Dividing Numbers in Scientific Notation,
Multiplying/Dividing Numbers in Scientific Notation,
Distance/Rate/& Time Units
Do Now - √4 + √49 /√100 + 7
 Please get out your guided notes from last week.
 Respond to Wednesday’s Do Now:
1.
Write an expression for the product of these two
numbers:
(3.2x109)
& (2.9x104)
DO NOT SOLVE!
1.
Solve. (2.4x105) x (5.2x107)
Class Averages
100
90
80
70
85
70
88 85 85
85
72
70
66
85
63
68
60
Quiz 1
50
Quiz 2
40
Big Goal
30
20
10
0
3rd Period
5th Period
6th Period
7th Period
85% of Higher MATHLETES!
 3rd Period
 5th Period
 Gerardo
 Torez
 Chyna
 Katelyn
 Dezmond
 Solomon
 Luke
 Reggie
 DeRico
 Abdul
 Jalen
 Vicki
 Wesley
 Ceirsten
 Mario
 6th Period
 Jaycee
 Mallory
 Ellie
 7th Period
 Autumn
 Grace
 Jordan
100% Math All-Stars!
 3rd Period
 JaWaun
 5th Period  6th Period
 Tristan
 Tylesha
 Aliciah
 Steven
 Freeman
 Jayla
 Brandon
 Jim
 7th Period
 Kalei
 Jack
Tracking Your Quiz
 You are to track your quiz on your own.
 Please write down your class average so you can do this
on your own time.
 3rd period – 66%
 5th period – 86%
 6th period – 63%
 7th period – 68%
Week Agenda
 Monday – Dividing Numbers in Scientific
Notation
 Tuesday – Simplifying Scientific Notation
Expressions
 Wednesday – Adding/Subtracting Numbers in
Scientific Notation
 Thursday – Scientific Notation Word Problems
 Friday - Quiz
Today’s Agenda
 Do Now – 6 minutes
 Quiz Return/ Shout Outs – 4 minutes
 Agenda – 1 minutes
 Rules of Exponents – 5 minutes
 Dividing Numbers in Scientific Notation INM - 10
minutes
 Dividing Numbers in Scientific Notation GP & IP – 15
minutes
 Exit Ticket – 5 minutes
Today’s Objective
SWBAT divide
numbers in
scientific
notation.
Computing with Scientific Notation
 Last week we worked with adding numbers in
scientific notation and today we will divide numbers in
scientific notation.
 Like last week, we will learn hand motions to help us
remember the concept.
Dividing Exponents
 When divide numbers with different exponents, you simply
subtract the exponents, if the base number is the same.
 Example 1:
10315 ÷ 10-10
 If the base number is the same, you subtract the exponents.
 Solution: ____________________
 Examples 2:
103 ÷ 10-4
 If the base number is the same, you subtract the exponents.
 Solution: ____________________
 Examples 3:
10-20 ÷ 103
 If the base number is the same, you subtract the exponents.
 Solution: ____________________
Dividing Numbers in Scientific
Notation
 If you remember, there are two factors to a number in
scientific notation:
Factor 1: A number that is greater than 1, but less than
10.
2. Factor 2: A power of 10.
1.
 When you divide numbers in scientific notation, we
divide all factor 1 numbers, and then subtract the
exponents of factor 2 together.
Dividing Numbers in Scientific
Notation
 Example 4: (8.4 x 103) ÷ (2.1 x 10-4)
 First, we ID our factor 1 numbers.

8.4 & 2.1
 Second, we divide our factor 1 numbers.
 8.4 ÷ 2.1 = 4
 This is now our new factor 1 of our quotient.
 Third, we divide the numbers with exponents.
 103 ÷ 10-4
 Remember we subtract the exponents when the base is the same.
 10 (3-(-4)) = 107
 Fourth, we combine our factors to get our final answer.
 Factor 1: 4
 Factor 2: 107
 Final answer: 4 x 107
Dividing Numbers in Scientific
Notation
 Example 5: (1.8 x 10 ) ÷ (7.5 x 10 )
6
2
 First, we ID our factor 1 numbers.
 1.8 & 7.5
 Second, we divide our factor 1 numbers.
 1.8 ÷ 7.5 = .24
 This is now our new factor 1 of our quotient.
 Third, we divide the numbers with exponents.
 106 ÷ 102
 Remember we subtract the exponents when the base is the same.
 10 (6-2) = 104
 Fourth, we combine our factors to get our final answer.
 Factor 1: .24
 Factor 2: 104
 Temporary Final answer: .24 x 104
 But your answer MUST BE IN CORRECT scientific notation form.
 We need to move the decimal point one place to the right so our factor 1 is
greater than 1, but less than 10  2.4
 When we do this, we must account for the change in factor 2. Factor 2 goes
from 104 to 1o3.
 Actual final answer: 2.4 x 103
Dividing Numbers in Scientific
Notation
 Example 6: (1.2 x 10-8) ÷ (9.6 x 1012)
 First, we ID our factor 1 numbers.

