Sample 8 Grade
th
Lesson Cycle
Teamwork Questions and Answers
Name
Team Mastery
5
1) The typical height of the Space Shuttle in orbit is about 3 × 10 meters. The diameter of the planet
6
Mercury is about 5 × 10 meters.
About how many times smaller is the height of the Space Shuttle’s orbit than the diameter of
Mercury? Explain your thinking.
4
2) University of Maryland’s football stadium holds about 5 × 10 people. Ohio State University’s football
5
stadium holds about 1 × 10 people.
About how many times more people does Ohio State’s stadium hold than University of Maryland’s?
3) The size of a grain of salt is 0.0001 meters. Write the thickness as an estimate using a single digit
times a power of 10. Explain your thinking.
4) Maurice’s cereal company produced 120,000 boxes of cereal this year. Write the number of boxes of
cereal produced as an estimate using a single digit times a power of 10.
–7
5) The size of the wavelength of violet light is about 4 × 10 meters, and the size of the wavelength of
–7
red light is about 7 × 10 meters.
How many times smaller is violet light’s wavelength than red light’s wavelength?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
1
6) In Fall 2012, Arizona State University had about 60,000 students enrolled. Write the number of
students as an estimate using a single digit times a power of 10.
Challenge
7) For question 1, 2, or 5, make a scale drawing that uses bars to compare the sizes of the
8
two measurements. Include the scale in your drawing (for example, Scale: 1 cm = 10 m)
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
Team Mastery Answer Sheet
1) The height of the Space Shuttle’s orbit is about 17 times smaller than the diameter of Mercury.
Possible explanation: To find how many times smaller, I divided the greater value by the lesser value.
5
I wrote the division as a fraction. I factored out the 10 from both numerator and denominator because
it is a factor of both numbers. Then I was left with 50 over 3 which is about 17.
2) Ohio State’s stadium holds about twice as many people as University of Maryland’s stadium does.
–4
3) 1 × 10
Possible explanation: To get from 1 to 0.0001, I moved the decimal place to the right four times.
–4
–4
That’s the same as multiplying by 10 . 1 × 10 = 0.0001
5
4) 1 × 10
5) Violet light’s wavelength is about 2 times smaller than, or about half the size of, red light’s
wavelength.
4
6) 6 × 10
7) Answers will vary.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
3
Quick Check
Name
12
The mean distance from the Sun to Uranus is 3 × 10
12
Pluto is 6 × 10 meters.
meters. The mean distance from the Sun to
How many times longer is the distance from Sun to Pluto than from the Sun to Uranus?
Level H Unit 3 Cycle 2 Lesson 5
Quick Check
PowerTeaching: i3
© 2012 Success for All Foundation
Quick Check
Name
12
The mean distance from the Sun to Uranus is 3 × 10
12
Pluto is 6 × 10 meters.
meters. The mean distance from the Sun to
How many times longer is the distance from Sun to Pluto than from the Sun to Uranus?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we estimated the value of very large and very small quantities using a math shorthand. Then we
compared those numbers in that shorthand. Here’s an example!
Rita’s company pays its employees a total of $46.8 million a year in salaries.
Paul’s company pays its employees a total of $7.38 million a year in salaries.
We can estimate the values by writing them as a single digit times a power of 10.
7
46.8 million = 46,800,000 or about 5 × 10
6
7.38 million = 7,380,000 or about 7 × 10 .
This will help us determine how many times greater Rita’s company spends on salaries each year than
does Paul’s company.
Think of solving a simpler problem. If Rita’s company pays $50 dollars per year in salaries and Paul’s
pays $5 per year, how many times greater is $50 than $5?
To solve, we would divide $50 by 5 which is Rita’s value divided by Paul’s value. So we do the same for
the estimated values written using math shorthand.
101
7
5 × 10 = 5 × 10 7 = 5 × 10 1 = 50 = about 7 time greater.
7
7 × 10 6
7 × 10 6
7
1
6
After factoring out 10 from both numerator and denominator, we have 50 over 7. We can estimate this as
49 ÷ 7 = 7, so Rita’s company spends about 7 times more on salaries than does Paul’s.
3
4
1) A café sold 2 × 10 cupcakes in its first year of business and 4 × 10 in the second year of business.
About how many times larger are the second year sales than the first year sales?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Homework Problems
1
2) The thickness of a dollar bill is 0.00011 meters. Write the thickness as an estimate using a single digit
times a power of 10.
