Scientific Notation Operations with
Transcript of Scientific Notation Operations with
![Page 1: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/1.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 1/6
L E S S O N
2.4Operations withScientific Notation
8.EE.4
Perform operations … inscientific notation. …choose units of appropriatesize for measurements … .Interpret scientific notation… generated by technology.
ESSENTIAL QUESTIONHow do you add, subtract, multiply, and divide usingscientific notation?
Adding and Subtracting withScientific NotationNumbers in scientific notation can be added and subtracted, either directly orby rewriting them in standard form.
EXAMPLE 1 8.EE.4
The table below shows the population of the three largest countries inNorth America in 2011. Find the total population of these countries.
Country
Population
United States
3.1 × 108
Canada
3.38 × 107
Mexico
1.1 × 108
Method 1:
STEP 1 First, write each population with the same power of 10.
United States: 3.1 × 108
Canada:
Mexico:
0.338 × 108
1.1 × 108
STEP 2 Add the multipliers for each population.
3.1 + 0.338 + 1.1 = 4.538
STEP 3 Write the final answer in scientific notation: 4.538 × 108.
Method 2:
STEP 1 First, write each number in standard notation.
United States: 310,000,000
Canada:
Mexico:
33,800,000
110,000,000
STEP 2 Find the sum of the numbers in standard notation.
310,000,000 + 33,800,000 + 110,000,000 = 453,800,000
STEP 3 Write the answer in scientific notation: 4.538 × 108.
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
• Im
age
Cred
its: ©
Getty
Imag
es
Lesson 2.4 51
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company
![Page 2: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/2.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 2/6
1. Using the population table above, how many more people live in Mexicothan in Canada? Write your answer in scientific notation.
Multiplying and Dividing withScientific NotationNumbers in scientific notation can be multiplied and divided directly by usingproperties of exponents.
EXAMPLE 2 8.EE.4
When the Sun makes an orbit around the center of the Milky Way, it travels
2.025 × 1014 kilometers. The orbit takes 225 million years. At what rate doesthe Sun travel? Write your answer in scientific notation.
Analyze Information
The answer is the number of kilometers per year that the Sun travelsaround the Milky Way.
Formulate a Plan
Set up a division problem using to represent the situation.
Solve
STEP 1 Substitute the values from the problem into the Rate formula.
Could you write 2.025 × 1014 in standard
notation to do the division? Would this be a good way
to solve the problem?
STEP 2 Write the expression for rate with years in scientific notation.
225 million = 2.25 × 108
STEP 3 Find the quotient by dividing the decimals and using the lawsof exponents.
Divide the multipliers.
Divide the powers of 10.
STEP 4
Combine the answers to write the rate in scientific notation.
Justify and Evaluate
Check your answer using multiplication.
The answer is correct.
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
• Im
age C
redi
ts: ©
Alam
y Im
ages
52 Unit 1
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company
![Page 3: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/3.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 3/6
2. Light travels at a speed of 1.86 × 105 miles per second. It takes lightfrom the Sun about 4.8 × 103 seconds to reach Saturn. Find theapproximate distance from the Sun to Saturn. Write your answer
in scientific notation.
3. Light travels at the speed of 1.17 × 107 miles per minute. Pluto’saverage distance from the Sun is 3,670,000,000 miles. On average, howlong does it take sunlight to reach Pluto? Write your answer in scientific
notation.
Scientific Notation on a CalculatorOn many scientific calculators, you can enter numbers in scientific notationby using a function labeled “ee” or “EE”. Usually, the letter “E” takes the place of“×10”. So, the number 4.1 × 109 would appear as 4.1E9 on the calculator.
EXAMPLE 3
The table shows the approximate areas for three continents givenin square meters. What is the total area of these three continents?Write the answer in scientific notation using more appropriate units.
Continent
Area (m2)
Asia
4.4 × 1013
Africa
3.02 × 1013
Europe
1.04 × 1013
8.EE.4
Find 4.4 × 1013 + 3.02 × 1013 + 1.04 × 1013.
Enter 4.4E13 + 3.02E13 + 1.04E13 on your calculator.
Write the results from your calculator: 8.46E13.
Write this number in scientific notation: 8.46 × 1013m2.
