Download Scientific Notation - Waterford Public Schools

Scientific Notation
Scientific Notation
• Can be also called standard form or
exponential notation
• Used to write numbers that are very large
or very small so that they can be easily
understood and used for calculations
• Conveys the number of significant digits
and order of magnitude
Example – the speed of light
• The speed of light is 300,000,000 meters
per second –that is a lot of zeros!
• You can change this number into scientific
notation by counting the number of
decimal places you have to move so that
the first digit will be between 1 and 9
inclusively and multiplying by a factor of
10.
Example – the speed of light
• Therefore, you count how many spaces
you need to move the decimal so that it is
just after the 3 in 300,000,000
• You have to move it 8 to the left.
• Therefore, to the speed of light in
scientific notation is:
• 3 x 108 meters per second
Scientific notation for small
numbers
• You can do the same process for small numbers, but you
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need to multiply by a negative exponent.
For example, the number
0.0000000061 g is very small
Again, you count how many places you need to move
the decimal so that the first number is between 1 and 9
inclusively. Then you multiply by a factor of ten and
include a negative sign in front of the exponent.
You have to move the decimal 9 places so it is written
as:
6.1×10−9 g
Other examples
• What is 3000 written in scientific notation?
• 3×103
• What is 0.0000000789 written in scientific
notation?
• 7.89×10-8
Taking numbers out of scientific
notation
• To take numbers out of scientific notation, you
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just do the reverse process. Just move the
decimal over the number of places indicated by
the exponent.
For example, the circumference of the Earth is
about 4×107 m
You just move the decimal 7 places to the right.
This is written as 40,000,000 m
Significant figures in scientific
notation
• Be sure to include the appropriate number of
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significant figures when using scientific notation.
The Earth's mass is about
5,973,600,000,000,000,000,000,000 kg. In
scientific notation, this is written 5.9736×1024 kg
The Earth’s mass that was used had 5 significant
figures, so the scientific notation should have 5
significant figures.
Significant figures in scientific
notation
• An electron's mass is about
0.00000000000000000000000000000091093822 kg.
• In scientific notation, this is written
9.1093822×10−31 kg.
• Note that all the zeros before the 9 are
not significant.
Now you try! Put the following
numbers either into or out of
scientific notation.
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2.99792458×108 m/s
answer: 299792458 m/s
7.6 x 10-4 cm
answer: 0.00076 cm
.0000003509
answer: 3.509 x 10-7
400 L
answer: 4 x 102 L
Adding and subtracting with
Scientific Notation
• You can only add and subtract in scientific
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notation if the exponents are the same
If the exponents are the same, you just add or
subtract the numbers and leave the exponent
alone
Here is an example: 4000 + 2000= 6000
In scientific notation 4000 = 4 x 103
and 2000 = 2 x 103
(4 x 103 ) + (2 x 103 ) = 6 x 103
Note that the numbers were added, but the
exponents remained the same
Adding and subtracting with
Scientific Notation
• If you have two numbers in scientific notation,
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you have to make the exponents the same
before you can add or subtract
Here is an example:
10,000 – 5,000 = 5,000
(1 x 104) – (5 x 103)
You need to change one of them so that their
exponents are equal!
(10 x 103) – (5 x 103) = 5 x 103
Multiplying with scientific notation
• When you multiply in scientific notation,
you multiply the numbers and then add
the exponents. Here is an example:
• (3.2 x 107 )(1.0 x 1010) = 3.2 x 1017
• (2.5 x 1012)(2.00 x 10-4)
• = 5.0 x 108
Dividing with Scientific Notation
• When you divide in scientific notation, you divide
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the numbers and then subtract the exponents.
Here is an example:
6.2 x 1012 = 2.0 x 107
3.1 x 105
9.0 x 10-16 = ???
3.00 x 105
= 3.0 x 10-21