–6
3) The diameter of a red blood cell is 8 × 10 meters. The diameter of the average bacterium cell is
–6
1 × 10 meters. About how many times smaller is the bacterium cell than the red blood cell?
Explain your thinking.
4) The average altitude of GPS satellites is 20,200,000 meters. Write the altitude as an estimate using a
single digit times a power of 10.
Mixed Practice
5) What value of a will make this a proportion?
6 = a
18 48
6) Mariah’s dinner bill was $24.52. She left an 18% tip. How much did she pay in all?
7) You are rolling a number cube numbered 1–6 and flipping a coin. What is the probability that you roll
a 2 and flip heads?
8) Solve. Classify the solution as: natural number, whole number, integer, rational number.
(Use all that apply.)
7• 4
3 9
Word Problem
9) Sound travels at a distance of 3,430 meters per second. Write the speed as an estimate using a
single digit times a power of 10. Then, write the speed in centimeters per second and millimeters per
second as an estimate using a single digit times a power of 10.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Homework Problems
For the Guide on the Side
Today your student used powers of 10 to estimate really large and really small quantities. Your student
also used his or her knowledge of exponents and operations to compare the numbers. This work is
preparing your student to begin working with scientific notation in the next lesson. Scientific notation is a
convention used to write very large and very small quantities so that they are easier to understand.
Scientific notation is widely used in biology, astronomy, physics, and chemistry and is useful in social
sciences like economics and finance. Being comfortable with these ways of representing values will help
your student make sense of the world around him or her.
Your student should be able to answer these questions about estimating with powers of 10:
1) How did you estimate this number? Explain why.
2) Is rewriting these numbers with exponents helpful? Why do you think so?
3) How did you figure out how many times greater this number is than that one?
4) Draw a picture or describe a model that shows how many times smaller this number is than
that one.
Here are some ideas to work with estimation with powers of 10:
1) Come up with a list of everyday things that can be estimated with powers of 10. For example,
how wide is a grain of rice?
2) Watch a video from Khan Academy.
https://www.khanacademy.org/math/arithmetic/exponents-radicals/scientific-notation/v/scientificnotation--old
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Homework Problems
3
Homework Answers
1) The second year sales are about 20 times larger than the first year sales.
–4
2) 1 × 10 m
3) The diameter of the average bacterium is about 8 times smaller than the diameter of a red blood cell.
Possible explanation: To find how many times smaller the diameter of the bacterium is than the red
blood cell, I divided the greater value by the lesser value and wrote it as a fraction. I factored out the
–6
10 from both numerator and denominator because it is a factor of both numbers. Then I was left
with 8 over 1 which is 8.
7
4) 2 × 10 m
Mixed Practice
5) a = 16
6) Mariah paid $28.93 in all.
7) The probability that you roll a 2 and flip heads is 8.3% or 1 .
12
8) 1 1 ; rational number
27
Word Problem
3
5
9) Sound travels at a speed of about 3 × 10 meters per second, 3 × 10 centimeters per second, or
6
3 × 10 millimeters per second.
4
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 5
Homework Problems
Teamwork Questions and Answers
Name
Team Mastery
Directions for questions 1–6: Solve. Write your answer in scientific notation.
1) A space station is in orbit 2 of the distance from the Earth to the Moon. If the Moon is
15
8
3.844 × 10 meters from Earth, how far is the space station from Earth?
6
2) A plane flies 9.084 × 10 meters on a trip from London to Los Angeles. Then the plane taxis
518 meters to the arrival gate at the airport in Los Angeles. How much distance does the plane
cover in all?
3) The typical thickness of a piece of paper is 8.382 ×10
of paper?
–5
meters. How thick is a stack of 125 sheets
8
4) The area of the Pacific Ocean is 1.652 × 10 square kilometers. The Atlantic Ocean’s area is about
2 of the area of the Pacific Ocean. What is the area of the Atlantic Ocean?
3
5) Mount Everest, Earth’s tallest mountain, was formed 60 million years ago. How long ago was Mount
Everest formed in scientific notation?
6) Light travels 17,987,550,000 meters in one minute, in a vacuum. How far does light travel in a minute,
in scientific notation?
Directions for questions 7 and 8: Solve. Write your answer in decimal notation.
–5
7) The diameter of human hair is 2.5 × 10 meters. What is the diameter in decimal notation?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
1
7
8) The diameter of Uranus at its equator is 5.1118 × 10 meters. What is the diameter in
decimal notation?
