PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

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PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
ADDITION AND SUBTRACTION
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Review
Scientific notation expresses a number in the
form
M x 10n
n is an integer
Any number between 1 and 10
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IF the exponents are the same, we simply add or
subtract the numbers in front and bring the
exponent down unchanged.
4 x 106
3 x 106
_______________
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x 106
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If the exponents are NOT the same, we must move a
decimal to make them the same.
4 x 106
3 x 105
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• Determine which of the numbers has the smaller
  exponent.
• Change this number by moving the decimal place to
  the left and raising the exponent, until the
  exponents of both numbers agree. Note that this
  will take the lesser number out of standard form.
• Add or subtract the coefficients as needed to get
  the new coefficient.
• The exponent will be the exponent that both
  numbers share.
• Put the number in standard form.

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4.00 x 106
4.00 x 106
.30 x 106
3.00 x 105
Move the decimal on the smaller number to the
left and raise the exponent !
Note This will take the lesser number out of
standard form.
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4.00 x 106
4.00 x 106
.30 x 106
3.00 x 105
4.30
x 106
Add or subtract the coefficients as needed to get
the new coefficient. The exponent will be the
exponent that both numbers share.
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Make sure your final answer is in scientific
notation. If it is not, convert is to
scientific notation.!
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A Problem for you
2.37 x 10-6
3.48 x 10-4
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Solution
2.37 x 10-6
002.37 x 10-6
3.48 x 10-4
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Solution
0.0237 x 10-4
3.48 x 10-4
3.5037 x 10-4
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PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
MULTIPLYING AND DIVIDING
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• Rule for Multiplication
• When multiplying with scientific notation
• Multiply the coefficients together.
• Add the exponents.
• The base will remain 10.

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(2 x 103) (3 x 105)
6 x 108
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(4.6x108) (5.8x106) 26.68x1014 Notice What is
wrong with this example?
Although the answer is correct, the number is not
in scientific notation.
To finish the problem, move the decimal one space
left and increase the exponent by one.
26.68x1014 2.668x1015
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((9.2 x 105) x (2.3 x 107)
21.16 x 1012 2.116 x 1013
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(3.2 x 10-5) x (1.5 x 10-3)
4.8 10-8
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• Rule for Division
• When dividing with scientific notation
• Divide the coefficients
• Subtract the exponents.
• The base will remain 10.

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(8 106) (2 103)
4 x 103
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Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4)
(3 x 105) x (7 x 104)
(5.63 x 108) x (2 x 100)
(4.55 x 10-14) x (3.77 x 1011)
(8.2 x10-6) x (9.4 x 10-3)
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Please multiply the following numbers.
(5.76 x 102) x (4.55 x 10-4)
2.62 x 10-1
(3 x 105) x (7 x 104)
2.1 x 1010
(5.63 x 108) x (2 x 100)
1.13 x 109
(4.55 x 10-14) x (3.77 x 1011)
1.72 x 10-2
(8.2 x10-6) x (9.4 x 10-3)
7.71 x 10-8
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Please divide the following numbers.

1. (5.76 x 102) / (4.55 x 10-4)
2. (3 x 105) / (7 x 104)
3. (5.63 x 108) / (2)
4. (8.2 x 10-6) / (9.4 x 10-3)
5. (4.55 x 10-14) / (3.77 x 1011)

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Please divide the following numbers.

1. (5.76 x 102) / (4.55 x 10-4) 1.27 x 106
2. (3 x 105) / (7 x 104) 4.3 x 100 4.3
3. (5.63 x 108) / (2 x 100) 2.82 x 108
4. (8.2 x 10-6) / (9.4 x 10-3) 8.7 x 10-4
5. (4.55 x 10-14) / (3.77 x 1011) 1.2 x 10-25

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PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
Raising Numbers in Scientific Notation To A Power
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(5 X 104)2 (5 X 104) X (5 X 104) (5 X 5) X
(104 X 104) (25) X 108 2.5 X 109
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Try These

• (3.45 X 1010)2
• (4 X 10-5)2
• (9.81 X 1021)2

1.19 X 1021
1.6 X 10-9
9.624 X 1043

1. (3.45 X 1010)2 (3.45 X 3.45) X (1010 X 1010)
   (11.9) X (1020) 1.19 X 1021
2. (4 X 10-5)2 (4 X 4) X (10-5 X 10-5) (16) X
   (10-10) 1.6 X 10-9
3. (9.81 X 1021)2 (9.81 X 9.81) X (1021 X 1021)
   (96.24) X (1042) 9.624 X 1043

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Scientific Notation Makes These Numbers Easy
9.54x107 miles
1.86x107 miles per second