Unit 3.2 - Magnification
Name: ________________ Per: ___ Score: ____
Unit 3.2 Big Ideas
I can…
❏ Translate between scientific notation, standard form,
and verbal descriptions
❏ Calculate using values in scientific notation
❏ Solve contextual problems involving scientific
notation
❏ Interpret scientific notation results using technology
Assignments:
Complete
● Magnitude
Partial Incomplete
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p3
o Magnitude (p2)
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p4
o Scientific Notation
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p5
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p6
● A Million Dollars
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p7
● Estimating Quantities
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p8
o Estimating Quantities (p2)
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p9
o Estimating Quantities (p3)
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p10
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p11
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p12
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p13
● Operations w/Sci Notation
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p14
o Operations (p2)
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p15
● Scientific Notation Multipl.
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p16
o Sci Notation Division
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p17
● Operations w/Sci Notation
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p18
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p19
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p20
● Mars Task (no paper)
o Size it up
● Cost of the Superbowl
o Superbowl (p2)
● Operations w/Sci Notation (no paper)
o Exponent Review
o Operations w/Sci Notation
● What operation? (no paper)
o Hidden Message
Lesson 7: Magnitude
Classwork
Fact 1: The number 10𝑛 , for arbitrarily large positive integers 𝑛, is a big number in the sense that given a number 𝑀
(no matter how big it is) there is a power of 10 that exceeds 𝑀.
Fact 2: The number 10−𝑛 , for arbitrarily large positive integers 𝑛, is a small number in the sense that given a positive
number 𝑆 (no matter how small it is), there is a (negative) power of 10 that is smaller than 𝑆.
Exercise 1
Let 𝑀 = 993,456,789,098,765. Find the smallest power of 10 that will exceed 𝑀.
Exercise 4
The chance of you having the same DNA as another person (other than an identical twin) is approximately 1 in 10 trillion
(one trillion is a 1 followed by 12 zeros). Given the fraction, express this very small number using a negative power of
10.
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10 000 000 000 000
Exercise 5
The chance of winning a big lottery prize is about 10−8 , and the chance of being struck by lightning in the U.S. in any
given year is about 0.000 001. Which do you have a greater chance of experiencing? Explain.
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Exercise 6
There are about 100 million smartphones in the U.S. Your teacher has one smartphone. What share of U.S.
smartphones does your teacher have? Express your answer using a negative power of 10.
1.
What is the smallest power of 10 that would exceed 987,654,321,098,765,432?
2.
What is the smallest power of 10 that would exceed 999,999,999,991?
3.
Which number is equivalent to 0.000 000 1: 107 or 10−7 ? How do you know?
4.
Sarah said that 0.000 01 is bigger than 0.001 because the first number has more digits to the right of the decimal
point. Is Sarah correct? Explain your thinking using negative powers of 10 and the number line.
5.
Order the following numbers from least to greatest:
105
10−99
10−17
1014
4
10−5
1030
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Size It Up
1. The table contains seven measurements written in decimal and scientific notation.
(a) Complete the table so that each measurement is written in both decimal and scientific notation.
(b) In the last column, rank the measurements in order of size.
(1 = smallest, 2 = next smallest, and so on up to 7 = largest)
Decimal Notation
Scientific Notation
1 × 10−2 m
=
0.004 m
=
200 m
=
8 × 105 m
=
40,000,000 m
=
40 m
=
8 × 10−4 m
=
2 (a)
Rank
1 = smallest
7 = largest
Complete the following statement using two numbers in decimal notation from the table.
× 4000 =
2 (b)
Complete the following statement using two numbers in scientific notation from the table.
× 50,000 =
Student materials
Estimating Length Using Scientific Notation
© 2015 MARS, Shell Center, University of Nottingham
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S-1
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Lesson 8: Estimating Quantities
Classwork
Exercise 1
The Federal Reserve states that the average household in January of 2013 had $7,122 in credit card debt. About how
many times greater is the U.S. national debt, which is $16,755,133,009,522? Rewrite each number to the nearest
power of 10 that exceeds it, and then compare.
Exercise 2
There are about 3,000,000 students attending school, kindergarten through Grade 12, in New York. Express the number
of students as a single-digit integer times a power of 10.
The average number of students attending a middle school in New York is 8 × 102 . How many times greater is the
overall number of K–12 students compared to the average number of middle school students?
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Exercise 3
A conservative estimate of the number of stars in the universe is 6 × 1022 . The average human can see about
3,000 stars at night with his naked eye. About how many times more stars are there in the universe compared to the
stars a human can actually see?
Exercise 4
The estimated world population in 2011 was 7 × 109 . Of the total population, 682 million of those people were lefthanded. Approximately what percentage of the world population is left-handed according to the 2011 estimation?
Exercise 5
The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of
10.
If the average American lives about 80 years (or about 30,000 days), how many total breaths will a person take in her
lifetime?
1.
The Atlantic Ocean region contains approximately 2 × 1016 gallons of water. Lake Ontario has approximately
8,000,000,000 gallons of water. How many Lake Ontarios would it take to fill the Atlantic Ocean region in terms of
gallons of water?
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2.
U.S. national forests cover approximately 300,000 square miles. Conservationists want the total square footage of
forests to be 300,0002 square miles. When Ivanna used her phone to do the calculation, her screen showed the
following:
a.
What does the answer on her screen mean? Explain how you know.
b.
c.
2.
a. Given that the U.S. has approximately 4 million square miles of land, is this a
reasonable goal for conservationists? Explain.
