Name Class Date. Using Scientific Notation

MCC8.EE.3

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Name Class Date

Using Scientific Notation

The weights of various sea creatures are shown in the table. You can write the weights in scientific notation.

Sea Creature Blue Whale Whale Shark Eel Minnow

Weight (lb) 250,000 41,200 133.25 0.95

Write the weight of the blue whale in scientific notation.

A Move the decimal point in 250,000 to the left as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

What number did you find?

B Divide 250,000 by your answer to ^A . Write your answer as a power of 10.

C Combine your answers to ^A and ^B to represent 250,000.

250,000 = × 10

Write the weight of the minnow in scientific notation.

D Move the decimal point in 0.95 to the right as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

What number did you find?

E Divide 0.95 by your answer to D . Write your answer as a power of 10.

F Combine your answers to ^D and E to represent 0.95.

0.95 = × 10

E X P L O R E

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Scientific Notation

Going Deeper

Essential question: How can you use scientific notation to express very large and very small quantities?

Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10.

3-3

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MCC8.EE.3

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REFLECT

1a. What do you notice about the sign of the exponent for weights greater than one pound?

1b. What do you notice about the sign of the exponent for weights less than one pound?

To translate between standard notation and scientific notation, you can count the number of places the decimal point moves.

Writing a Number in Scientific Notation An estimate of the world population in 2010 was 6,880,000,000.

Write the world’s population in scientific notation.

To write 6,880,000,000 in scientific notation, move the decimal point as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

Place the decimal point: 6 8 8 0 0 0 0 0 0 0 Which direction did you move the decimal point?

What number did you find?

How many places did you move the decimal point?

When 6,880,000,000 is written in scientific notation, should the exponent of the power of 10 be positive or negative? Explain.

The world’s population, 6,880,000,000, written in scientific notation is

× 10 .

E X A M P L E

2

Writing Numbers in Scientific Notation When the number is greater than or equal

to 1, use a positive exponent.

84,000 = 8.4 × 10 ⁴ The decimal point moves 4 places.

When the number is less than 1, use a negative exponent.

0.0783 = 7.83 × 10 ^–2 The decimal point moves 2 places.

To translate between scientific notation and standard notation, you can move the decimal point the number of places indicated by the exponent in the power of 10. When the exponent is positive, move the decimal point to the right. When the exponent is negative, move the decimal point to the left.

Module 3 70 Lesson 3

MCC8.EE.3

MCC8.EE.3

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Writing a Number in Standard Notation Write each number in standard notation.

A 4.18549 × 1 0 ¹²

What is the exponent of the power of 10?

Which direction should you move the decimal point?

Place the decimal point. Add placeholder zeros if necessary.

4 1 8 5 4 9

The number 4.18549 × 1 0 ¹² written in standard notation is .

B 2.568 × 1 0 ^-6

What is the exponent of the power of 10?

Which direction should you move the decimal point?

Place the decimal point. Add placeholder zeros if necessary.

2 5 6 8

The number 2.568 × 1 0 ^-6 written in standard notation is .

Comparing Numbers in Scientific Notation

The approximate weight of a whale shark is 4 × 1 0 ⁴ pounds. The approximate weight of a common dolphin is 2 × 1 0 ² pounds. How many times as great as the weight of the whale shark is the weight of the dolphin?

First compare the values between 1 and 10.

The 4 in 4 × 1 0 ⁴ is times as great as the 2 in 2 × 1 0 ² . Next compare the powers of 10.

1 0 ⁴ is times as great as 1 0 ² . Circle the most reasonable answer.

The weight of the whale shark is 2 / 20/ 200 / 2000 times as great as the weight of the dolphin.

REFLECT

4a. Scientists captured and released a whale shark that weighed about 6 × 1 0 ⁵ units.

Circle the best choice for the units this measurement is given in: ounces /pounds/tons.

4b. Explain how you chose a unit of measurement in 4a.

E X A M P L E

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E X A M P L E

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P R A c t i c E

1. 58,927

3. 0.000487

5. 0.000059

7. 13,300

2. 1,304,000,000

4. 0.000028

6. 6,730,000

8. 0.0417

9. 4 × 10 ⁵

11. 8.3 × 10 ^-4

13. 2.97 × 10 ^-2

15. 8.456 × 10 ⁷

10. 1.8499 × 10 ⁹

12. 3.582 × 10 ^-6

14. 6.41 × 10 ³

16. 9.06 × 10 ^-5

17. 8 × 10 ⁵ is 2/20/200/ 2,000 times as great as 4 × 10 ² .

