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Exponents and Scientific Notation

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**53 Powers and Exponents The base is the number that is multiplied.**

The exponent tells how many times the base is used as a factor. 53 The number that is expressed using an exponent is called a power. “Five to the Third Power”

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**53 = 5×5×5=125 Standard Notation Expanded Notation**

Exponential Notation “five to the third power”

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**Place Value and Powers of Ten**

____ ____ ____ , ____ ____ ____. ____ ____ ____ 105 104 103 102 101 100 10-1 10-2 10-3 100,000 105 = 1 x 10 x 10 x 10 x 10 x 10 104 1 x 10 x 10 x 10 x 10 103 1 x 10 x 10 x 10 102 1 x 10 x 10 101 1 x 10 100 1 1 x 1 x x 1 x x x 10,000 1,000 100 10 1 0.1 10-1 0.01 10-2 0.001 10-3

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**Any number to the power of zero is 1.**

Remember… 120 = 1 2340 = 1 560 = 1

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You try… Express each number in both expanded and standard notation. 1) 73 1 x 7 x 7 x 7 343 2) 54 1 x 5 x 5 x 5 x 5 625 3) 26 1 x 2 x 2 x 2 x 2 x 2 x 2 64 4) 240 1 1 5) 35 1 x 3 x 3 x 3 x 3 x 3 243

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**Scientific Notation is a shorthand way of expressing very large or very small numbers.**

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**An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms.**

The length of this number in standard notation makes it awkward to work with.

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To express any number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. . . 97,700,000,000,000,000,000,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 9.77 x 1022

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**The average size of an atom is about 0.00000003 centimeters across.**

Again, the length of this number in standard notation makes it awkward to work with.

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To express any number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. . . 1 2 3 4 5 6 7 8 3 x 10-8

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A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

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You try… Express each number in scientific notation. 1) ,000 1.35 x 105 2) 1.653 x 10-5 3) 4,600,000 4.6 x 106 4) 7.089 x 10-3 5) 2.1 x 10-8

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**Let’s try in reverse… 1) 7.02 x 104 70,200 2) 9.12 x 10-2 0.0912**

Express each number in standard form. 1) x 104 70,200 2) x 10-2 0.0912 3) x 107 64,000,000 4) x 10-5 5) x 109 3,490,000,000

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