Adding and Subtracting
Numbers in Scientific Notation
A.Oman
Ellerbruch.nmu.edu
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.
General Formulas
• (N X 10x) + (M X 10x) = (N + M) X 10x
• (N X 10y) - (M X 10y) = (N-M) X 10y
Example 1
• Given: 2.56 X 103 + 6.964 X 103
• Add: 2.56 + 6.964 = 9.524
• Answer: 9.524 X 103
Example 2
• Given: 9.49 X 105 – 4.863 X 105
• Subtract: 9.49 – 4.863 = 4.627
• Answer: 4.627 X 105
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 either right or left so
that they will have the same
exponent.
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.
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.
Example 1
• 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
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(-1+4)
• Subtract: 5.762 X 103-.000265 X 103
• Answer: 5.762 X 103
Practice Worksheet
• Practice Adding and Subtracting in
Scientific Notation
• Answers to Worksheet
Links for more
information and practice
• Addition and Subtraction with
Scientific Notation
• Problem Solving--Scientific Notation
• Scientific Notation