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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 103 )+ (6.964 X 103 )
 Add: 2.56 + 6.964 = 9.524
 Answer: 9.524 X 103
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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.
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Addition
(1 .5 X103)+ (2.3 X 102)+ (2.0 X 103)
All NUMBERS MUST HAVE THE SAME
POWERS OF TEN
Change 2.3 x 102 by moving decimal to
the left, 0.23 x 103
(1.5 + 0.23 + 2.0) X 103 = 1.73 X 103
Addition





Given: (2.46 X 106) + (3.476 X 103)
Shift decimal 3 places to the left for 103.
Move: .003476 X 103+3
Add: 2.46 X 106 + .003476 X 106
Answer: 2.463 X 106
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Subtraction
 (8.96 x 107) – (3.41 x 107)
 8.96 – 3.41 = 5.55
 5.55 x 107
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Subtraction





Given: (5.762 X 103) – (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 103-.000265 X 103
Answer: 5.762 X 103
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Addition/Subtraction
Add/Subtract:
A. (2.0 X 104)- (3.0 X 103)
B. (6.4 X 102)+ (2.3 X 103) + (4.5 X 104)
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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.
Multiplying
 Multiplication
(3.5 x 102) x (2.0 x 103) = ?
 Multiply the coefficients, add
exponents.
(3.5 x 2.0) x 10(2 + 3) = 7.0 x 105
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Multiplying
 Multiplication
(2.41 x 104) x (3.09 x 102) = ?
 Multiply the coefficients, add
exponents.
(2.41 x 3.09) x 10(4 + 2) = 7.45 x 106
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Multiplying
Multiply the following:
A. (2.1 x 103)x (2.0 x 102)
B. (3.1 x 10-1) x (3.0 x 10-2)
4.2 x 105
9.3 x 10-3
C. (4.0 x 105) x (2.0 x 10-3) 8.0 x 102
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Dividing
 Division
4.2 x 104 / 2.0 x 102 = ?
 Divide the coefficients, subtract the
exponents
(4.2/2.1) x 10(4-2) = 2.1 x 102
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Dividing
 Division
4.89 x 107/ 2.74 x 104 = ?
 Divide the coefficients, subtract the
exponents
(4.89/2.74) x 10(7-4) = 1.78 x 103
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Dividing
Divide the following:
A. (3.4 x 105)/(1.7 x10-2)
2.0 x 107
B. (6.3 x10-3)/(2.1 x 10-3)
3.0 x 100
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Operations on Scientific
Notation
Homework
Textbook
Pg. AT4
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