Transcript Scientific Notation

Scientific Notation
What is scientific Notation?

a way of expressing really big numbers
or really small numbers in a more
concise form.
Consists of:

Coefficient
– A number greater
than 1 and less than
10

Base
– 10

Exponent
– “power” of 10
Nx
x
10

Scientific Notation
6.02 x
6
10 m

Standard form
6,020,000 m
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 in standard form
was less than 1, then the exponent is
negative.
 If the original number in standard form
was greater than 1, then the exponent is
positive.

Example 1
Convert 289,800,000 to scientific notation
 Place the decimal so there is one non-zero digit to its
left :
– 289,800,000
2.898

Count the number of places the decimal was moved
to determine exponent
– moved 8 places, so exponent is 8
 Determine if exponent is + or – based on value of
number in standard form
– Original number in standard form is greater than one, so
exponent is +

Final Answer: 2.898 x 108
Example 2
Convert 0.000567 to scientific notation
 Place the decimal so there is one non-zero digit to its
left :
– 0.000567
5.67


Count the number of places the decimal was moved
to determine exponent
– moved 4 places, so exponent is 4
Determine if exponent is + or – based on value of
number in standard form
– Original number in standard form is less than one, so
exponent is -

Final Answer: 5.67 x 10-4
Practice

Use the link below to practice
converting standard form to scientific
notation.
– Converting to Scientific Notation
To change scientific notation to
standard form…



Just move the decimal the number of places given by the
exponent
Positive exponents will result in numbers greater than one when
in standard form
– So just think “which way do I move the decimal to make the
resulting number greater than one?”
– To the right!
Negative exponents will result in numbers less than one when in
standard form
– So just think “which way do I move the decimal to make the
resulting number less than one?”
– To the left!
(Use zeros as placeholders!)
Example 3





Convert 5.093 x 106 to standard form.
The exponent is 6, so move the decimal 6
places.
The exponent is positive, meaning the result
in standard form is greater than one.
– Decimal must be moved to the right to get
a result greater than one.
5.093 000 (note that three 0’s needed to hold
places)
Answer: 5,093,000 (moved 6 places to the
right)
Example 4
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


Convert 1.976 x 10-4 to standard form.
The exponent is 4, so move the decimal 4
places.
The exponent is negative, meaning the result
in standard form is less than one.
– Decimal must be moved to the left to get a
result less than one.
00001.976 (note the 0’s added as
placeholders)
Answer: 0.0001976 (moved 4 places to the
left)
Practice

Use the link below to practice
converting scientific notation to standard
form
– Converting to Standard Form
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
Using scientific notation in
calculations: multiplication and
division
When multiplying numbers in scientific
notation, multiply the coefficients and
add the exponents.
 When dividing numbers in scientific
notation, divide the coefficients and
subtract the exponents.

Example 5
(2.0 x 105) x (1.5 x 10-2)= ?
 Multiply the coefficients

2.0 x 1.5=3.0

Add the exponents
5 + (-2) = 3 (new exponent)
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Answer: 3.0 x 103
Example 6
(6.0 x 105) / (1.5 x 10-2)= ?
 Divide the coefficients
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6.0 / 1.5= 4.0
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Subtract the exponents
5 - (-2) = 7 (new exponent)
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Answer: 4.0 x 107
Using scientific notation in
calculations: addition and
subtraction
When adding or subtracting numbers in
scientific notation, the exponents MUST
MATCH (unless you punch it into a
calculator!)
 The exponent on the final answer is the
same as the exponent on the terms in
the problem.

Changing the exponent
(1.5 x 10-1) + (2.5 x 102) = ??
 The first thing we have to do is make
our exponents match- they both either
need to be -1 or 2, it doesn’t matter
which, as long as they match, without
changing the magnitude (value) of the
quantity represented.


1.5 x 10-1 = _____x 102
– We are moving three powers of 10 to get
from -1 to 2 (10-1  100  101  102)
– Think : 2 – (-1)= 3
– So we need to move our decimal 3 places
– Now which direction?
– Since our original number is less than one,
it has to stay less than one, so which way
do we go? To the left!

1.5 x 10-1 = 0.0015 x 102

Note that we moved in the positive direction
to change the exponent from -1 to 2, and
the negative direction to change the
decimal.
Now we can add our numbers together
 (1.5 x 10-1) + (2.5 x 102) =
 (0.0015 x 102) + (2.5 x 102) =
 (0.0015 +2.5) x 102= 2.5015 x 102

Let’s try to make both exponents
-1…
(1.5 x 10-1) + (2.5 x 102) =
 2.5 x 102 =____ x 10-1
 To get from 102 to 10-1, we must move
three places in the negative direction.
 So we will move our decimal 3 places in
the positive direction
 2.5 x 102 =2500 x 10-1

Now we can add our numbers
 (1.5 x 10-1) + (2500 x 10-1) =
 (1.5 + 2500) x 10-1= 2501.5 x 10-1

Note that our answer is not in correct
form (one nonzero digit to left of
decimal) so we need to put it in correct
form: use the same logic
 Move decimal three places in negative
direction, then move exponent three
places in positive direction
 2501.5 x 10-1 = 2.5015 x 102

So, to change an exponent…
If you are going in the positive direction
to get to the new exponent, move the
decimal in the negative direction.
 If you are going in the negative direction
to get to the new exponent, move the
decimal in the positive direction.

A note about scientific notation
and your calculator…

On the graphing calculator, scientific
notation is best done with the
button.
4.58 x 106 is typed 4.58
6

The other option is to use the
4.58 x 10
6
But you have to be careful with this when dividing and
make sure you use parantheses!
Use a calculator to evaluate:
-5
4.5 x 10
1.6 x 10-2

Type 4.5
-5
1.6
-2
You must include parentheses if you
don’t use the !! key but 10
instead!
 (4.5 x 10
-5)
(1.6 x 10
-2)

=0.0028125
 Write in scientific notation.
 =2.8125 x 10-3
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DON’T FORGET!!!
 When you are copying an answer from
your calculator screen make sure you
include the scientific notation if present.
 If your calculator answer was
1.93E-2 you would copy down 1.93 x 10-2
on your paper. The “E” in the answer
means “x 10”
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