3.
The average American is responsible for about 20,000 kilograms of carbon emission pollution each year. Express
this number as a single-digit integer times a power of 10.
4.
The United Kingdom is responsible for about 1 × 104 kilograms of carbon emission pollution each year. Which
country is responsible for greater carbon emission pollution each year? By how much?
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Name:__________________________________________
Date:_____________ Period:____
The cost of a Super Bowl XLIX ad
The 2015 Super Bowl should bring in at least $ 2.93 ● 108, (if not more). What on earth do those numbers
mean? I did a little research on these weird numbers: $ 2.93 ● 108 and it turns out that it is a number written in
something called scientific notation.
So what is scientific notation? We use scientific notation to write really large or really small numbers as the
product of a number and a power of ten.
$ 2.93 ● 108 is a shorter way to write the dollar amount of $293,000,000.
The 2.93 is called the coefficient. If the coefficient is positive then it must be written as a number
greater than or equal to 1, and less than 10 (1≤ positive coefficient < 10).
If the coefficient is negative, then it must be written as a number less than or equal to -1, and greater than -10
(−1≥ negative coefficient < −10).
The 10 is called the base. When we write numbers in scientific notation the base is always ten, thus giving us
powers of ten. The 8 is the exponent. It tells us how many times to multiply the base by itself.
So in this case we have 2.93 ● 108 = 2.93 ● 10 ● 10 ● 10 ● 10 ● 10 ● 10 ● 10 ● 10
Let’s try a little a Super Bowl math with scientific notation:
The average price of a Super Bowl commercial in 2014 was approximately 4.0 million U.S dollars for a 30
second slot. Now for 2015, ads are selling for $4.5 million dollars for 30 seconds of ad time.
1. Audi of America (Volkswagen) had one 60-second ad during 2014 Super Bowl XLVIII. If they buy the same
length ad for Super Bowl XLVIX, how much will that ad cost? Write your answer in scientific notation.
2. With the chart below we can make some interesting observations. The numbers get really big.
So, please write your answers in both standard notation and scientific notation.
Commercial
length in
seconds
Length of
commercial in
minutes
Cost written in
standard form
30
4,500,000
60
90
120
150
180
210
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Cost written in
scientific notation
4.5•106
Name:__________________________________________
Date:_____________ Period:____
3. If Pepsi will has two 30-second commercials, how much money will they spend? Write
your answer in scientific notation.
4. How much would a 15-second commercial cost this year? (In both standard and scientific
notation)
5. How much would a 10-second commercial cost this year? (In both standard and scientific notation)
6. How much would a 1-second commercial cost this year? (In both standard and scientific notation)
7. What might a 1-second commercial be like?
8. If 10 commercials cost $4.5 ● 107 and 100 commercials cost $4.5 ● 108, how much would 110
commercials cost? Write your answer in scientific notation.
9. During the entire Super Bowl game (It lasts about 4 hours), about how many minutes do you think
will be filled with commercials?
10. How much would it cost (in scientific notation) to buy all of that commercial time?
11. What is the equation that expresses the relationship on the table?
12. Using this equation, how much would a 5 minute commercial cost?
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Operations with Scientific Notation
Classwork
Exercise 1
The mass of a proton is
0.000 000 000 000 000 000 000 000 001 672 622 kg.
In scientific notation it is
Exercise 2
The mass of an electron is
0.000 000 000 000 000 000 000 000 000 000 910 938 291 kg.
In scientific notation it is
Exercise 3
Write the ratio that compares the mass of a proton to the mass of an electron.
Exercise 4
Compute how many times heavier a proton is than an electron (i.e., find the value of the ratio). Round your final answer
to the nearest one.
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Exercise 3
The mass of Earth is 5.9 × 1024 kg. The mass of Pluto is 13,000,000,000,000,000,000,000 kg. Compared to Pluto, how
much greater is Earth’s mass than Pluto’s mass?
Exercise 4
Using the information in Exercises 2 and 3, find the combined mass of the moon, Earth, and Pluto.
Exercise 5
How many combined moon, Earth, and Pluto masses (i.e., the answer to Exercise 4) are needed to equal the mass of the
sun (i.e., the answer to Exercise 2)?
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Lesson 9: Scientific Notation
Use the table below to complete Exercises 7 and 8.
The table below shows the debt of the three most populous states and the three least populous states.
State
California
New York
Texas
North Dakota
Vermont
Wyoming
Debt (in dollars)
Population
(2012)
407,000,000,000
337,000,000,000
276,000,000,000
4,000,000,000
4,000,000,000
2,000,000,000
38,000,000
19,000,000
26,000,000
690,000
626,000
576,000
Exercise 7
a.
What is the sum of the debts for the three most populous states? Express your answer in scientific notation.
b.
What is the sum of the debt for the three least populous states? Express your answer in scientific notation.
c.
How much larger is the combined debt of the three most populous states than that of the three least populous
states? Express your answer in scientific notation.
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Exercise 8
a.
What is the sum of the population of the three most populous states? Express your answer in scientific
notation.
b.
What is the sum of the population of the three least populous states? Express your answer in scientific
notation.
c.
Approximately how many times greater is the total population of California, New York, and Texas compared to
the total population of North Dakota, Vermont, and Wyoming?
Exercise 9
All planets revolve around the sun in elliptical orbits. Uranus’s furthest distance from the sun is approximately 3.004 ×
109 km, and its closest distance is approximately 2.749 × 109 km. Using this information, what is the average distance
of Uranus from the sun?
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