Transcript Physics_Scientific_Notation_Week 3 PPT

Do NOW
• Please complete your Do
NOW located in your
packet
• I will collect it at the end
of class in at end of class.
• Please work silently and
independently
Scientific Notation
Objective
• SWBAT correctly convert from standard numbers into scientific
notation, and back.
What is Scientific Notation?
• Scientific Notation is used to express very large
and very small numbers more easily.
• It is a way of writing a number with “Powers of
Ten”
• If number is greater than 1 : the Power of Ten is
POSITIVE.
• If number is smaller than 1: the Power of Ten is
NEGATIVE.
SN in Practice: Hope Diamond
• Made of the element Carbon
• Weight: 45 carats
• Weight: 9000 mg = 9 g
• Mass of one Carbon atom: 2X10-23 g
• 4.6X1023 atoms
• LOTS OF ZEROS! TOO MUCH TO WRITE.
$200–$250 million
RULES
1.23 x
4
10
EXPONENT:
Positive for big
numbers, Negative
for fractions!
BASE: Always 10!
NUMBER: Decimal
always after first
digit
Conversion: #’s Greater than 1
Greater Than 1
1. Write a decimal after
the first digit on the left
2. Count how many
numbers are still after
decimal and stop at
original decimal point
3. Write the coefficient *
10 POSITIVE exp
Example
• Hillary Clinton makes:
• Standard Notation:
$186,600.00 per year
• Step 1: 1.86600.00
• Step 2: Count 5 numbers to
decimal
• Step 3: coefficient is 5
• Answer: 1.86 x 10 5
Conversion: #’s Less than 1
Less than 1
1. Look where the decimal
already is
2. Move the decimal to
the right of the first
non-zero digit
3. Count how many digits
you moved
4. Write this as your base
10 NEGATIVE exp
Example
• A germ is:
• .00000179 centimeters
long, convert to Sci Not.
• Step 1: 1.79
• Step 2: moved 6 digits to
the right
• Step 3: the exponent will
be -6 (we moved to the
right)
• Answer 1.79 x 10 -6
Guided Practice
• Chris Paul has 2,966 career assists.
Write this in scientific notation
• Will Smith makes $35,000,000 per
film. Write this in scientific notation.
Guided Practice
• LaDainian Tomlinson makes 3.825 x 10 6
dollars/year. Write this in standard
notation.
3,825,000
• A human hair is 56 x 10 -6 meters thick.
Write this in standard notation.
0.0000056 meters
Independent
• On your own, worksheet!
Adding and Subtracting in
Scientific Notation
Adding and Subtracting…
• The important thing to remember about adding or subtracting
is that the exponents must be the same!
• If the exponents are not the same then it is necessary to
change one of the numbers so that both numbers have the
same exponential value.
Adding and Subtracting…
• The general format for adding is as follows…
(N x 10x) + (M x 10x) = (N + M) x 10x
• The first step, if necessary, is to change one of the numbers so
that both numbers have the same exponential value.
• Secondly, add the N and M numbers together and express as
an answer.
• The final step is to multiply the result by the 10x.
• (It may be necessary to put the resulting answer into proper
scientific notation.)
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.
(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.
(4.89 x 107)/(2.74 x 104)
4.89 / 2.74 = 1.78
7–4=3
***1.78 x 103***
Independent Practice
• On your own, worksheet!