1. Representing Numbers Numbers can be represented in different forms:
Standard form
Written form
Expanded form
Powers of 10
Scientific Notation
Today you will be learning about Expanded form with powers of 10. Last class we covered the first three representations

2. Expanded Form
The face value and place value are shown for each numeral
Examples:
574 in expanded form: 5x x10 + 4x1
in expanded form: 9x x x x x10 + 5x1

3. Expanded Form with Powers of 10
Expanded form written with the place value shortened into exponential form with a power of 10
Exponential form is used to show repeated multiplication where the base is multiplied by ITSELF the number of times
indicated by the exponent
104
In this case, 10 is the base, 4 is exponent and the number is 10x10x10x10 which is

4. Powers of 10
In math, a Power of 10 is any integer power of the number ten.
power or exponent
base number
In other words, ten multiplied by itself a certain number of times.
Pronounced “ten to the third power”

5. Powers of 10 Can anyone see a pattern?
Here are a few powers of 10:
Can anyone see a pattern?
If you said that each exponent equals the number of zeros in each product, you’re right!

6. 2 x becomes 2 x 104
104 means 10 x 10 x 10 x 10
Examples:
5 x x x 1
9 x x x x x x 1

7. The “power” indicates that there will be no 3’s
Powers of 10
The Exponent, or power, indicates how many bases should be multiplied. When the power is a zero, that means that there are no bases.
The “power” indicates that there will be no 3’s
Copyright © Lynda Greene Aguirre 2009

8. Powers of 10 However, this is not equal to zero, it is defined as:
Definition of a Zero Exponent:
Anything raised to the zero’th power is equal to “1”
It doesn’t matter what is being raised the power of zero, it will be equal to the number “1”.
Copyright © Lynda Greene Aguirre 2009

9. Examples
in expanded form with powers of 10 is: 9x105+2x104+3x103+2x102+3x10+5x in expanded form with powers of 10: 2x102+7x100