Adding and Subtracting Numbers in Scientific Notation

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Adding and Subtracting Numbers in Scientific
Notation

• Created by Langan, Kansky, Nizam, ODonnell, and
  Matos

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Using Scientific Notation in Multiplication,
Division, Addition and Subtraction
Scientists must be able to use very large and
very small numbers in mathematical calculations.
As a student in this class, you will have to be
able to multiply, divide, add and subtract
numbers that are written in scientific notation.
Here are the rules.
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• When adding or subtracting numbers in scientific
  notation, the exponents must be the same.

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Adding/Subtracting when Exponents are THE SAME

• Step 1 - add/subtract the decimal
• Step 2 Bring down the given exponent on the 10

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Example 1

• (2.56 X 103) (6.964 X 103)
• Step 1 - Add
• 2.56 6.964
• 9.524
• Step 2 Bring down exponent
• 9.524 x 103

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Example 2

• (9.49 X 105) (4.863 X 105)
• Step 1 - Subtract
• 9.49 4.863
• 4.627
• Step 2 Bring down exponent
• 4.627 x 105

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The sum of 5.6 x 103 and 2.4 x 103 is
A
8.0 x 103
B
8.0 x 106
C
8.0 x 10-3
D
8.53 x 103
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The sum of 5.6 x 103 and 2.4 x 103 is
A
8.0 x 103
B
8.0 x 106
C
8.0 x 10-3
D
8.53 x 103
The exponents are the same, so add the
coefficients.
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8.0 x 103 minus 2.0 x 103 is
A
6.0 x 10-3
B
6.0 x 100
C
6.0 x 103
D
7.8 x 103
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8.0 x 103 minus 2.0 x 103 is
A
6.0 x 10-3
B
6.0 x 100
C
6.0 x 103
D
7.8 x 103
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Adding/Subtracting when the Exponents are
DIFFERENT

• When adding or subtracting numbers in scientific
  notation, the exponents must be the same.
• If they are different, you must move the decimal
  so that they will have the same exponent.

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Moving the Decimal

• It does not matter which number you decide to
  move the decimal on, but remember that in the end
  both numbers have to have the same exponent on
  the 10.

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Adding/Subtracting when the Exponents are
DIFFERENT

• Step 1 Rewrite so the exponents are the same
• Step 2 - add/subtract the decimal
• Step 3 Bring down the given exponent on the 10

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Adding With Different Exponents

• (4.12 x 106) (3.94 x 104)
• (412 x 104) (3.94 x 104)
• 412 3.94 415.94
• 415.94 x 104
• Express in proper form 4.15 x 106

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Subtracting With Different Exponents

• (4.23 x 103) (9.56 x 102)
• (42.3 x 102) (9.56 x 102)
• 42.3 9.56 32.74
• 32.74 x 102
• Express in proper form 3.27 x 103

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Example 3

• (2.46 X 106) (3.4 X 103)
• Step 1 Rewrite with the same exponents
• 3.4 X 103 ?
• 0.0034 X 1033
• New Problem (2.46 X 106) (0.0034 X 106)
• Step 2 Add decimals
• 2.46 0.0034
• 2.4634
• Step 3 Bring Down Exponents
• 2.4634 X 106

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Example 4

• (5.762 X 103) (2.65 X 10-1)
• Step 1 Rewrite with the same exponents
• 2.65 X 10-1 ?
• 0.000265 X 10(-14)
• New Problem (5.762 X 103) (0.000265 X 103)
• Step 2 Subtract Decimals
• 5.762 0.000265
• 5.762
• Step 3 Bring down decimals
• 5.762 X 103

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7.0 x 103 plus 2.0 x 102 is
A
9.0 x 103
B
9.0 x 105
C
7.2 x 103
D
7.2 x 102
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7.0 x 103 plus 2.0 x 102 is
A
9.0 x 103
B
9.0 x 105
C
7.2 x 103
D
7.2 x 102
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7.8 x 105 minus 3.5 x 104 is
A
7.45 x 105
B
4.3 x 104
C
4.3 x 106
D
4.3 x 1010
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7.8 x 105 minus 3.5 x 105 is
A
7.45 x 105
B
4.3 x 104
C
4.3 x 106
D
4.3 x 1010
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Adding and Subtracting

• The important thing to remember about adding or
  subtracting is that the exponents must be the
  same!
• If the exponents are not the same then it is
  necessary to change one of the numbers so that
  both numbers have the same exponential value.

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Practice

• (3.45 x 103) (6.11 x 103)
• (4.12 x 106) (3.94 x 104)
• (8.96 x 107) (3.41 x 107)
• (4.23 x 103) (9.56 x 102)