Scientific Notation
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Transcript Scientific Notation
COEFFICIENT
It must be
more than 1 but
less than 10
COEFFICIENT
It must be
more than 1 but
less than 10
BASE
THE EXPONENT or
POWER OF TEN
COEFFICIENT
It must be
more than 1 but
less than 10
BASE
• Scientific notation: A method for
expressing, and working with, very large or
very small numbers.
Copyright © 2010 Ryan P. Murphy
• Scientific notation: A method for
expressing, and working with, very large or
very small numbers.
Copyright © 2010 Ryan P. Murphy
• “5 point 7 times ten to the sixth power”
• “5 point 7 times ten to the sixth”
To write a number in scientific notation:
– Put a decimal point after the first digit and drop the
zeroes.
– 146,000,000 = 1.46
To find the exponent, count the number of
places from the decimal to the end of the
numbers.
– In 1.46000000 there are 8 places.
8
– Therefore we write 146,000,000 as 1.46 x 10
Note that the places
start after the
decimal point
• What is 567,000 in scientific
notation?
Copyright © 2010 Ryan P. Murphy
• 5.67000
5
• 5.67 x 10
• What is 40,100,000,000,000 in
scientific notation?
– This is the distance from earth to the nearest star
Proxima Centauri.
Copyright © 2010 Ryan P. Murphy
• Answer! 40,100,000,000,000 = 4.01 x 10
13
Copyright © 2010 Ryan P. Murphy
• What is 8,000,000,000 in
scientific notation?
– A projection for the number of people on earth!
Copyright © 2010 Ryan P. Murphy
9
• Answer! 8,000,000,000 = 8 x 10
Copyright © 2010 Ryan P. Murphy
7
What is 9.9 x 10 ?
- Work in the opposite direction
– This is the distance from the Earth to Mars in
Kilometers.
Copyright © 2010 Ryan P. Murphy
7
• Answer! 9.9 x 10 = 99,000,000
– There needs to be six places after the decimal. Since
the .9 is the first, you would add 6 zeroes to equal
107.
5
• What is 3.844 x 10 ?
– The distance in kilometers from the Earth to the
Moon.
5
• Answer! 3.844 x 10
is 384,400
km
Scientific notation can be used for very
small numbers as well.
– The decimal number 0.00000065 written in
-7
scientific notation would be 6.5 x 10
Copyright © 2010 Ryan P. Murphy
• What is 0.00053 in scientific notation?
Copyright © 2010 Ryan P. Murphy
-4
• Answer! 0.00053 = 5.3 x 10
Copyright © 2010 Ryan P. Murphy
• What is 0.00000042 in scientific notation?
Copyright © 2010 Ryan P. Murphy
-7
• Answer! 0.00000042 is 4.2 × 10
Copyright © 2010 Ryan P. Murphy
What is 9,780,000,000,000,000,000,000,000,000
in scientific notation?
Copyright © 2010 Ryan P. Murphy
• Answer!
• 9,780,000,000,000,000,000,000,000,000
27
• 9.78 x 10
Copyright © 2010 Ryan P. Murphy
4
3
What is (2 x 10 ) x (4 x 10 ) ?
Copyright © 2010 Ryan P. Murphy
4
3
What is (2 x 10 ) (4 x 10 ) ?
1) Multiply the coefficients
2) Add the exponents (base 10 remains)
• What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy
4
3
What is (2 x 10 ) (4 x 10 ) ?
7
• Answer! 8 x 10 or 80,000,000
Copyright © 2010 Ryan P. Murphy
DO THE PROBLEMS
Write these numbers using
the scientific notation
5
(5 10 )(7 10 ) 35 x 105 = 3.5 x 106
10
6
4
(3 10 )(2 10 ) 6 x
7
−10
10
(5.5 10 )(4.2 10 ) 9.7 x 10−3
4
6
(5 10 )(8 10 )(4.2 10 ) 1.7 x 10
7
4
8
4
/
3
What is (3 x 10 ) (2 x 10 ) ?
Copyright © 2010 Ryan P. Murphy
What is (3 x 10 ) / (2 x 10 ) ?
4
3
1) Divide the coefficients
2) Subtract the exponents (base 10 remains)
• What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy
4
3
What is (3 x 10 ) / (2 x 10 ) ?
1) Multiply the coefficients
2) Subtract the exponents (base 10 remains)
Example 1: (3 x 104) / (2 x 103) = 1.5
x 101
• What is (2 x 104) (4 x 103)
Copyright © 2010 Ryan P. Murphy
DO THE PROBLEMS
Write these numbers using the scientific
notation. Round them to 2 decimal
places,
(3 106 )
1.50
4
(2 10 )
(7 105 )
10
(2 10 )
(1.5 107 )
4
(3 10 )
(3 107 )
6
(8 10 )
x 10−2
−15
3.50 x 10
0.50 x
−11
10
=
3.75 x
12
10
5.00x 10
−12
Scientific Notation exercise
• How do you solve this??
4
3
(3.0 x 10 ) + (2.0 x 10 ) =
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
?
32 x 10
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
?
32 x 10
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
?
32 x 10
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
3
32 x 10
Scientific Notation exercise
• How do you solve this??
4
3
3
3
(3.0 x 10 ) + (2.0 x 10 ) =
(30.0 x 10 ) + (2.0 x 10 ) =
3
4
32 x 10 = 3.2 x 10