Download To write a number in scientific notation

Bell Ringer
Scientific
Notation
Copyright © Science Stuff
Copyright © Science Stuff
Using Scientific
Notation in
Multiplication,
Division, Addition
and Subtraction
Scientists must be able
to use very large and
very small numbers in
mathematical
calculations. As a
student in this class,
you will have to be
able to multiply, divide,
add and subtract
numbers that are
written in scientific
notation. Here are the
rules.
How to Use Scientific
Notation
•In scientific notation, a number is
written as the product of two
numbers…..
…..A coefficient and
10 raised to a
power.
The number 4,500 is written in scientific
notation as ________________.
4.5 x 103
The coefficient is _______.
4.5
The coefficient must be a number
greater than or equal to 1
and smaller than 10.
The power of 10 or exponent in this
example is _____.
3
The exponent indicates how many times the
coefficient must be multiplied by 10 to equal
the original number of 4,500.
Rules to Remember!
If a number is greater than
10, the exponent will be
__________
positive and is equal to
the number of places the
decimal must be moved to
the _____
left to write the
number in scientific
notation.
Rules to Remember!
If a number is less than 1, the
exponent will be
___________
negative and is equal to
the number of places the
decimal must be moved to
the _______
right to write the
number in scientific
notation.
A number will have an
exponent of zero if:
….the number is equal
to or greater than 1,
but less than 10.
1. Move the decimal to the right of the
first non-zero number.
2. Count how many places the decimal
had to be moved.
3. If the decimal had to be moved to the right,
the exponent is negative.
4. If the decimal had to be moved to the left,
the exponent is positive.
To emphasize again: The exponent counts how many places you
move the decimal to the left or right.
***VERY IMPORTANT***
When computing with Scientific Notation, sometimes
you have to change the exponent. To do so, count how
many times you need to move the decimal.
 If you move the decimal forward, ADD that number
to the exponents.
 If you move the decimal backward, SUBTRACT
that number to the exponents
Write as Scientific Notation
1) 0.00012
2) 1000
3) 0.01
4) 12
5) 0.987
Write as Scientific Notation
1) 1.2 x 10-4
2) 1 x 103
3) 1 x 10-2
4) 1.2 x 101
5) 9.87 x 10-1
Write as Whole Number or
Decimal
1) 4.9 x 102
2) 3.75 x 10-2
3) 5.95 x 10-4
4) 9.46 x 103
5) 3.87 x 101
Write as Whole Number
or Decimal
1) 490
2) 0.0375
3) 0.000595
4) 9460
5) 38.7
Rule for Multiplication
When multiplying numbers written in scientific
notation…..
Step 1: Multiply the decimal numbers
Step 2: Add the exponents (follow Exponent
Rule)
Step 3: Make sure you have one digit (non
zero) in front of the decimal
Guided Practice
2
6
(8.4 x 10 ) ( 2.5 x 10 )
STEP 1: Multiply decimal # (8.4 x 2.5) = 21
STEP 2: Add the exponents  (102 x 106) = 108
STEP 3: Put it all together…  (21 x 108)
WAIT! Is it in Scientific Notation!?!?
STEP 4: (2.1 x 109)
Guided Practice
2
−4
(2.63 x 10 )(2.5 𝑥 10 )
STEP 1: Multiply decimal #  (2.63 x 2.5) = 6.575
2 x 10-4) = 10-2
(10
STEP 2: Add the exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4: (6.575 x 10-2)
(6.575 x 10-2)
Rule for Division
When dividing numbers written in
scientific notation…
Step 1: Divide the decimal numbers
Step 2: Subtract exponents (follow
Exponent rules)
Step 3: Make sure you have one digit (non
zero) in front of the decimal
Guided Practice
1.2 𝑥 107
2.4 𝑥 103
STEP 1: Divide the decimal #s  (1.2 ÷ 2.4) = 0.5
STEP 2: Subtract exponents  (107 ÷ 103) = 107-3 = 104
STEP 3: Put it all together…  (0.5 x 104)
WAIT! Is it in Scientific Notation!?!?
STEP 4: (5.0 x 104)
Guided Practice
4.64 𝑥 10−4
2.9 𝑥 10−6
STEP 1: Divide the decimal #s  (4.64 ÷ 2.9) = 1.6
STEP 2: Subtract exponents 
(10-4 x 10-6) = 10-4-(-6) = 102
STEP 3: Put it all together…  (1.6 x 102)
WAIT! Is it in Scientific Notation!?!?
STEP 4: (1.6 x 102)
Rule for Addition and Subtraction
To add or subtract numbers written in scientific
notation, you must….express them with the same
power of ten.
Step 1: Make sure that both exponents are the SAME! ** you
might have to move a decimal forward or backward to have
same exponent #s
Step 2: Add coefficients decimal #’s together
Step 3: Make sure it is in SCIENTIFIC NOTATION!
Example
Evaluate each expression. Express in Scientific Notation.
(6.89 x 104 ) + (9.24 x 105 )
Step 1: Exponents MUST be the same. Let’s make
9.24 x 105 as 92.4 x 104
Step 2: Add coefficients decimal #s (6.89 + 92.4) = 99.29
(99.29 x 104)
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
4)
(9.929
x
10
Step 4: Put in Scientific Notation
Example: Graphic
Organizer
Evaluate each expression. Express in Scientific Notation.
(1.03 x 109 ) - (4.7 x 107 )
Step 1: Exponents MUST be the same.
103 x 107
Step 2: Subtract coefficients decimal #s (103 – 4.7) = 98.3
7)
(98.3
x
10
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
(9.83 x 108)
Guided Practice: Adding
(worksheet)
Evaluate each expression. Express in Scientific Notation.
593,000+ (7.89 x 106 )
Step 1: Exponents MUST be the same. 0.593 x 106
(0.593 + 7.89) =
8.483
Step 3: Put it all together! (8.483 x 106)
WAIT!? Is it in Scientific Notation?
Step 2: Add coefficients decimal #s
Step 4: Put in Scientific Notation (8.483 x 106)