Download Compute With Scientific Notation

Scientific
Notation
Copyright © Science Stuff
Copyright © Science Stuff
Bell Ringer
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.
***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
Rule for Multiplication
(on graphic organizer)
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
Example
(write all steps on Graphic organizer next to the written steps)
Evaluate (7.2 x 103 ) (1.6 x 104 ). Express in Scientific Notation.
STEP 1: Multiply decimal #s 
STEP 2: Add the exponents 
STEP 3: Put all together…
WAIT! Is that in Scientific Notation!!??!!??
STEP 4: Move decimal forward 1.. Add 1 to exponent
Guided Practice
(turn paper over or pg 220 )
(8.4 x 102 ) ( 2.5 x 106 )
STEP 1: Multiply decimal # 
STEP 2: Add the exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Guided Practice
(turn paper over or pg 220 )
2
6
(2.63 x 10 )(2.5 𝑥 10 )
STEP 1: Multiply decimal # 
STEP 2: Add the exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Rule for Division
(on graphic organizer)
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
Example
(write all steps on Graphic organizer next to the written steps)
8.37 𝑥 108
Evaluate
. Express in Scientific Notation.
3
2.7 𝑥 10
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation???????
Yes. 3.1 is in between #s 1 and 10
Guided Practice
(turn paper over or pg 222 )
1.2 𝑥 107
2.4 𝑥 103
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
Guided Practice
(turn paper over )
4.64 𝑥 10−4
2.9 𝑥 10−6
STEP 1: Divide the decimal #s 
STEP 2: Subtract exponents 
STEP 3: Put it all together… 
WAIT! Is it in Scientific Notation!?!?
STEP 4:
Classwork: Complete
worksheet. Will check for
accuracy
HW pg 223 EVEN #s
Rule for Addition and Subtraction
(on Graphic Organizer)
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: Graphic
Organizer
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
Step 3: Put it all together! 99.29 x 104
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
9.929 x 105
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.
Step 2: Add coefficients decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice: Adding
(worksheet)
Evaluate each expression. Express in Scientific Notation.
(8.41 x 103 ) + (9.71 x 104 )
Step 1: Exponents MUST be the same.
Step 2: Add coefficients decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice: Adding
(worksheet)
Evaluate each expression. Express in Scientific Notation.
593,000+ (7.89 x 106 )
Step 1: Exponents MUST be the same.
Step 2: Add coefficients decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice:
Subtracting (worksheet)
Evaluate each expression. Express in Scientific Notation.
(1.263 x 109 ) + (1.525 x 107 )
Step 1: Exponents MUST be the same.
Step 2: Add coefficients decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Guided Practice:
Subtracting (worksheet)
Evaluate each expression. Express in Scientific Notation.
11,610,000 - (7.83 x 108 )
Step 1: Exponents MUST be the same.
Step 2: Subtract coefficients decimal #s
Step 3: Put it all together!
WAIT!? Is it in Scientific Notation?
Step 4: Put in Scientific Notation
Independent Work
MULTIPLY THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN
SCIENTIFIC NOTATION.
Problems:
1. (6 x 105) (1 x 102)
2. (4 x 106) (2 x 10-5)
3. (3.4 x 106) (1.8 x 103)
4. (8.1 x 10-7) (3.6 x 102)
5. (4.9 x 104) (6 x 10-3)
6. (5 x 10-5) (2 x 10-6)
7. (0.000 000 015) *
(101,654,000,000)
8. (10,456,300,950) *
(9,754,321)
1.
2.
3.
4.
5.
6.
7.
8.
Answers:
x 107
6
8 x 101
6.12 x 109
2.92 x 10-4
2.94 x 102
1 x 10-10
1.53 x 103
1.02 x 1017
DIVIDE THE FOLLOWING NUMBERS. GIVE YOUR ANSWER IN
SCIENTIFIC NOTATION.
Problems:
1. (6 x 105)  (2 x 104)
2. (8 x 103)  (2 x 10-5)
3.(7.4 x 104)  (1.8 x 103)
4.(8.19 x 10-4)  (1.6 x
102)
5.(4.3 x 103)  (6.1 x 10-3)
6. (8 x 10-5)  (2 x 10-6)
7. (0.000 009 023) 
(101,351,000)
8. (12,701,300,950) 
(4,754,321)
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
3 x 101
4 x 108
4.11 x 101
5.12 x 10-6
7.05 x 105
4 x 101
8.9 x 10-14
2.67 x 103
ADD OR SUBTRACT EACH OF THE FOLLOWING NUMBERS. GIVE
YOUR ANSWER IN SCIENTIFIC NOTATION.
Problems:
1. (6 x 104) + (3 x 104)
2. (6 x 10-5) - (3 x 10-5)
3. (1.4 x 105) + (1.4 x 103)
4. (8 x 104) - (1.6 x 102)
5. (4.9 x 105) + (6.1 x 10-3)
6. (8 x 10-5) - (5 x 10-6)
7. (0.079 323) +
(0.196,351,000)
8. (12,701,555,950) (40,754,321)
Answers:
1. 9 x 10 4
2. 3 x 10 -5
3. 1.41 x 10 5
4. 7.98 x 10 4
5. 4.9 x 10 5
6. 7.5 x 10 -5
7. 2.76 x 10 -1
8. 1.27 x 10 10
Created by Amy Brown – Science
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