 Operations on Scientific Notation Addition and Subtraction 1. If they have the same exponent - add/subtract the number in front - keep the same exponent.

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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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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