Adding and Subtracting Numbers in Scientific Notation

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Adding and Subtracting Numbers in Scientific
Notation

• A.Oman
• Ellerbruch.nmu.edu

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Adding/Subtracting when Exponents are Equal

• When the exponents are the same for all the
  numbers you are working with, add/subtract the
  base numbers then simply put the given exponent
  on the 10.

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General Formulas

• (N X 10x) (M X 10x) (N M) X 10x
• (N X 10y) - (M X 10y) (N-M) X 10y

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Example 1

• 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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Example 2

• Given 9.49 X 105 4.863 X 105
• Subtract 9.49 4.863 4.627
• Answer 4.627 X 105

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Adding/Subtracting when the Exponents are
Different
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• When adding or subtracting numbers in scientific
  notation, the exponents must be the same.
• If they are different, you must move the decimal
  either right or left so that they will have the
  same exponent.

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Moving the Decimal

• 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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Continued

• 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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Example 1

• Given 2.46 X 106 3.476 X 103
• Shift decimal 3 places to the left for 103.
• Move .003476 X 1033
• Add 2.46 X 106 .003476 X 106
• Answer 2.463 X 106

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Example 2

• Given 5.762 X 103 2.65 X 10-1
• Shift decimal 4 places to the right for 10-1.
• Move .000265 X 10(-14)
• Subtract 5.762 X 103-.000265 X 103
• Answer 5.762 X 103

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Practice Worksheet

• Practice Adding and Subtracting in Scientific
  Notation
• Answers to Worksheet

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Links for more information and practice

• Addition and Subtraction with Scientific Notation
• Problem Solving--Scientific Notation
• Scientific Notation