Transcript Define scientific notation Convert numbers into

Scientific Notation
Scientific Notation
At the conclusion of our time
together, you should be able to:
1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard
number
What is Scientific Notation?
 Scientific notation is a way of expressing really big
numbers or really small numbers.
 For very large and very small numbers, scientific
notation is more concise.
Scientific Notation Consists Of Two Parts:
 A number between 1 and 10
 A power of 10
Nx
x
10
Scientific Notation
Mx
n
10
 M is the coefficient 1<M<10
 10 is the base
 n is the exponent or power of 10
Other Examples:
5.45E+6
5.45 x 10^6
Chemical Compound Quiz
What do sand and water have in common from
a chemical point of view?
Oxygen
Numbers Less Than 1 Will Have A
Negative Exponent.
A millionth of a second is:
0.000 001 sec
1.0E-6 s
1 x 10-6 s
1.0 x 10^-6 s
To Change Standard Form To
Scientific Notation…
 Place the decimal point so that there is one non-
zero digit to the left of the decimal point.
 Count the number of decimal places the decimal
point has “moved” from the original number. This
will be the exponent on the 10.
 If the original number was less than 1, then the
exponent is negative. If the original number was
greater than 1, then the exponent is positive.
Examples
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Given:
289 800 000 m
Use:
2.898 m (moved 8 places)
Answer: 2.898 x 108 m
Easier Way = M term smaller, so make
n term larger - 100 to 108
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Given:
0.000 567 m
Use:
5.67 m (moved 4 places)
Answer: 5.67 x 10-4 m
Easier Way = M term larger, so make
n term smaller - 100 to 10-4
To Change Scientific Notation To
Standard Form…
 Simply move the decimal point to the right for
positive exponent of 10.
 Move the decimal point to the left for negative
exponent of 10.
(Use zeros to fill in places.)
Example
 Given:
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5.093 x 106 m
Answer: 5 093 000 m (moved 6 places to
the right)
Easier Way = 106 to 100 = n smaller, so make
M term larger!
Given:
1.976 x 10-4 m
Answer: 0.000 197 6 m (moved 4 places to the
left)
Easier Way = 10-4 to 100 = n larger, so make
M term smaller!
Scientific Notation
Let’s see if you can:
1. Define scientific notation
2. Convert numbers into scientific notation
3. Convert scientific notation to a standard
number
Testing Skill #5
I feel much better now...
that I have given up hope!!!
Learning Check
 Express these numbers in Scientific
Notation:
1)
2)
3)
4)
5)
405 000 cm
0.003 872 cm
3 000 000 000 cm
2 cm
0.000 000 478 cm
4.05 x 105 cm
3.872 x 10-3 cm
3 x 109 cm
2 x 100 cm
4.78 x 10-7 cm
Scientific Notation
Calculations
Scientific Notation
At the conclusion of our time
together, you should be able to:
1. Multiply and divide numbers that are in
scientific notation
2. Add and subtract numbers that are in
scientific notation
Example #16
 (3 x 102 m)(8 x 10-4 m)
 Answer:
multiply M terms
 24
 Add n terms
 -2
 24 x 10-2 m2
 Adjust to correct scientific notation
 2.4 x 10-1 m2
 Adjust to correct number of sig figs
 2 x 10-1 m2
Example #17
 (5.000 x 105 m)/(3500 m)
 Answer:
divide M terms
 0.001 428
 Subtract n terms
 5
 0.001 428 x 105
 Adjust to correct scientific notation
 1.428 x 102
 Adjust to correct number of sig figs
 1.4 x 102
Example #18
 (5.0 x 104 m)(8.230 x 106 m)
 Answer:
/(1.99 x 1018 m)
multiply and divide M terms
 20.678 m
 Add and subtract n terms
 -8
 20.678 x 10-8 m
 Adjust to correct scientific notation
 2.0678 x 10-7 m
 Adjust to correct number of sig figs
 2.1 x 10-7 m
Example #13
 (5.0 x 10-3 m)-(5.0 x 10-8 m)
 Answer:
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can only subtract like powers
Adjust to larger power
(5.0 x 10-3 m)-(0.000050 x 10-3 m) =
4.999950 x 10-3 m
Adjust to correct number of decimal places
5.0 x 10-3 m
Adjust to correct scientific notation
5.0 x 10-3 m
Example #14
 (5.0 x 10-3 m) + 0.774 m
 Answer:
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can only add like powers
Adjust to larger power
(0.0050 x 100 m) + 0.774 m =
0.7790 m
Adjust to correct number of decimal places
0.779 m
Adjust to correct scientific notation
7.79 x 10-1 m
Example #15
 (5.0 x 10-3 m) + (5.0 x 10-4 m) - 0.009 38 m
 Answer:
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can only add like powers
Adjust to larger power
(0.0050 x 100 m) + (0.000 50 m) – 0.009 38 m
-0.003 88 m
Adjust to correct number of decimal places
-0.003 9 m
Adjust to correct scientific notation
-3.9 x 10-3 m
Familiar Saying
Surveillance should precede salientation.
Look before you leap!!!
Scientific Notation
Let’s see if you can:
1. Multiply and divide numbers that are in
scientific notation
2. Add and subtract numbers that are in
scientific notation