Challenge
9) According to 2012 data from the CIA World Factbook, the world’s population is 7,021,836,029.
Explain how writing this number as “about 7 billion” is similar to scientific notation. Explain how
“about 7 billion” is also not similar to scientific notation.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
Team Mastery Answer Sheet
7
1) The space station is about 5.1253 × 10 meters from Earth.
6
2) The plane travels 9.084518 × 10 meters in all.
–2
3) A stack of 125 sheets of paper is 1.04775 × 10 meters thick.
8
4) The Atlantic Ocean’s area is about 1.101333333 × 10 square meters.
7
5) Mount Everest was formed 6.0 × 10 years ago.
6) Light travels 1.798755 × 10
10
meters in a minute.
7) Human hair’s diameter is 0.000025 meters.
8) The diameter of Uranus at its equator is 51,118,000 meters.
9) Answers will vary.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
3
Quick Check
Name
Write your answer in scientific notation.
8
The diameter of Saturn at its equator is 1.2053 × 10 meters. If scientists wanted to explore 2% of the
crust of the planet in one location, how far down would they have to drill?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Quick Check
Quick Check
Name
Write your answer in scientific notation.
8
The diameter of Saturn at its equator is 1.2053 × 10 meters. If scientists wanted to explore 2% of the
crust of the planet in one location, how far down would they have to drill?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we converted numbers in and out of scientific notation and performed simple operations on
numbers in scientific notation. Here’s an example:
8
The diameter of Saturn at its equator is 1.2053 × 10 meters. If scientists
wanted to explore 2% of the crust of the planet in one location,
how far down would they have to drill?
Scientific notation is the expression of a value represented as a certain kind of product, the product of a
number from 1–10 multiplied by a power of 10.
To convert to ordinary or decimal notation, find the product.
8
1.2053 × 10 = 1.2053 × 100,000,000 = 120,530,000
10^8 means the decimal will move 8 places to the right.
8
8
To find 2% of 1.2053 × 10 , find the product of 0.02 and 1.2053 × 10 .
8
2% of 1.2053 × 10 m
8
0.02(1.2053 × 10 m)
8
(0.02 × 1.2053) × 10 m
8
Check if your answer is still in scientific notation.
0.024106 × 10 m
6
2.4106 × 10 m
Moving the decimal point to the right decreases the power of 10.
6
So to explore 2% of Saturn’s crust, scientists would have to drill down 2.4106 × 10 meters.
1) A flea weighs 0.0049 grams. What is its weight in scientific notation?
2) A normal red blood cell count for a child is about 4,700,000 per microliter. What is a normal red blood
cell count for children in scientific notation?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Homework Problems
1
6
3) The Moon’s diameter is 3.4748 × 10 meters. What is the Moon’s diameter in decimal notation?
4) The largest known bacterium is 7.5 × 10
–4
meters. What is the bacterium’s size in decimal notation?
Directions for questions 5–8: Solve. Write your answer in scientific notation.
4
5) Deonna is taking trail through the woods that is 4.6 × 10 meters long. She plans to walk half of the
trail and bike the other half. How much of the trail will she walk?
7
6) An astronomical unit is about 9.3 × 10 miles. Mercury is 0.38 astronomical units from the Sun. What
is Mercury’s the distance from the Sun, in miles?
–2
7) Five hummingbirds were perched on a window sill. One hummingbird weighs 5.6 × 10 ounces.
What is the total weight of the hummingbirds on the window sill?
8) A rock scientist drilled 25% of the distance to the center of Earth. The total distance to the center of
6
the Earth is 6.37814 ×10 meters. How far down did the rock scientist drill?
Mixed Practice
9)
–
11c – 7 = 15
10) Find the simple interest on a loan for $1,280 for 3 months if the yearly interest is 5%.
11) Find the area of the circle when r = 16 cm and π = 3.14
12) Determine whether the events are dependent or independent: Choosing roast beef for a sandwich
and water for a drink for lunch.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Homework Problems
Word Problem
13) Explain how to convert 0.00000057802 to scientific notation.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Homework Problems
3
For the Guide on the Side
Today your student worked with numbers written in scientific notation. Any value can be represented this
way; it simply means the product of a number between 1 and 10 times a power of 10. For example, 9
0
written in scientific notation is 9 × 10 . Scientific notation is not only a useful shorthand for representing
very large and very small numbers (like 0.0000000000058009932), but also allows for quicker
comparison and operations on values like this.
Your student should be able to answer these questions about scientific notation:
1) Describe how to convert a number to scientific notation.
