Download Scientific Notation

Powers of Ten /
Scale
Mr. Davis
Why do we care?

Cannot describe many things in science apart
from powers of 10

Scientific notation useful in Physics,
Chemistry, Economics, Programming,
Engineering, …
http://powersof10.com/film
Scientific Notation
By Jenny Erickson
What is scientific Notation?
Scientific notation is a 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
Which of these are in scientific notation?
What are the common equivalents?
1.0 X 100
10.2 X 102
0.1
100
1.5 x 101
Changing standard form to
scientific notation.
To change standard form to
scientific notation…
Place the decimal point so that there is
one non-zero digit to the left of the
decimal point.
 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 is negative. If the
original number was greater than 1,
then the exponent is positive.
Example 1
Given: 289,800,000
 Use: 2.898 (moved 8 places)
 Answer: 2.898 x 108

Example 2
Given: 0.000567
 Use: 5.67 (moved 4 places)
 Answer: 5.67 x 10-4

Changing scientific notation to
standard form.
To change scientific notation to
standard form…
Simply move the decimal point to the
right for positive exponent 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
 Answer: 5,093,000 (moved 6 places to
the right)

Example 4
Given: 1.976 x 10-4
 Answer: 0.0001976 (moved 4 places to
the left)

How do I convert these to scientific notation?
0.123456789
123456789
1,000,000,000,000,000,000
0.000000000123456789
( 0.000 000 000 123456789)
Multiplying and
Dividing
Multiplying in Scientific Notation
Multiplying…
The general format for multiplying is as
follows…
 (N x 10x)(M x 10y) = (N)(M) x 10x+y
 First multiply the N and M numbers
together and express an answer.
 Secondly multiply the exponential parts
together by adding the exponents
together.
 Finally multiply the two results for the
final answer.

Multiplying…

(2.41 x 104)(3.09 x 102)
2.41 x 3.09 = 7.45
4 + 2 = 6
7.45 x 106
Dividing in Scientific Notation
Dividing…
The general format for dividing is as
follows…
 (N x 10x)/(M x 10y) = (N/M) x 10x-y
 First divide the N number by the M
number and express as an answer.
 Secondly divide the exponential parts
by subtracting the exponent from the
exponent in the upper number.
 Finally multiply the two results together
to get the final answer.

Dividing…
 (4.89 x 107)/(2.74 x 104)
 4.89
/ 2.74 = 1.78
7 – 4 = 3
 1.78
x 103
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
Quiz Time!!!

Below is a set of links for a quiz on
multiplying and dividing numbers in
scientific notation, and there is a link to
get the answers to the quiz.
Quiz on Multiplying and Dividing
 Answers to Quiz
