Download Scientific Notation

OBJECTIVE
September 9, 2013
In our study of
SCIENTIFIC NOTATION (Supporting)
the students will be able to
Express numbers in standard form
(COMPREHENSION)
and show what they learned by
Converting Numbers.
(COMPREHENSION)
SCIENTIFIC NOTATION
A QUICK WAY TO WRITE
REALLY, REALLY
BIG
OR
REALLY, REALLY SMALL
NUMBERS.
Examples of REALLY BIG
NUMBERS!
100 quadrillion cells make up the human body
The largest known number that
can't be expressed in terms of
any smaller numbers, aka a
PRIME NUMBER, was
discovered in 2008, is 243,112,609 .
The total
number
of
Which is a number
with
nearly
particles in the universe, is
13 million digits
generally thought to be
around 1080 !
Examples of
NUMBERS.
really, really small
•the charge on an electron: roughly
1.6 × 10-19 C (negative)
Mathematicians
are Lazy!!!
They decided that by
using powers of 10,
they can create short
versions of long
numbers.
Scientific Notation
A number is expressed in
scientific notation when it is
in the form
ax
n
10
where a is between 1 and 10
and n is an integer
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?
To change a # to scientific notation
Ex. 1,530,000
Steps
1.put decimal between #’s so you get a #
between 1 and 10
it can NOT be bigger than 10
(The amount has to be greater than $1, but less than $10!)
2. how many places you moved the decimal
is the exponent
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.
Ex. 1,530,000
1.53 x 10
6
45620
.00236
2.36 x 10
-3
4
4.562 x 10
Ex. 0.000 000 000 753 kg
7.53  10
10
This is the mass of a dust particle!
Ex 7,100,000,000
7.1 10
9
This is the distance from Earth
to Pluto in miles
Example 3
Given:
289,800,000
Move the decimal: 2.898
(moved 8 places)
Answer: 2.898 x 108
Example 4
Given:
0.000567
Move the decimal: 5.67
(moved 4 places)
Answer: 5.67 x 10-4
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
1 = 100
Do you see a pattern?
The nucleus of a human cell is
about 0.00000704 meters in
diameter. What is the length in
scientific notation?
7.04 X
-6
10
A ribosome, another part of a cell, is
about 0.00000000375 of a meter in
diameter. Write the length in
scientific notation.
-9
3.75 X 10
Practice – Convert from Standard Form to
Scientific Notation
1.
2.
3.
4.
5.
0.1333
60000000
23450
0.007904
0.0000035093
1) Decide whether the number is in scientific notation. If not, tell
why the number is not in correct scientific notation
a. 0.54 x 103
b. 2.2 x 100.3
c. 800 x 105
2) Write the following numbers using scientific notation:
a.
7234
b.
0 .085
c.
1.11
Write in scientific notation.
1.
0.0053 =
2.
634,000 =
3. 55,600,000 =
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:
6
10
5.093 x
Answer: 5,093,000
(moved 6 places to the
right)
Example 4
Given:
-4
10
1.976 x
Answer: 0.0001976
(moved 4 places to the
left)
Practice
1.
2.
3.
4.
5.
5
10
1.493 x
-4
2.908 x 10
2
3.90284 x 10
-1
1.333 x 10
7
6.0000009 x 10
Practice
6.
7.
8.
9.
10.
2.345 x 104
0
4.50000 x 10
-3
7.904 x 10
3.5093 x 10-6
-2
2.309 x 10
Additional Example : Life Science Application
A human skin cell has a diameter of
approximately 4.11 x 10-5 meters. A cell from
the liver has a diameter of 1.5 x 10-5 meters.
Which cell has a greater diameter?
4.11 x 10-5
1.5 x 10-5
10-5 = 10-5
Compare powers of 10.
4.11 > 1.5
Compare the values
between 1 and 10.
4.11 x 10-5 > 1.5 x 10-5
The first cell has a greater diameter.
1.
5.3 X
-3
10 =
6.34 X
5
10 =
3. 5.56 X
7
10 =
2.
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
Changing standard form to
scientific notation.
http://www.youtube.com/watch?v=HtXTKrigYqk&feature=relmfu