: (4 x 10^{3}) + (9 x 10^{2}) + (8 x 10^{1}) + (1 x 10^{0})

**Example:** 15,807

10,000 + 5,000 + 800 + 7

**Method 2:** (1 x 10,000) + (5 x 1,000) + (8 x 100) + (7 x 1) or (1 x 10^{4}) + (5 x 10^{3}) + (8 x 10^{2}) + ( 7 x 10^{0})

**Expanded Notation with Decimals**

Using the powers of ten, we can also write numbers with decimals in expanded notation.

**Example:** 89.34

We will start by using the first method. This will help us build to method #2.

80 + 9 + 0.3 + 0.04

(8x 10) + (9 x 1) + (3 x + (4 x )

The expanded notation helps us to see that the 3 is in the tenths place and the 4 is in the hundredths place.

**Example:** 713.052

700 + 10 + 3 + 0.05 + 0.002

(7 x 100) + (1 x 10) + (3 x 1) + (5 x ) + (2 x )

Writing the numbers this way helps us to see that the 5 is in the 100ths places and the 2 is in the 1,000ths place.