5.1 Notes (filled in)

5.1 Notes (filled in) - 5.1 Exponenfs and Scientific...

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Unformatted text preview: 5.1 Exponenfs and Scientific Notation Goal: Simplify or- evalua’re expressions conlaining exponen’rs Purpose: Many equafions modeling real life problems conTain exponenTs. Very large and very small numbers are often wriT’ren using exponents. ProducT Rule for Exponen‘rs: If m and n are posi’rive integers and a is a real number, Then CImfln : c1rn+n Examples: Zero Exponenf If a does no? equal 0, Then a0 = 1 Example: (4x + 5)0 = l Quotient Rule for Exponents If a is a nonzero real number and n and In are integers, then am = am—n Er? Negative Exponents If a is a real number other than 0 and n is an integer, then 1 _n__-_ (I —an When a factor containing an exponent is moved from the numerator to the denominator or from the denominator to the numerator, the sign of its exponent changes. Examples: 8 l x — X3 1 ‘4 F4 = 0‘ HW: p. 282 #1-37 odd Scientific Notation is a shorthand way of writing very large and very small numbers. Write a positive number as the product of a number a and an integer power r of 10: a x 10r where 1 s a < 10 Writing a Scientific Notation Number in Standard Notation: Move the decimal point in the number the same number of places as the exponent on 10. If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. Examples: 8.6 x107: 8U,OO0,000 3.022 x10"l : 0.000%011 Steps for writing a number in Scientific Notation: _ 1. Move the decimal point in the original number until the new number has a value between 1 and 10. 2. Count the number of decimal places the decimal point was moved in Step 1. If the original number is 10 or greater, the count is positive. If the original number is less than 1, the count is negative. 3. Write the product of the new number in Step 1 by 10 raised to an exponent equal to the count found in Step 2. Examples: Write each number in scientific notation. to 1,700,000: H X lo ,4 0.00028: 256" X W HW: p.283 #63—72, 81-90 acch Oriel ...
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5.1 Notes (filled in) - 5.1 Exponenfs and Scientific...

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