Operations and Numbers
in Scientific Notation
Foundations of Algebra
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.
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 right
for 106.
• Move: 2460 X 106-3
• Add: 2460 X 103 + 3.476 X 103
• Answer: 2463.476 X 103
•
Answer:
2.463476 X 106
Example 2
• Given: 5.762 X 103 – 2.65 X 10-1
• Shift decimal 4 places to the left for
10-1.
• Move: .000265 X 10(-1+4)
• Subtract: 5.762 X 103-.000265 X 103
• Answer: 5.762 X 103
Multiplying and Dividing
• Reminders:
1) The first number must be between 1 and 10
2) Make sure your decimal point is VERY clear
3) Number larger than one has a positive exponent
4) Number smaller than one has a negative exponent
Multiplying with Scientific
Notation
• Add the Exponents
• 102 X 103 = 105
• 100 X 1000 = 100,000
Multiplying with Scientific
Notation
(2.3 X 102)(3.3 X 103)
• 230 X 3300
Multiply the Coefficients
• 2.3 X 3.3 = 7.59
• 102 X 103 = 105
• 7.59 X 105
• 759,000
Add the Exponents
Multiplying with Scientific
Notation
• (4.6 X 104) X (5.5 X 103) = ?
• (3.1 X 103) X (4.2 X 105) = ?
Dividing with Scientific
Notation
• Subtract the Exponents
• 104/103 = 101
• 10000/ 1000 = 10
Dividing with Scientific
Notation
(3.3 X 104)/ (2.3 X 102)
• 33000 / 230 = 143.4783 Divide the Coefficients
• 3.3/ 2.3 = 1.434783
• 104 / 102 = 102
• 1.4347823 X 102
• 143.4783
Subtract the Exponents
Dividing with Scientific
Notation
• (4.6 X 104) / (5.5 X 103) = ?
• (3.1 X 103) / (4.2 X 105) = ?