11/12/2020 National Go Math Middle School, Grade-8

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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.

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Lesson 2.4 51

Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company

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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.

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52 Unit 1

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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

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Lesson 2.4 53

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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?

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54 Unit 1

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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.

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Lesson 2.4 55

Copyright © 2012 by Houghton Mifflin Harcourt Publishing Company

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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

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