19. 4 × 1 0 ^-5 is 0.02/0.2/2/20 times as great as 2 × 1 0 ^-4 .

18. 9 × 1 0 ¹⁰ is 30 / 300 / 3,000 / 30,000 times as great as 3 × 1 0 ⁷ .

20. 4 × 1 0 ^-12 is 0.00001 / 0.0001 / 10 / 1000 times as great as 4 × 10 ^-8 .

Write each number in scientific notation.

Write each number in standard notation.

Circle the correct answer.

21. The mass of a proton is about 1.7 × 1 0 ^-24 g. The mass of a neutron is about the same as a proton. The nucleus of an atom of carbon has 6 protons and 6 neutrons.

The mass of the nucleus is about 2 × 1 0 ^-26 units. Circle the best choice for the units this measurement is given in: g/ kg /tons

22. The air distance between Los Angeles, California, and New York City, New York, is about 3.9 × 10 ³ units. Circle the best choice for the units this measurement is given in: cm / m / km

Module 3 72 Lesson 3

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Holt McDougal Mathematics

Exponents and Roots

Practice B: Scientific Notation Write each number in standard notation.

1. 2.54 u 10

2. 6.7 u 10

3. 1.14 u 10

4. 3.8 u 10

________________ ________________ _______________ ________________

5. 7.53 u 10

6. 5.6 u 10

7. 9.1 u 10

8. 6.08 u 10

________________ ________________ _______________ ________________

9. 8.59 u 10

10. 3.331 u 10

11. 7.21 u 10

12. 5.88 u 10

________________ ________________ _______________ ________________

Write each number in scientific notation.

13. 75,000,000 14. 208 15. 907,100

________________________ _______________________ ________________________

16. 56 17. 0.093 18. 0.00006

________________________ _______________________ ________________________

19. 0.00852 20. 0.0505 21. 0.003007

________________________ _______________________ ________________________

22. 5226 23. 0.04 24. 98,856

________________________ _______________________ ________________________

25. Jupiter is about 778,120,000 kilometers from the Sun. Write this number in scientific notation.

_________________________________________________________________________________________

26. The E. coli bacterium is about 5 u 10

meters wide. A hair is about 1.7 u 10

meters wide. Which is wider, the bacterium or the hair?

____________________________________________________________________________________________________________________________________

14 LESSON

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3-3 Additional Practice

Name Class Date

Module 3 73 Practice and Problem Solving

Name ________________________________________ Date __________________ Class__________________

Holt McDougal Mathematics

Exponents and Roots

Problem Solving: Scientific Notation Write the correct answer.

1. In June 2001, the Intel Corporation announced that they could produce a silicon transistor that could switch on and off 1.5 trillion times a second.

Express the speed of the transistor in scientific notation.

________________________________________

3. The elements in this fast transistor are 20 nanometers long. A nanometer is one-billionth of a meter. Express the length of an element in the transistor in meters using scientific notation.

________________________________________

2. With this transistor, computers will be able to do 1 u 10

calculations in the time it takes to blink your eye.

Express the number of calculations using standard notation.

________________________________________

4. The length of the elements in the transistor can also be compared to the width of a human hair. The length of an element is 2 u 10

times

smaller than the width of a human hair. Express 2 u 10

in standard notation.

________________________________________

Use the table to answer Exercises 5–9.

Choose the best answer.

5. Express a light-year in miles using scientific notation.

A 58.8 u 10

C 588 u 10

B 5.88 u 10

D 5.88 u 10

6. How many miles is it from Earth to the

star Sirius?

F 4.705 u 10

H 7.35 u 10

G 4.704 u 10

J 7.35 u 10

7. How many miles is it from Earth to the

star Canopus?

A 3.822 u 10

C 3.822 u 10

B 1.230 u 10

D 1.230 u 10

8. How many miles is it from Earth to the

star Alpha Centauri?

F 2.352 u 10

H 2.352 u 10

G 5.92 u 10

J 5.92 u 10

Distance From Earth To Stars Light-Year 5,880,000,000,000 mi.

Star Constellation Distance (light-years) Sirius Canis Major 8

Canopus Carina 650

Alpha

Centauri Centaurus 4

Vega Lyra 23

9. How many miles is it from Earth to the star Vega?

A 6.11 u 10

C 6.11 u 10

B 1.3524 u 10

D 1.3524 u 10

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14 LESSON

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Problem Solving

Module 3 74 Practice and Problem Solving