Transcript Scientific Notation

Scientific Notation
What is scientific Notation?
Scientific notation is an efficient way of
expressing really big numbers or really
small numbers.
 It is most often used in “scientific”
calculations where the analysis must be
very precise.

Why use scientific notation?
For very large and very small numbers,
these numbers can be converted into
scientific notation to express them in a
more concise form.
 Numbers expressed in scientific
notation can be used in a computation
with far greater ease.

Scientific notation consists of
two parts:

A number between 1 and 10

A power of 10
N x 10x
Are the following in scientific notation?
Changing standard form to
scientific notation.
To change standard form to
scientific notation…
Identify where the decimal point is on
the original number
 Move the decimal point so that the
original number becomes a number
between 1 and 10.
 Count the number of decimal places the
decimal point has “moved” from the
original number. This will be the
exponent on the 10.

Continued…

If the original number was less than 1,
then the exponent will be negative.

If the original number was greater than
1, then the exponent will be positive.
Example 1

Given:
289,800,000
Use: 2.898
 Decimal place moved 8 places
 Exponent is 8
 Exponent is positive because original
number is greater than 1


Answer:
2.898 x
8
10
Example 2

Given:
0.000567
Use: 5.67
 Decimal place moved 4 places
 Exponent is 4
 Original number less than 1 so …
 Exponent is negative


Answer:
5.67 x
-4
10
Changing scientific notation to
standard form.
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 10.
 Use zeros to fill in places.

Example 3
Given: 5.093 x 106
 Exponent is positive 6 , move 6 places to
make number bigger (to the right).
 1 place = 50.93 2 places = 509.3
 3 places = 5093. 4 places = 50930.
 5 places = 509300. 6 places = 5093000
 Answer: 5,093,000
 Decimal moved 6 places to the right

Example 4
Given: 1.976 x 10-4
 Exponent is negative 4, so the number
is less than 1.
 move decimal 4 places to the left to
make number less than 1.


Answer: 0.0001976 (moved 4 places
to the left)
Are These in Scientific Notation??
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23.98393 x 109
4.19385930 x 104
98920.188438 x 10-3
2.22221 x 100
9.002 x 1002
39.992934 x 100
0.1103827493920920284757 x 102
1.00 x 1056
2.39403 x 10-23
9.00078 x 10-1
Even More Practice

Below is a list of links to games and
activities all having to do with scientific
notation.
– http://www.aaamath.com/dec71idec2sci.html
– http://janus.astro.umd.edu/cgibin/astro/scinote.pl
– http://www.sciencejoywagon.com/physicsz
one/lesson/00genral/dectosci.htm
Now take the quiz to test your
scientific notation skills!

Click on the link below to take the quiz
and then use the answer key for the
correct answers.
– Quiz
– Answers