SCIENTIFIC NOTATION
DID YOU KNOW……..
• The distance from Earth to the North Star is
about 10,000,000,000,000,000,000 meters.
• The thickness of a soap bubble is 0.0000001
meter.
• The United States has 12,916,000 acres
reserved for state parks.
MATH FOLKS CAME UP WITH A WAY TO
DEAL WITH REALLY BIG NUMBERS AND
REALLY LITTLE NUMBERS
This method is called Scientific Notation.
Using scientific notation we can write a
number as the product of a power of 10 and
a number greater than or equal to 1, but less
than 10.
THE DISTANCE FROM EARTH TO THE NORTH
STAR IS ABOUT 10,000,000,000,000,000,000
METERS.
10,000,000,000,000,000,000 written out is called
“standard form”.
Using scientific notation, we can write the same
number like this:
1.0 ´10
19
THE THICKNESS OF A SOAP BUBBLE IS ABOUT
0.0000001 METER.
0.0000001 written out is called “standard form”.
Using scientific notation, we can write the same
number like this:
1.0 ´10
-7
RULES FOR SCIENTIFIC NOTATION
To be in proper scientific notation
the number must be written with
* a number between 1 and 10
* and multiplied by a power of
ten
23 X 105 is not in proper scientific
notation. Why?
HERE’S HOW IT WORKS:
137,000,000 can be rewritten
as
1.37 X
8
10
NOW YOU TRY
Using scientific notation, rewrite
the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104
NOW WORK BACKWARD. CONVERT
THESE TO STANDARD FORM:
1.23 X 105
123,000
6
6.806 X 10
6,806,000
TRY THESE
4,000
4 X 103
2.48 X 103
2,480
6.123 X 106
6,123,000
306,000,000
3.06 X 108
WHY DOES A NEGATIVE EXPONENT
GIVE US A SMALL NUMBER?
10000 = 10 x 10 x 10 x 10 = 104
1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 101
0
1 = 10
Do you see a pattern?
NOTICE THE PATTERN
= 10-1
1
10
1
100
1
1000
1
10000
=
=
=
= 10-2
1
10
2
= 10-3
1
10
3
1
10
4
= 10-4
HERE’S HOW IT WORKS WHEN YOU
HAVE A SMALL NUMBER:
.0307 can be rewritten as
3.07´10
-2
YOUR TURN
Using Scientific Notation,
rewrite the following numbers.
0.000882
8.82 X 10-4
0.00000059
5.9 X 10-7
0.00004
4 X 10-5
MORE EXAMPLES
1) 0.0004
2)
3)
4)
5)
4 X 10-4
1.248 X 10-6
.000001248
6.123 X 10-5
.00006123
0.00000306
3.06 X 10-6
0.000892
8.92 X 10-4
HOMEWORK
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