2) How many places does this number have after the decimal point?
3) Is this number greater than this number? How do you know?
4) How were you able to do this operation without having to convert to decimal notation? Do you get
the same answer if you do convert first?
Here are some ideas to work with scientific notation:
1) Look up distances from Earth to different planets. Discuss why you think these distances are
recorded in scientific notation.
2) Look through magazines, newspapers, or on the internet for very large numbers like population,
budgets, and very long distances. Are the numbers written in scientific notation? Are the numbers
estimates? Are there units printed with the numbers? Are very large units like trillion dollars or
gigawatts similar to scientific notation?
3) Video: How do you convert from scientific notation to decimal notation?:
http://virtualnerd.com/algebra-1/exponents-exponential-functions/decimal-to-scientific-notationconversion.php
4) Video: How do you convert from decimal notation to scientific notation?:
http://virtualnerd.com/algebra-1/exponents-exponential-functions/scientific-to-decimal-notationconversion.php
5) Video: Multiplying in Scientific Notation:
https://www.khanacademy.org/math/arithmetic/exponents-radicals/scientificnotation/v/multiplying-in-scientific-notation
4
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Homework Problems
Homework Answers
–3
1) A flea weighs 4.9 × 10
grams.
6
2) A normal red blood cell count for children is about 4.7 × 10 per microliter.
3) The Moon’s diameter is 3,474,800 meters.
4)
The bacterium’s size is 0.00075 meters.
4
5) Deonna will walk 2.3 × 10 meters on the trail.
7
6) Mercury is 3.534 × 10 miles from the sun.
–1
7) Five hummingbirds weigh 2.8 × 10
ounces.
6
8) The rock scientist drilled down 1.594535 × 10 meters.
Mixed Practice
–
9) c = 2
10) I = $1,280 • 0.05 • 0.25 = $16
11) Area = 803.84 cm²
12) Independent
Word Problem
13) Possible explanation: To convert 0.00000057802 to scientific notation, I moved the decimal point
so the first factor was between 1 and 10. Then I counted the number of spaces I moved the decimal
point and used this number as the exponent for my power of 10. So 0.00000057802 equals
–7
5.7802 × 10 , in scientific notation.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 6
Homework Problems
5
Teamwork Questions and Answers
Name
Team Mastery
1) The diameter of the head of an average pin is 1.7 × 10
–10
3 × 10 meters.
–3
meters. The diameter of a water molecule is
a. How many times larger is the head of a pin than the water molecule?
b. How many pin heads arranged in rows and columns could fit into the area of 1 square centimeter
of fabric?
c.
How many water molecules arranged in rows and columns could fit into a square dish that
has an area of 1 square centimeter?
2
2) The average breathing rate for an adult is 8.4 × 10 breaths per hour.
a. How many breaths does an average adult take in a week? Write the answer in scientific notation.
b. How many breaths does an average adult take in a year? Write the answer in scientific notation.
11
3) The mean distance from Earth to the Sun is 1.4959787 × 10 meters. This is also the definition of
1 astronomical unit (1 AU). If the mean distance from Jupiter to the Sun is 5.2028 AU, how many
kilometers is it from Jupiter to the Sun?
4
5
4) A section of forest is 9.5 × 10 meters by 3.2 × 10 meters.
a. What is the area of this section forest in square kilometers?
b. If a pair of warbler birds needs 25 square kilometers to raise a family, how many nesting pairs
can this forest section support?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
1
Challenge
6
5) The distance to the center of the Earth is 6.37814 × 10 meters. The diameter of a red blood cell is
–6
8.4 × 10 meters. About how many red blood cells could ring the Earth?
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
Team Mastery Answer Sheet
6
1) a. The head of a pin is 5.67 × 10 times larger than the water molecule.
b. 34 pins could fit into 1 square centimeter of fabric.
15
c. 1.1 × 10 water molecules could fit into a dish that is 1 square centimeter.
5
2) a. Adults take an average of 1.4112 × 10 breaths per week.
6
6
b. Adults take an average of 7.33824 × 10 or 7.3584 × 10 breaths per year.
(The first answer was calculated as the weekly number of breaths multiplied by 52 weeks.
The second answer was calculated as the daily number of breaths multiplied by 365 days.)
8
3) It is 7.78327798 × 10 kilometers from Jupiter to the Sun.
4
4) a. The section of forest is 3.04 × 10 square kilometers.
b. The section of forest can fit 1,216 nesting pairs.
