 # Exponents and Scientific Notation

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Exponents and Scientific Notation

Objectives Learn properties of exponents.
Convert from scientific notation to decimal notation Convert from decimal notation to scientific notation Solve applications

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

Properties of Exponents

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

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

Simplify. c.

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 =

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

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 =

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

Converting from Decimal to S.N.
Write each number in scientific notation: 4,600,000 Solution

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

Dividing Numbers in S.N. Recall:
Divide: Write the quotient in decimal notation. Solution:

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.

Application: National Debt (cont.)

Properties of Exponents