Square kilometers is more appropriate: 8.46 × 107 km2.
Because 1 km = 1,000 m, 1km2 = 1,0002 m2 , or 106
m2. Divide by 106.
YOUR TURN
Write each number using calculator notation.
4. 7.5 × 105 5. 3 × 10−7 6. 2.7 × 1013
Write each number using scientific notation.
7. 4.5E−1 8. 5.6E12 9. 6.98E−8
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Lesson 2.4 53
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company
![Page 4: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/4.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 4/6
Guided Practice
Add or subtract. Write your answer in scientific notation. (Example 1)
1. 4.2 × 106 + 2.25 × 105 + 2.8 × 106 2. 8.5 × 103 − 5.3 × 103 − 1.0 × 102
3. 1.25 × 102 + 0.50 × 102 + 3.25 × 102 4. 6.2 × 105 − 2.6 × 104 − 1.9 × 102
Multiply or divide. Write your answer in scientific notation. (Example 2)
5. 6.
7. 8.
Write each number using calculator notation. (Example 3)
9. 3.6 × 1011 10. 7.25 × 10−5 11. 8 × 10−1
Write each number using scientific notation. (Example 3)
12. 7.6E−4 13. 1.2E16 14. 9E1
ESSENTIAL QUESTION CHECK-IN
15. How do you add, subtract, multiply, and divide numbers written inscientific notation?
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
54 Unit 1
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company
![Page 5: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/5.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 5/6
Name Class Date
2.4 Independent Practice8.EE.4
16. An adult blue whale can eat 4.0 × 107 krill in a day. At that rate, how many krill can an adult blue whale eat in 3.65 × 102 days?
17. A newborn baby has about 26,000,000,000
cells. An adult has about 4.94 × 1013 cells. How many times as many cells does an adult have than a newborn? Write your answer in scientific notation.
18. What is the total amount of paper, glass,and plastic waste generated?
19. What is the total amount of paper, glass,and plastic waste recovered?
20. What is the total amount of paper, glass,and plastic waste not recovered?
21. Which type of waste has the lowestrecovery ratio?
Social Studies The table shows theapproximate populations of three countries.
Country China France Australia
Population 1.3 × 109 6.48 × 107 2.15 × 107Represent Real-World Problems The tableshows the number of tons of waste generatedand recovered (recycled) in 2010. 22. How many more people live in France than in
Australia?
23. The area of Australia is 2.95 × 106 squaremiles. What is the approximate averagenumber of people per square mile inAustralia?
Paper Glass Plastics
Tonsgenerated 7.131 × 107 1.153 × 107 3.104 × 107
Tonsrecovered 4.457 × 107 0.313 × 107 0.255 × 107
24. How many times greater is the populationof China than the population of France?Write your answer in standard notation.
25. Mia is 7.01568 × 106 minutes old. Converther age to more appropriate units usingyears, months, and days. Assume eachmonth to have 30.5 days.
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
• Im
age C
redi
ts: ©
Moo
dboa
rd/
Alam
y Im
ages
Lesson 2.4 55
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company
![Page 6: Scientific Notation Operations with](https://reader031.fdocuments.in/reader031/viewer/2022013001/61ca495b80d0752b185fd737/html5/thumbnails/6.jpg)
11/12/2020 National Go Math Middle School, Grade-8
https://my.hrw.com/content/hmof/math/gomath/na/gr8/interactive_student_edition_9780544083080_/index.html 6/6
26. Courtney takes 2.4 × 104 steps during her a long-distance run. Each step covers an average of 810 mm. What total distance (in mm) did Courtney cover during her run? Write your answer in scientific notation. Then convert the distance to the more appropriate unit kilometers. Write that answer in standard form.
27. Social Studies The U.S. public debt as of October 2010 was $9.06 × 1012. What was the average U.S. public debt per American if the population in
2010 was 3.08 × 108 people?
FOCUS ON HIGHER ORDER THINKING Work Area
28. Communicate Mathematical Ideas How is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?
29. Explain the Error A student found the product of 8 × 106 and 5 × 109 to be 4 × 1015. What is the error? What is the correct product?
30. Communicate Mathematical Ideas Describe a procedure that can be
used to simplify. Write the expression in scientific
notation in simplified form.
56 Unit 1
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company