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MAT111 Working with Scientific Notation or Was Scientific Notation Invented by Mad Scientists? epw 10/11/06 1 MAT111 Doctor Frankenstein • A scientist, Dr. Frankenstein, applied 5.0 x 104 volts for 6.66 x 10-2 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. epw 10/11/06 2 MAT111 Scientific Notation Another short review… epw 10/11/06 3 MAT111 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 epw 10/11/06 4 MAT111 Scientific Notation Converting to Scientific Notation 1. Move the decimal point to come after the first nonzero digit 1234 1.234 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 1.234 x 103 The power is negative if the decimal point moves to the right .01234 1.234 x 10-2 epw 10/11/06 5 MAT111 More Examples 3042 3.042 x 103 (decimal moves 3 places to the left) 0.00012 1.2 x 10-4 (decimal move 4 places right) 226 x 102 (2.26 x 102) x 102 = 2.26 x 104 epw 10/11/06 6 MAT111 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 epw 10/11/06 7 MAT111 Examples 1.23 x 102 123 3.6 x 106 3,600,000 5.7 x 10-3 0.0057 epw 10/11/06 8 MAT111 Scientific Notation Multiplying or Dividing Scientific Notation • Separately, – Operate on the powers of 10 – Operate on the other parts of the number epw 10/11/06 9 MAT111 Examples (6 x 102) x (4 x 105) = (6 x 4) x (102 x 105) = 24 x 107 = 2.4 x 108 (4.2 x 10-2) 4.2 10-2 ————— = —— x —— = 0.5 x 10-2 - (-5) (8.4 x 10-5) 8.4 10-5 = 0.5 x 103 = 5 x 102 epw 10/11/06 10 MAT111 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 epw 10/11/06 11 MAT111 Examples (7 x 1010) + (4 x 1010) = (7 + 4) x 1010 = 11 x 1010 = 1.1 x 1011 epw 10/11/06 12 MAT111 The End! epw 10/11/06 13