MAT111 epw 10/11/061 Working with Scientific Notation or Was Scientific Notation Invented by Mad Scientists?

MAT111 epw 10/11/062 Doctor Frankenstein A scientist, Dr. Frankenstein, applied 5.0 x 10 4 volts for 6.66 x seconds to the terminals on the neck of his monster Question: How many orders of McDonald’s™ supersized fries could he have fried up using that power instead? Answer: Who cares? He was mad.

MAT111 epw 10/11/063 Scientific Notation Another short review…

MAT111 epw 10/11/064 Scientific Notation Definition Scientific notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10

MAT111 epw 10/11/065 Scientific Notation Converting to Scientific Notation 1.Move the decimal point to come after the first nonzero digit 1234  x 10 ? 2.The power of 10 will be the number of places the decimal point moves The power is positive if the decimal point moves to the left 1234  x 10 3 The power is negative if the decimal point moves to the right  x 10 -2

MAT111 epw 10/11/066 More Examples 3042  x 10 3 (decimal moves 3 places to the left)  1.2 x (decimal move 4 places right) 226 x 10 2  (2.26 x 10 2 ) x 10 2 = 2.26 x 10 4

MAT111 epw 10/11/067 More Scientific Notation Tricks Converting from Scientific Notation 1.The power of 10 tells how many places to move the decimal point: Move it to the right if the power of 10 is positive Move it to the left if the power of 10 is negative 2.If moving the decimal point creates any “open places,” fill them with zeros

MAT111 epw 10/11/068 Examples 1.23 x 10 2  x 10 6  3,600, x 

MAT111 epw 10/11/069 Scientific Notation Multiplying or Dividing Scientific Notation Separately, –Operate on the powers of 10 –Operate on the other parts of the number

MAT111 epw 10/11/0610 Examples (6 x 10 2 ) x (4 x 10 5 ) = (6 x 4) x (10 2 x 10 5 ) = 24 x 10 7 = 2.4 x 10 8 (4.2 x ) ————— = —— x —— = 0.5 x (-5) (8.4 x ) = 0.5 x 10 3 = 5 x 10 2

MAT111 epw 10/11/0611 Scientific Notation Addition or Subtraction with Scientific Notation In general, must write numbers in ordinary notation before adding or subtracting Except when both numbers have the same power of 10, then we may factor out the power of 10 first

MAT111 epw 10/11/0612 Examples (7 x ) + (4 x ) = (7 + 4) x = 11 x = 1.1 x 10 11

MAT111 epw 10/11/0613 The End!