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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 #137 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, 8190
acch Oriel ...
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 Spring '08
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