October 05, 2015
6.2 Scientific Notation
The age of the Earth is about
4,540,000,000 years old.
As of September 3, 2013,
the official debt of the
United States government is
$16,738,618,787,875.
The mass of a helium atom is
0.000000000000000000000007 grams.
The Milky Way is about
1,000,000,000,000,000,000 km
wide.
October 05, 2015
exponent
x 10
base
a # between 1 & 10
1 < x < 10
October 05, 2015
Video Review
http://www.youtube.com/watch?v=AWof6knvQwE
October 05, 2015
October 05, 2015
Scientific Notation
for Large Numbers
Scientific notation is a way to write very large or very
small numbers.
In scientific notation, a number greater than or equal to 1
and less than 10 is multiplied by an integer power of 10.
decimal x 10exponent
2.3 x 105
Move the oval to see an example
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Place Value
October 05, 2015
1. Powers of 10
Use a calculator and write each power as a rational number.
101
102
103
104
105
106
______ ______ ______ ______ ______ ______
10-1
10-2
10-3
10-4
10-5
10-6
______ ______ ______ ______ ______ ______
What does it mean to have a positive exponent?
How are negative exponents used?
October 05, 2015
If your number
If your number
Is greater than 1
Is less than 1
Use a positive exponent
Use a negative exponent
Every time
Every time
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The base must be between 1 and 10:
1 < X < 10
2. Relocation of the Decimal Point: Relocate the decimal
point so that the new number lies between 1 and 10.
1) 34.63
2) 0.00257
_______
________
3) 0.000056
___________
4) 656,000,000,000
____________
3. Scientific Notation :Use the answers to Part 2 and write
each number in scientific notation.
1) 34.63
2) 0.00257
_______
________
3) 0.000056
___________
4) 656,000,000,000
____________
October 05, 2015
Sort the given values.
Not written in proper
scientific notation
Written in proper
scientific notation
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Drag the values that are NOT in scientific notation to the
trash can.
If you are correct, the values will disappear into the trash can.
1.000356 x 109
5.006 x 1021
0.035 x 108
8.2 x 106.5
78 x 1017
9 x 103
October 05, 2015
Decimal Notation to
Scientific Notation
The distance from Earth to Mars is
252,100,000,000 meters.
To write the distance in scientific notation, move the
decimal point behind the first digit in the number.
Leave off any zeros that would appear at the end
of the number behind the decimal point
The exponent will be the number of places you had to
move the decimal point.
2.521 x 10
Move the oval to see the answer
11
October 05, 2015
Fill in the blanks to convert the numbers into
scientific notation. (Pull the tabs to check your answer.)
x 10
=
x 10
70000900
Pull
903420000000000 =
9.0342
x 10
Pull
156800000000 =
Pull
x 10
Pull
2304000000 =
14
Click here for additional practice converting numbers into scientific notation.
October 05, 2015
Scientific notation is used to write really big numbers.
decimal notation
123,000,000,000
45,000,000
67,800,000,000,000
9,000
scientific notation
Move the star to count the
number of decimal
places.
The amount of moves will
give you the exponent
value.
October 05, 2015
Scientific notation is used to write really big numbers.
scientific notation
7.82 x 10
3
3.04 x 10
8
5 x 10
4
6.2103 x 10
decimal notation
10
The exponent tells you
how many decimal places
you need to move.
October 05, 2015
Scientific Notation to
Decimal Notation
Earth weighs 5.9721986 x 1024
kilograms.
To write the distance in decimal notation, move the
decimal point to the right the same number of places as
the exponent.
Move the oval to see the answer
5,972,198,600,000,000,000,000,000
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October 05, 2015
Scientific notation is used to write really small numbers.
decimal notation
scientific notation
0.000000034
0.0000000005609
0.000000000064
0.007
Move the star to count the
number of decimal
places.
The amount of moves will
give you the exponent
value.
October 05, 2015
Scientific notation is used to write really small numbers.
scientific notation
4.8 x 10
1.2 x 10
decimal notation
-6
The exponent tells you
how many decimal places
you need to move.
-12
-2
9 x 10
7.1034 x 10
-5
October 05, 2015
How do you know that a number written
in scientific notation will be really big or
really small ?
When do you write a
negative exponent when
converting to scientific
notation?
When do you write a positive
exponent when converting to
scientific notation?
October 05, 2015
Extra Practice
October 05, 2015
Extra Practice
October 05, 2015
Write the number in decimal notation in the white
box. Click on the number to check your answer.
8.002 x 10
8,002,000,000
9
Pull
7.65
x 106
7,650,000
1.70005 x 107
17,000,500
3.5 x 10
35,000,000,000,000
13
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October 05, 2015