12
5) About 4.770833 × 10
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© 2012 Success for All Foundation
red blood cells could ring the Earth.
Level H Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
3
Quick Check
Name
8
In 2012, the population of the U.S. was about 3.14 × 10 . The population of Wyoming was about
5
5.76 × 10 . About how many times larger was the population of the U.S. than the population of Wyoming?
Level H Unit 3 Cycle 2 Lesson 7
Quick Check
PowerTeaching: i3
© 2012 Success for All Foundation
Quick Check
Name
8
In 2012, the population of the U.S. was about 3.14 × 10 . The population of Wyoming was about
5
5.76 × 10 . About how many times larger was the population of the U.S. than the population of Wyoming?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we used what we know about scientific notation to solve more complex problems. Here is
one example:
4
The depth of Marianas Trench (the deepest point in the Earth’s oceans) is 1.0294 × 10 meters.
2
The height of the Washington Monument is 1.693 × 10 meters. How many Washington
Monuments, stacked top to bottom, can fit into the height of the Marianas Trench?
To help us figure out what we need to do, we can solve a simpler problem. If the trench was 10 units
deep and the monument was 2 units tall, then we could fit 10 ÷ 2 or 5 Washington Monuments into the
trench. So we divide the trench’s depth by the monument’s height.
2
Divide the
first factors.
10 is a common factor
of both numbers.
Factor that out.
Change to
scientific notation.
1.0294 × 10 4 = 1.0294 × 10 2 = 0.6080334 × 10 2 = 6.08033 × 101
1
1.693 × 1
1.693 × 10 2
About 60 monuments can fit into the height of the Marinas Trench.
Directions for questions 1–3: Solve. Write your answer in scientific notation.
13
1) In February 2013, the U.S. public debt was about 1.65 × 10 dollars.
8
a. With a U.S. population of 3.12 × 10 , what is the amount of debt for each person in the U.S.?
9
b. If the debt grows 3.82 × 10 dollars per day, what will the public debt be in 30 days?
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Homework Problems
1
2
2) A bag of candy has 2.05 × 10 chocolate drops. Each chocolate drop has a mass of 1.75 grams.
What is the total mass in kilograms of the chocolate drops in the bag?
3) The average orbital speed of the Moon is about 1.023 kilometers per second.
a. What is the speed in kilometers per hour?
b. How far, in kilometers, does the Moon travel in one week?
Mixed Practice
4) Talisha walks 0.8 miles in 1 hour. Write her
6
walking rate as miles per hour.
5) Solve.
6) A shampoo company is decreasing the
volume of their 500 milliliter shampoo bottle
by 16%. What is the volume of their new
shampoo bottle?
7) Write the probability of landing on 4 as a
decimal.
t – 34 = –14 • 2.5
7
Word Problem
3
8) The tallest mountain in the world, Mount Everest, is 8.848 × 10 meters high. The tallest mountain in
4
the U.S., Mount McKinley, is 2.032 × 10 feet high. How many Mount McKinleys would it take to reach
the peak of Mount Everest? Explain your thinking.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Homework Problems
For the Guide on the Side
Today your student used what he or she knows about scientific notation, exponent operations, and
rational number operations to solve complex scientific notation problems. Understanding the value of a
number in scientific notation can help your student make sense of many different phenomena in the
world. For example: How far away is the Moon? How much farther away is the nearest star? In addition,
these computational problems included fraction and decimal operation skills your student has already
learned. Building these skills helps your student as he or she will delve deeper into algebra this year and
in later years.
Your student should be able to answer these questions about scientific notation:
1) What’s going on in the problem?
2) Can you solve a simpler problem to help you see what to do?
3) Are the units the same in this problem? Do you need to convert units first?
Here are some ideas to work with scientific notation:
1) Look up distances from the Sun to the Earth and the other planets. Work with your student to
make a model of the solar system to scale.
2) Look up the width of very small things like atoms, molecules, or snowflakes. Compare these sizes
to the sizes of very large things like the diameter of the solar system.
3) Watch a video to review scientific notation.
https://www.khanacademy.org/math/arithmetic/exponents-radicals/scientificnotation/v/multiplying-in-scientific-notation
http://virtualnerd.com/algebra-1/exponents-exponential-functions/decimal-to-scientific-notationconversion.php
http://virtualnerd.com/algebra-1/exponents-exponential-functions/scientific-to-decimal-notationconversion.php
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Homework Problems
3
Homework Answers
4
1) a. The amount of debt per person is 5.25 × 10 dollars.