1.2 & 9.6
 Second, we divide our factor 1 numbers.
 1.2 ÷ 9.6 = .125
 This is now our new factor 1 of our quotient.
 Third, we divide the numbers with exponents.
 10-8 ÷ 1012
 Remember we subtract the exponents when the base is the same.
 10 (-8-12) = 10-20
 Fourth, we combine our factors to get our final answer.
 Factor 1: .125
 Factor 2: 10-20
 Temporary Final answer: .125 x 10-20
 But your answer MUST BE IN CORRECT scientific notation form.
 We need to move the decimal point one place to the right so our factor 1 is greater than 1,
but less than 10  1.25

When we do this, we must account for the change in factor 2. Factor 2 goes from 10-20 to
1o-21.
 Actual final answer: 1.25 x 10-21
Dividing Numbers in Scientific
Notation
 Example 7: (3.4 x 103) ÷ (6.8 x 10-2)
 First, we ID our factor 1 numbers.

3.4 & 6.8
 Second, we divide our factor 1 numbers.
 3.4 ÷ 6.8 = .5
 This is now our new factor 1 of our quotient.
 Third, we divide the numbers with exponents.
 103 ÷ 10-2
 Remember we subtract the exponents when the base is the same.
 10 (3-(-2) = 105
 Fourth, we combine our factors to get our final answer.
 Factor 1: .5
 Factor 2: 105
 Temporary Final answer: .5 x 105
 But your answer MUST BE IN CORRECT scientific notation form.
 We need to move the decimal point one place to the right so our factor 1 is greater than 1,
but less than 10 5

When we do this, we must account for the change in factor 2. Factor 2 goes from 105 to
104.
 Actual final answer: 5 x 104
Dividing Numbers in Scientific
Notation
 Example 8: (9 x 10 ) ÷(2.4 x 10 )
-11
8
Dividing Numbers in Scientific
Notation
 Example 9: (9.45 x 10 ) ÷(1.5 x 10 )
10
6
Dividing Numbers in Scientific
Notation
 Work on this one with your partner.
 Example 10:
(3.24 x 10-4) ÷(8.1 x 10-7)
Dividing Numbers in Scientific
Notation
 Work on this one with your partner.
 Example 11:
(4.2 x 10-8) ÷(1.68 x 10-2)
Dividing Numbers in Scientific
Notation
 Work on this one on your own.
 Example 12:
(4.64 x 10-4) ÷(2.9 x 10-6)
Dividing Numbers in Scientific
Notation
 Work on this one on your own.
 Example 13:
(3.7x 105) ÷ (2.9 x 1011)
Dividing Numbers in Scientific
Notation
 Example 14: Which one of these expressions correctly
identifies the quotient of these two numbers
x 10-2) ÷ (9.5 x 10-4)?
a) (7.9 x 9.5) x 10(-2+-4)
b) (7.9 x 9.5) x 10(-2--4)
c) (7.9 ÷ 9.5) x 10(-2+-4)
d) (7.9 ÷ 9.5) x 10(-2--4)
(7.9
Exit Ticket
 Each of you will complete your exit ticket on a note
card.
 There are 3 problems.
 You will complete the exit ticket in 5 minutes and it
must be turned in before you can exit the classroom.
 You must work SILENTLY and INDEPENDENTLY.
 HOMEWORK – Math Book Page 120: #s 5-8 & 20-25!

