Download Adding and Subtracting Numbers in Scientific Notation

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
page
11
page
12
page
13
page
14
page
15
page
16
page
17
Document related concepts
no text concepts found
Transcript 
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) = ?
Related documents