0 Unit Two Standards: 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. Name: ____________________________________Period: ______
46
Embed
Unit Two - Mr. Dirago · 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
0
Unit Two
Standards:
8.EE.1 Know and apply the properties of integer exponents to generate equivalent
numerical expressions.
8.EE.3 Use numbers expressed in the form of a single digit times an integer power
of 10 to estimate very large or very small quantities, and to express how
many times as much one is than the other.
8.EE.4 Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used. Use
scientific notation and choose units of appropriate size for measurements
of very large or very small quantities. Interpret scientific notation that has
Write the following in order from least to greatest:
1.25 x 10-3, 1.28 x 10-4, 1.2 x 10-4, 1.255 x 10-3, 1.3 x 10-4
31
Lesson #26 Multiplying and Dividing Numbers in Scientific Notation
Sometimes when multiplying and dividing a number will not be written correctly in
scientific notation. Be sure to rewrite it so it does!
Try the following:
1. 24.8 x 108 = 2.48 x 10 2. 36.5 x 107 = 3.65 x 10 3. 917.83 x 1012 = 9.1783 x 10 4. 825.31 x 106 = 8.2561 x 10 5. 0.584 x 109 = 5.84 x 10 6. 0.1183 x 1010 = 1.183 x 10 7. 0.03629 x105 = 3.629 x 10 8. 0.00258 x 106 = 2.58 x 10
Multiplying Numbers In Scientific Notation: A shooting star travels at a rate of 300,000 mph for 600 hours. How many miles did it
travel?
* Distance = rate x time
Rewrite each of the numbers above in scientific notation.
_____________ x _____________ = ______________
(rate) (time) (distance)
Describe below how you can easily multiply numbers written in scientific
notation.
1. (1.5 x 106)(6 x 103) 2. (2.4 x 1012)(4 x 10-4)
32
3. (3.2 x 10-5)(2.8 x 10-3) 4. (1.5 x 106)(6 x 103)
5. (6.8 x 10-8)(1.12 x 102) 6. (4.09 x 109)(3 x 105)
Dividing Numbers In Scientific Notation:
A rocket travels 7,200,000 miles in 8,000 hours. How fast does the rocket travel?
* Rate = Distance ÷ time
Rewrite each of the numbers above in scientific notation.
_____________÷_____________ = ______________
(Distance) (time) (rate)
Describe below how you can easily divide numbers written in scientific notation.
7. (8.4 x 1012) ÷ (3 x 105) 8. (7.2 x 1018) ÷ (6 x 106)
9. (9.6 x 1012) ÷ (8 x 105) 10. (8.75 x 1018) ÷ (2.5 x 106)
11. (6.48 x 1011) ÷ (4 x 10-5) 12. (4.872 x 10-9) ÷ (2.4 x 10-3)
33
HW #26 Multiplying and Dividing Numbers in Scientific Notation
Try the following. Make sure the results are written correctly in Scientific Notation:
1. (2.9 x 103)(3.0 x 10-3) 2. 7.50 𝑥 104
2.5 𝑥 103
3. (2.55 x 10-2)(3.00 x 10-3) 4. 6.80 𝑥 10−5
3.40 𝑥 10−8
5. (4 x 102)(2.5 x 10-5) 6. 5.25 𝑥 106
1.5 𝑥 104
7. (1.28 x 10-3)(5 x 10-1) 8. 9.8 𝑥 102
1.4 𝑥 10−5
34
Lesson #27 Scientific Notation Word Problems with Multiplication and Division
Procedure:
1. ____________ the problem.
2. _________________ whether the questions should be solved by doing multiplication
or division.
3. _________________ the problem by multiplying or dividing the base numbers and
by applying laws of exponents to the powers of 10.
When multiplying, ___________ the exponents.
When dividing, _____________ the exponents.
4. Be sure that your answer is correctly written in _____________________, with only
________ digit to the left of the decimal.
Calculate each answer using Scientific Notation without a calculator!
1. The United States Debt is approximately 16,000,000,000,000 and the population of
the United States is approximately 400,000,000 people. If each person is equally
responsible for the national debt, how much does each person owe?
2. Our national debt increases by approximately 4,000,000,000 per day. How much
does the national debt increase per year?
3. A rectangle has length of 3,250,000 centimeters and a width of 200,000
centimeters. Find the area of the rectangle.
35
4. A rectangle has an area of 96,400,000 centimeters and a width 4,000,000
centimeters. Find the length of the rectangle.
5. The temperature halfway to the Sun from Mercury is approximately 1,800 °C and
Scientists theorize that it may be up to 26,000 times hotter at the center of the Sun.
Approximately how hot is it at the center of the Sun?
6. Each shrimp weighs approximately 0.00027 grams and a shrimp company can
bring in over 8,370,000 grams of shrimp per year. Approximately how many shrimp
is this?
7. A Blue Whale can eat 300,000,000 krill in a day, which is about 6,300,000,000 mg
worth of food. About how much does each krill weigh?
8. McDonald’s has about 2,100,000 managers and each makes and average of
$39,000 per year. How much money does McDonald’s spend on managers each
year?
36
HW#27 Scientific Notation Word Problems with Multiplication and Division
Calculate each answer using Scientific Notation.
1. The circumference of the earth at the equator is approximately 25,000 miles and a
commercial jet cruises at a rate 500 mph. Express each of the numbers in scientific
notation, then determine how long it will take the jet to fly around the earth at that
speed (t = d ÷ r).
2. The state of Colorado is 612,000 meters east to west and 451,000 meters north to
south. Write each of these numbers in scientific notation, then calculate the
approximate area of Colorado. Express your answer in scientific notation (A = lw).