Exit Ticket
1.
(3.4 X 106) ÷ (2 X 108) =
2. (4.8 X 10-5) ÷ (3.2 X 10-6) =
3. (10.5 X 1020) ÷ ( 1.2 X 10-14) =
 HOMEWORK – Math Book Page 120: #s 5-8 &
20-25 & STUDY FOR QUIZ! 
Do Now - √81 / √81+√81
 Please pick up your guided notes and respond to the
following SILENTLY & INDEPENDENTLY.
1. Solve. (6.5 x 10-6) (4.5 x 109)
2. Solve. (5.6  10 )
5
(10 .5  10 )
12

Today’s Agenda
 Do Now – 6 minutes
 Agenda – 1 minutes
 Computing Numbers in Scientific Notation
Investigation – 10 minutes
 Computing Numbers in Scientific Notation IP – 5
minutes
 GP & IP – 14 minutes
 Exit Ticket – 5 minutes
Today’s Objective
SWBAT simplify
scientific
notation
expressions.
Math Investigation
 You are in groups of 4.
 Together, you will work together to try to solve
the problem given to you.
 You may use your notes, your partners, but not
your calculators.
 Together, you CAN solve the problem – Use
your rules of exponents to help you!
 I will be cycling around to monitor your
progress and check your final answers.
Simplifying Scientific Notation
Expressions
(2  10 )( 3  10 )
3
7
8
 Example 1: Simplify.
(2  10 )
 First, we take care of the numerator.



Multiply the factor 1 numbers: 2 x 3 = 6
Multiply factor 2 numbers by adding exponents: 10-3 x 107 = 104
Combine both factors to get your product: 6 x 104

 Second, divide your new product by the denominator.
 Your new problem is:


6  10
4
2  10
8
Divide factor 1 numbers: 6 ÷2 = 3
Divide factor 2 numbers by subtracting exponents: 10(4-(-8)) = 1012
 Last, combine your factors.

Final answer:3 x 1012
Simplifying Scientific Notation
Expressions
(6  10 )( 2  10 )
4
7
10
 Example 2: Simplify.
(4  10 )
 First, we take care of the numerator.



Multiply the factor 1 numbers: 6 x 2 = 12
Multiply factor 2 numbers by adding exponents: 104 x 107 = 1011
Combine both factors to get your product: 12 x 1011

 Second, divide your new product by the denominator.
11
 Your new problem is: 12  10
4  10
Divide factor 1 numbers: 12 ÷4 = 3
Divide factor 2 numbers by subtracting exponents: 10(11-10) = 101
10


 Last, combine your factors.
 Final answer:
 3 x 101
Simplifying Scientific Notation
Expressions
(7  10 )(1  10 )
12
6
8
 Example 3: Simplify.
(14  10 )
 First, we take care of the numerator.



Multiply the factor 1 numbers: 7 x 1 = 7
Multiply factor 2 numbers by adding exponents: 10-12 x 106 = 10-6
Combine both factors to get your product: 7 x 10-6

 Second, divide your new product by the denominator.
 Your new problem is:
7  10
6
14  10


8
Divide factor 1 numbers: 7 ÷14 = 0.5
Divide factor 2 numbers by subtracting exponents: 10(-6-(-8)) = 102
 Last, combine your factors.


Final answer:
 0.5 x 102
CORRECT SCIENTIFIC NOTATION ANSWER: 5 x 101
Simplifying Scientific Notation
9
7
Expressions
(5  10 )( 6  10 )
 Example 4: Simplify.

( 3  10 )
5
Simplifying Scientific Notation
5
10
Expressions
(8  10 )( 4  10 )
 Example 5: Simplify.

(8  10 )
9
Simplifying Scientific Notation
17
 10
Expressions
(5  10 )( 4  10 )
 Example 6: Simplify.

(2  10 )
5
Simplifying Scientific Notation
7
14
Expressions
(9  10 )( 4  10 )
 Example 7: Simplify.

(6  10 )
4
Simplifying Scientific Notation
7
14
Expressions
(5.6  10 )( 3.6  10 )
 Example 8: Simplify.

(5  10 )
4
Simplifying Scientific Notation
Expressions
(6.4  10 )( 2.9  10 )
5
 Example 9: Simplify.

12
(9.8  10 )
5
Simplifying Expressions in Scientific
Notation
(4.8  10 )( 3.9  10 )
8
 Example 10: Simplify.

4
(7  10 )
3
Exit Ticket
 Each of you will complete your exit ticket on a
note card.
 There are 2 problems.
 You will complete the exit ticket in 5 minutes
and it must be turned in before you can exit the
classroom.
 You must work SILENTLY and
INDEPENDENTLY.
 HOMEWORK – Worksheet! 

