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

Expanded Form The face value and place value are shown for each numeral Examples: 574 in expanded form: 5x100 + 7x10 + 4x1 923 235 in expanded form: 9x100 000 + 2x10000 + 3x1000 + 2x100 + 3x10 + 5x1

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 10 000

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”  

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!

2 x 10000 becomes 2 x 104 104 means 10 x 10 x 10 x 10 Examples: 5 x 102 + 7 x 101 + 4 x 1 9 x 105 + 2 x 104 + 3 x 103+ 2x102 + 3x101 + 5 x 1

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

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

Examples 923 235 in expanded form with powers of 10 is: 9x105+2x104+3x103+2x102+3x10+5x100 207 in expanded form with powers of 10: 2x102+7x100