3. The speed of light is 300,000,000 meters/second. If the sun is
150,000,000,000 meters from earth, how many seconds does it take light to reach
the earth?
4. The area of the Pacific Ocean is 60,680,000 square miles. The area of the Atlantic
Ocean is 29,600,000 square miles. How many times greater is the area of the
Pacific Ocean than the Atlantic Ocean?
37
Lesson #28 Simplifying Ratios in Scientific Notation
When a question asks what part of a number is another number, it is asking for a
______________________________. With scientific notation you would want to
simplify the ratio as much as possible and write the numbers in
______________________________.
Try the following:
1. What part of 3.6 x 107 is 1.5 x 106?
2. What part of 7.5 x 106 is 2.5 x 104?
3. What part of 1.2 x 104 is 9 x 103?
4. What part of 1.6 x 106 is 6.4 x 105?
38
Word Problems:
5. The population of New York is approximately 2 x 107 people. The population of the
United States is approximately 3 x 108 people. What part of the Unites States
population lives in New York? Express your answer as a ratio and a percent.
6. Snapchat is valued at $8.4 x 108. If the CEO and cofounder of Snapchat, Evan
Spiegel makes $1.4 x 106 per year, what part of the company’s value is he earning?
7. Mr. Bills made $1.08 x 105 last year. $2.52 x 104 was paid toward his mortgage.
How much of his salary went towards paying for his house?
8. There are approximately 1.14 x 107 drivers in New York. Last year there were 2.5 x
105 car accidents reported. Assuming that each driver was in no more than one
accident, approximately what percentage of drivers were in an accident last year?
39
HW #28 Simplifying Ratios in Scientific Notation
Write each ratio in simplest form.
1. What part of 9 x 105 is 2.7 x 103?
2. What part of 7.2 x 106 is 1.2 x 102?
3. The population of Colorado is 5.2 x 106 people, while the United States population
is approximately 3.14 x 108 people. What part of the United States population
resides in Colorado?
4. A survey was conducted to see how people spend the majority of their money.
2 x 105 people were surveyed and 1.6 x 104 said that they spend most of their
money on food. What part of the total number of people surveyed is this?
40
Lesson #29 Adding and Subtracting with Scientific Notation
In order to add or subtract numbers written in Scientific Notation, the numbers must
have the same ____________________.
If the given numbers have the same ______________________, simply add the
____________________________ and keep the power of ten the same.
If the given numbers do not have the same _______________________, you will need
to rewrite them so they do.
To rewrite a number in Scientific Notation, with a different power of ten consider the
following:
If the decimal number increases, the power of ten ________________________.
Example:
2.48 x 106 = 24.8 x 105
If the decimal number decreases, the power of ten _______________________.
Example:
3.15 x 108 = 0.315 x 109
Try the following:
1. 4.782 x 105 = __________ x 106 2. 3.961 x 107 = ___________ x 109
3. 2.5 x 10-6 = ________ x 10-5 4. 1.74 x 10-5 = __________ x 10-3
Rewrite the following numbers so that they have the same exponent, then add or
subtract.
5. 1.68 x 109 + 3.99 x 108 6. 9.763 x 1010 + 4.8 x 107
41
7. 2.98 x 106 – 5.3 x 105 8. 7.02 x 1012 – 9.37 x 1010
9. 7.5 x 10-4 + 1.24 x 10-5 10. 3.005 x 10-2 – 9 x 10-4
11. The population of the United States is approximately 3.189 x 108 people,
Canada’s is about 3.516 x 107, Alaska’s is about 7.367 x 105 and Mexico’s is
about 1.223 x 108. Determine the approximate population of North America.
12. There are approximately 3.236 x 108 cubic kilometers of water in the Atlantic
Ocean and 1.386 x 109 cubic kilometers in all the oceans combined. If the Atlantic
Ocean dried up how much water will be left?
42
HW #29 Adding and Subtracting with Scientific Notation
Show your work for each of the following questions. Answers should be written
in Scientific Notation.
1. 3.275 x 105 + 5 x 103 2. 4.18 x 10-3 + 7 x 10-4
3. 2.09 x 108 – 5.98 x 106 4. 1.004 x 10-2 – 8.6 x 10-4
5. The population of New York is 1.957 x 107 people. The population of New York City
is 8.337 x 106? How many NY state residents do not live in the city?
43
Lesson #30 Mixed Scientific Notation Problems
Complete the following with your group. Check in with a teacher before moving
onto the next problem.
1. 2.89 x 10-2 + 3.8 x 10-3 2. 7.208 x 108 – 3.6 x 106
3. (5.12 x 10-3)(3 x 10-4) 4. 4.8 𝑥 105
3 𝑥 10−2
Work on the following problems with your partners.
5. 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? Express your answer in Scientific Notation.
44
6. The average person takes about 3 x 104 breaths per day. If the average American
lives about 78 years (or about 28,000 days), how many total breaths will a person
take in his/her lifetime? Express your answer in Scientific Notation.
7. 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?
8. The estimated world population in 2011 was 7 × 109. Of the total population, 682
million of those people were left-handed. Approximately what percentage of the
world population is left-handed according to the 2011 estimation?
45
HW #30 Mixed Scientific Notation Problems
1. 7.5 x 10-4 + 4.206 x 10-2 2. 3.109 x 109 – 5.6 x 107
3. (1.278 x 10-2)(5 x 103) 4. 3.6 𝑥 106
4 𝑥 10−1
5. Here are the masses of the so-called inner planets of the Solar System.
Mercury: 3.3022 × 1023 kg Earth: 5.9722 × 1024 kg
Venus: 4.8685 × 1024 kg Mars: 6.4185 × 1023 kg
What is the average mass of all four inner planets? Write your answer in scientific