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Operations on Scientific Notation Addition and Subtraction 1. If they have the same exponent - add/subtract the number in front - keep the same exponent 2. If they don’t have the same exponent - change the smaller to the larger exponent -repeat step #1

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Addition Given: (2.56 X 10 3 )+ (6.964 X 10 3 ) Add: 2.56 + 6.964 = 9.524 Answer: 9.524 X 10 3 2

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Addition/Subtraction If the exponents are different, you must move the decimal either right or left so that they will have the same exponent. For each move of the decimal to the right you have to add -1 to the exponent. For each move of the decimal to the left you have to add +1 to the exponent. 3

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Addition (1.5 X10 3 )+ (2.3 X 10 2 )+ (2.0 X 10 3 ) All NUMBERS MUST HAVE THE SAME POWERS OF TEN Change 2.3 x 10 2 by moving decimal to the left, 0.23 x 10 3 (1.5 + 0.23 + 2.0) X 10 3 = 1.73 X 10 3

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Addition Given: (2.46 X 10 6 ) + (3.476 X 10 3 ) Shift decimal 3 places to the left for 10 3. Move:.003476 X 10 3+3 Add: 2.46 X 10 6 +.003476 X 10 6 Answer: 2.463 X 10 6 5

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Subtraction (8.96 x 10 7 ) – (3.41 x 10 7 ) 8.96 – 3.41 = 5.55 5.55 x 10 7 6

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Subtraction Given: (5.762 X 10 3 ) – (2.65 X 10 -1 ) Shift decimal 4 places to the right for 10 -1. Move:.000265 X 10 (-1+4) Subtract: 5.762 X 10 3 -.000265 X 10 3 Answer: 5.762 X 10 3 7

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Addition/Subtraction Add/Subtract: A. ( 2.0 X 10 4 )- (3.0 X 10 3 ) B. (6.4 X 10 2 )+ (2.3 X 10 3 ) + (4.5 X 10 4 ) 8

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Operations on Scientific Notation Multiplication and Division 1. Mult. / Divide the number in front 2. If Mult., add the exponents 3. If Division, subtract the exponents.

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Multiplying Multiplication (3.5 x 10 2 ) x (2.0 x 10 3 ) = ? Multiply the coefficients, add exponents. (3.5 x 2.0) x 10 (2 + 3) = 10 7.0 x 10 5

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Multiplying 11 Multiplication (2.41 x 10 4 ) x (3.09 x 10 2 ) = ? Multiply the coefficients, add exponents. (2.41 x 3.09) x 10 (4 + 2) = 7.45 x 10 6

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Multiplying Multiply the following: A. (2.1 x 10 3 )x (2.0 x 10 2 ) B. (3.1 x 10 -1 ) x (3.0 x 10 -2 ) C. (4.0 x 10 5 ) x (2.0 x 10 -3 ) 12 4.2 x 10 5 9.3 x 10 -3 8.0 x 10 2

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Dividing Division 4.2 x 10 4 / 2.0 x 10 2 = ? Divide the coefficients, subtract the exponents (4.2/2.1) x 10 (4-2) = 13 2.1 x 10 2

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Dividing Division 4.89 x 10 7 / 2.74 x 10 4 = ? Divide the coefficients, subtract the exponents (4.89/2.74) x 10 (7-4) = 14 1.78 x 10 3

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Dividing Divide the following: A. (3.4 x 10 5 )/(1.7 x10 -2 ) B. (6.3 x10 -3 )/(2.1 x 10 -3 ) 15 2.0 x 10 7 3.0 x 10 0

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Operations on Scientific Notation HomeworkTextbook Pg. AT4 #29 - 40

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