Exit Ticket
(2.7  10
7
)( 5.2  10 )
12
(2  10
(1.6  10
8
8
)
)( 3  10 )
9
( 5  10 )
2
Do Now
1.
2.
3.
4.
5.
3x – 10 = 17
5x – 10 = -20
-½ x + 8 = -4
¾x + 9 = 35
-9= 8 – 16x
Do Now – (√9)2 /√361/√16 + √64
 Please respond to the following on the Wednesday
area of your guided notes SILETNLY &
INDEPENDENTLY.
1. Simplify. (4.6  10 3 )( 3.2  10 7 )
(7  10 )
9
2. Write the steps to the problem you just solved above.

Today’s Agenda
 Do Now – 8 minutes
 Agenda – 1 minutes
 Adding & Subtracting Number in Scientific Notation
INM – 10 minutes
 GP & IP – 26 minutes
 Exit Ticket – 5 minutes
Today’s Objective
SWBAT add and
subtract number
in scientific
notation.
Adding and Subtracting Numbers in
Scientific Notation
 After multiplying, dividing, and combining operations
with numbers in scientific notation, we will finish
computing with the numbers by adding and
subtracting them.
 Before we begin, work with your partner and come up
with 2 examples of where we would need to add and
subtract numbers in scientific notation.
Adding and Subtracting Numbers in
Scientific Notation
 There are two different ways to adding and
subtract numbers in scientific notation.
 I will model both to you, and then you can
chose which one works best for you!
Adding and Subtracting Numbers in
Scientific Notation
 Example 1: (6.89 x 104) + (9.24 x 105)
 Method One:
Convert all numbers into standard form.
1.


6.89 x 104 = 68,900
9.24 x 105 = 924,000
2. Complete the operation indicated to solve.
 68,900 + 924,000 = 992,900
Adding and Subtracting Numbers in
Scientific Notation
 Example 2: (6.89 x 104) + (9.24 x 105)
 Method Two:
1. Check to see if the powers of 10 have the same exponent.
2. Convert numbers to the same by power of 10 by moving the
decimal point.


6.89 x 104 = 6.89 x 104
9.24 x 105 = I want the power to be 4, so I need to subtract 1 from
the exponent. When I subtract I move the decimal right. = 92.4 x
104
Add the factor ones and keep the power of ten to solve.
3.

92.4 + 9.89 = 99.29 x 104
Convert to proper scientific notation form.
4.

