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**Exponents and Scientific Notation**

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**Objectives Learn properties of exponents.**

Convert from scientific notation to decimal notation Convert from decimal notation to scientific notation Solve applications

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**Exponential Notation a3 = a· a· a 53 = 5· 5· 5 = 125**

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**Properties of Exponents**

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Example Simplify a. 70=1 b. c. (5)0 = 1 d. 50 = 1

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Example If m ≠ 0, m is natural number, then

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Simplify. c.

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Power of 10 A positive exponent tells how many zeros follow the For example, 109, is a 1 followed by 9 zeros: 109 = 1,000,000,000. A negative exponent tells how many places there are to the right of the decimal point. For example, 10-9 has nine places to the right of the decimal point. 10-9 =

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Scientific Notation A number expressed in the form a 10n , Where 1 ≤ a < 10 and n is an integer. E.g., = x 10-2

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**To Convert S.N to Decimal**

If n is positive, move the decimal point in a to the right n places · 104 = 12300 If n is negative, move the decimal point in a to the left |n| places · 10-3 =

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**Example Write each number in decimal notation: 2.6 107 1.1 10-4**

Solution

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**Converting from Decimal to S.N.**

Write each number in scientific notation: 4,600,000 Solution

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**Multiplying Numbers in S.N.**

Recall: (a 10n) (b 10m) = (a b) 10n+m Multiply: (3.4 109)(2 10-5). Write the product in decimal notation. Solution: (3.4 109)(2 10-5) = (3.4 2)(109 10-5) = 6.8 109+(-5) = 6.8 = 68,000

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**Dividing Numbers in S.N. Recall:**

Divide: Write the quotient in decimal notation. Solution:

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**Application: National Debt**

As of December 2008, the national debt was $10.8 trillion, or 10.8 1012 dollars. At that time, the U.S. population was approximately 306,000,000, or 3.06 108. If the national debt was evenly divided among every individual in the United States, how much would each citizen have to pay? Solution: The amount each citizen would have to pay is the total debt, 1.08 1013, divided among the number of citizens, 3.06 108.

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**Application: National Debt (cont.)**

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**Properties of Exponents**

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