13
b. The public debt will be 1.661 ×10 dollars in 30 days.
–1
2) The bag of candies has a mass of 3.5875 ×10
kilograms.
3
3) a. The Moon travels 3.6828 × 10 kilometers per hour.
5
b. The Moon travels 6.1871 × 10 kilometers in one week.
Mixed Practice
4) 4.8 mile per hour (mph)
–
5) t = 7
6) The new shampoo bottle is 420 milliliters.
7) 0.25
Word Problem
8) It would take 1.429 Mount McKinleys to reach the peak of Mount Everest.
Possible explanation: To compare the heights, they first need to be in the same unit, so I converted
4
–1
feet to meters for the height of Mount McKinley. 2.032 × 10 feet • 3.048 × 10 meters in 1 foot =
3
6.19× 10 meters. Then I divided the height of Mount Everest by the height of Mount McKinley. 8.848
3
3
× 10 ÷ 6.19× 10 = 1.429. That means it would take 1.429, almost 1.5, Mount McKinleys to reach the
peak of Mount Everest.
4
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lesson 7
Homework Problems
Unit Check
Name
1) Evaluate.
–3
5
–7
–6
2) Rayna found the value of 8 and Ted found the value of 8 .
Describe how the two values are related.
–1
3) Evaluate. 3
5) Evaluate.
6
0
2
–5
·3 ·7
4) Evaluate. 2 ÷ 2
49 – 15
6) Evaluate. ( 3) +
–
2
3
64
7) Solve for m.
3
–2
m – 3 (5 ) = 7
5
11
8) In 2011, the value of Italy’s exports in U.S. dollars was about 5 × 10 . The value of China’s exports in
12
U.S. dollars was about 2 × 10 . About how many times greater was the value of China’s exports than
Italy’s exports? Explain your thinking.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lessons 1–7
Unit Check
1
–5
9) The thickness of a human hair has been measured as 2.5 × 10 meters.
a. Write this thickness in decimal notation.
b. What is the thickness of four human hairs bonded together? Write your answer in both decimal
and scientific notation.
10) The distance from New York to Los Angeles is 3,962 kilometers. The diameter of the moon is about
3
6
3.5 × 10 meters. The diameter of the sun at its equator is about 1.39 × 10 meters.
a. About how many full trips from New York to Los Angeles would fit into the diameter of the moon?
b. About how many full trips from New York to Los Angeles would fit into the diameter of the sun?
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PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lessons 1–7
Unit Check
Assessment Answers
Lesson 1: Evaluate numeric terms with exponents, including integer exponents.
1)
1
125
–7
2) Possible answer: Both of these values are powers of 8. 8 is the fraction 1/(8 · 8 · 8 · 8 · 8 · 8 · 8) and
–6
–6
–7
–7
8 is the fraction 1/(8 · 8 · 8 · 8 · 8 · 8). To get from 8 to 8 , you’d multiply by 1 . So 8 is 1 the
8
8
–6
–6
–7
value of 8 , or 8 is 8 times greater than 8 .
Lesson 2: Evaluate numeric expressions with exponents, including integer exponents.
5
3) 3 or 243
7
4) 2 or 128
Lesson 3: Understand and use square root and cube root symbols.
5)
–
8
6) 13
Lesson 4: Solve algebraic and numeric equations that include integer exponents and square and
cube roots.
7) m =
3
7.024
Lesson 5: Estimate very small and very large quantities with powers of 10 and understand their values in
relation to each other.
8) The value of China’s exports was about 4 times greater than the value of Italy’s exports.
Possible explanation: To find how many times greater China’s value was than Italy’s, I divided the
11
greater value by the lesser value and wrote it as a fraction. I then factored out 10 from both
1
numerator and denominator because it is a factor of both numbers. Then I was left with 2 × 10 over
1
5. I know that 2 × 10 = 20, so then I divided 20 by 5 and got 4.
Lesson 6: Understand and compute with scientific notation.
9) a. 0.000025 m
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b. 0.0001 m or 1 × 10 m
Lesson 7: Perform operations on numbers expressed in scientific notation in real-world contexts.
10) a. Almost one full trip from NY to LA would fit into the diameter of the moon.
b. About 350 trips from NY to LA would fit into the diameter of the sun.
PowerTeaching: i3
© 2012 Success for All Foundation
Level H Unit 3 Cycle 2 Lessons 1–7
Unit Check
3