September
Scientific Notation Notes
Count all the stars in this picture,
be as accurate as you can.
Scientific Notation
• Scientific Notation- is a way
to write a number multiplied by
a power of ten.
–Makes numbers easier to work
with
Scientific Notation
RULE:
#’s that are greater than 1 have a
POSITIVE exponent
• EXAMPLE 300,000,000
• 3.0 x 10 8 = 300,000,000
– it must be a number between 1 and 10
– this is always there ( x 10 )
– this is the number of places the decimal point is
moved.
Scientific Notation
#’s that are less than 1 (0.blah) have a
NEGATIVE exponent
•EXAMPLE
.0027
2.7 x 10 –3 = 0.0027
number between 1 and 10
always there
the number of places the decimal
point is moved.
Positive EXAMPLE
• 3.0 x 10 8 = 300,000,000
– number between 1 and 10
– 10 is always there
– the number of places the decimal point
is moved.
– If the starting number is positive (10 8),
move the decimal to the right.
– If the starting number is greater then 10
(3000,000,000), move the decimal to the
left.
Negative EXAMPLE
2.7 x 10 –3 = 0.0027
– number between 1 and 10
– 10 always there
– the number of places the decimal point
is moved.
– If the starting number is negative (10 -3),
move the decimal to the left.
– If the starting number is less then one
(.0027), move the decimal to the right.
Step by step
5,000,000,000
Write in scientific
notation
Step by Step
5,000,000,000.0
add decimal point if It is
not already there
Step by Step
5,000,000,000.0
Your answer needs to be
a number between 1-9.
In this example, the
answer should be 5.
Step by Step
5,000,000,000.0
Count the number of places
the decimal will need to be
moved to get that whole
number.
Step by Step
5, 0 0 0 , 0 0 0, 0 0 0 .0
9
8 7
6
5 4
3
2 1
Step by Step
5. 0 0 0 0 0 0 0 0 0
You moved it 9 places
Step by step
5.
Remove the extra
zeros
Step by step
5.0 x 10
Write down the X
symbol and the 10
because they are
always there.
Step by Step
5.0 X 10
9
Write the exponent behind the10.
This number should be the number of places
you moved the decimal point.
• Multiplication –
Step 1. multiply numbers before the
X sign.
Step 2. add the exponents.
Step 3. Simplify to a number
between 1-10
For Example:
(4 x 102) x (4 x 102) =
=16x104
=1.6 x10 5
Division –
Step 1. divide the numbers before
the x sign
Step 2. subtract exponents
Step 3. Simplify to a number
between 1-10
For example:
(4 x 102) / (4x103) =
=1 x 10-1
For example:
(4 x 103) / (4x102) =
=1 x 101
Scientific Notation
• Addition/Subtractionexponents must be the same.
–If exponents aren’t same,
change the numbers before the
x sign to do the math.
–If exponents are same, do math,
keep exponent same.
Scientific Notation
• Addition/Subtractionexponents must be the same.
–If exponents aren’t same,
change the numbers before the
x sign to do the math.
–If exponents are same, do math,
keep exponent same.