99.29 x 104 = 9.929 x 105
Adding and Subtracting Numbers in
Scientific Notation
 After seeing both methods, I want you to think,
why would I want to know how to use both
methods?
 When would the standard form method be
useful?
 When would the exponent method be useful?
 You will have one minute to think about this with
your partner.
Adding and Subtracting Numbers in
Scientific Notation
 Example 3: (7.38 x 108) – (1.161 x 107)
Method 1
Method 2
Adding and Subtracting Numbers in
Scientific Notation
 Example 4: (8.41 x 103) + (9.71 x 104)
Method 1
Method 2
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one with your partner.
 Example 5: (1.263 x 109) – (1.525 x 107)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one with your partner.
 Example 6: (2.85 x 107) + (1.61 x 109)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one with your partner.
 Example 7: (8.23 x 106) + (6.91 x 105)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one on your own.
 Example 8: (4.9 x 1018) + (5.8 x 1015)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one on your own.
 Example 9: (9.3 x 10-5) – (3.25 x 10-3)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one on your own.
 Example 10: (5.12 x 10-4) – (2.9 x 10-3)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one on your own.
 Example 11: (4.1 x 10-2) + (8.4 x 10-3)
Adding and Subtracting Numbers in
Scientific Notation
 Work on this one on your own.
 Example 12: (3.5 x 1013) + (7.3 x 1012)
Exit Ticket
 Each of you will complete your exit ticket on a note
card.
 There are 2 problems.
 You will complete the exit ticket in 5 minutes and it
must be turned in before you can exit the classroom.
 You must work SILENTLY and INDEPENDENTLY.
 HOMEWORK – Math book page 120: 10 – 13 & page
121: 28 - 35! 
Exit Ticket
1.
(2.18 x 1010) – (5.61 x 108)
2. (6.85 x 106) + (9.7 x 105)
HOMEWORK – Math book page 120: 10 – 13 & page
121: 28 - 35! 
Do Now –
2
3
/
2
4
+
2
2
 Please get out your guided notes and respond to the
following on the Thursday area SILENTLY &
INDEPENDENTLY.
1. (3.5 x 104) + (2.76 x 105)
2. (7.34 x 1015) – (4.67 x 1014)
Today’s Agenda
 Do Now – 8 minutes
 Agenda – 1 minute
 Scientific Notation Word Problems INM – 10 minutes
 GP & IP – 25 minutes
 Exit Ticket – 5 minutes
 Quiz Topics – 1 minute
Today’s Objective
SWBAT solve word
problems involving
scientific notation.
Scientific Notation Word Problems
 Example 1: In 2006, Blue Ridge Parkway was visited by
about 1.9 x 107 people. That same year, Great Smoky
Mountains National Park was visited by about 9.3 x 106
people. How many more people visited Blue Ridge
Parkway than Great Smoky Mountains National Park
in 2006? What operation will be used to solve this
problem?
Scientific Notation Word Problems
 Example 2: In 2006, the US had a Gross Domestic
Product (GDP) of 1.313 x 1013. The United Kingdom had
a GDP of 1.93 x 1012. What were the combined GDPs of
the US and the UK in 2006? What operation will be
used to solve this problem?
Scientific Notation Word Problems
 Example 3: One cell has a diameter of 4.5 x 10-6. If
there are 20 cells growing in a lab, what is their
combined diameters? What operation will be used
to solve this problem?
Scientific Notation Word Problems
 Example 4: The average distance from Earth to the
Sun is 1.46 x 108 kilometers. The average distance from
Earth to the Moon is 3.84 x 105 kilometers. About many
more times as great is the distance from Earth to the
Sun than to the Moon? What operation will be used
to solve this problem?
Scientific Notation Word Problems
 Example 5: About 8.73 x 108 people in the world speak
Chinese. About 3.22 x 108 speak Spanish. In scientific
notation, how many more people speak Chinese than
Spanish? What operation will be used to solve this
problem?
Scientific Notation Word Problems
 Example 6: Great Lake Superior covers an area of 3.17
x 104 square miles. The smallest Great Lake, Ontario,
covers an area of 7.34 x 103 square miles. About how
many times as great is the area covered by Lake
Superior than Lake Ontario? What operation will be
used to solve this problem?
Scientific Notation Word Problems
 Example 7: The income following incomes are
recorded for music artists in 2010.
Artist
2010 Income
Jay-Z
2.56 x 107
Yo Gotti
5.1 x 106
 How much more money did Jay-Z make over Yo Gotti?
What operation will be used to solve this
problem?
Scientific Notation Word Problems
 Example 8: The distance between Memphis and Sand
Francisco is 1.2 x 103 miles. The distance between
Memphis and Nashville is 2.5 x 102. How much further
is San Francisco than Nashville from Memphis? What
operation will be used to solve this problem?
Scientific Notation Word Problems
 Example 9: The largest planet in our solar system is
Jupiter with a diameter of about 1.43 x 105 kilometers.
The smallest planet in our solar system is Mercury with
a diameter of about 4.9 x 103 kilometers. About how
many times greater is the diameter of Jupiter than the
diameter of Mercury? What operation will be used
to solve this problem?
Scientific Notation Word Problems
 Example 10: In 2006, China had 1.311 x108 internet
users. That same year, Japan had 9.09 x 107 internet
users. How many internet users did the two countries
have combined? What operation will be used to
solve this problem?
Scientific Notation Word Problems
 Example 11: With nearly 3.0 x 108 books, the Library of
Congress is the largest library in the US. The
University of Tennessee has about 2.97 x 107 books in
its library. How many more books does the Library of
Congress have than the University of Tennessee?
What operation will be used to solve this
problem?
Exit Ticket
 Each of you will complete your exit ticket on a note
card.
 There are 2 problems.
 You will complete the exit ticket in 5 minutes and it
must be turned in before you can exit the classroom.
 You must work SILENTLY and INDEPENDENTLY.
 HOMEWORK – Worksheet & Study for Quiz! 
Exit Ticket
 1. The average distance from star A to the star B is 3.56 x 109
kilometers. The average distance from Star A to Star C is 4.8
x 1012 kilometers. About much further is the distance from
Star A to Star C than to Star B? What operation will be
used to solve this problem?
 2. In 2010, USA had 2.31 x105 IPhone users. That same year,
Europe had 1.49 x 104 IPhone users. How many IPhone
users did the USA and Europe have combined? What
operation will be used to solve this problem?
Homework – Worksheet & Study! 
Do Now - √81 / √25 -
2
2
 Please clear off your desk of
everything except a pencil,
calculator, and a plain sheet of
paper (to cover your quiz with).
 The longer it takes you to complete this, the
less time you will have for your quiz.