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Math 8 Unit 11

Scientific Notation

Extra Help: Thursday, March 21, 7:40am

Thursday, March 28, 2:40pm

Name:________________

Date Lesson Topic Homework

3/13 1 Introduction to Scientific Notation Lesson 1 – Page 4

3/14 PI DAY ACTIVITIES

3/15 2 Converting Scientific Notation Lesson 2 – Page 8

3/18 3 Compare and Order Scientific Notation Lesson 3 – 1

3/19 4 Multiply and Divide Lesson 4 – Page 15

3/20 5 Add and Subtract Lesson 5 – Page 19

3/21

Quiz Review Finish Review & Study!

3/22 Quiz

3/25 6 Scientific Notation with a Calculator Lesson 6 – Page 27

3/26 7 Application of Scientific Notation Lesson 7 – Page 31

3/27 Activity Review Page 32

3/28 Review Check Review solutions on website

3/29 Test

3

Lesson 1 – Introduction to Scientific Notation

Aim: What is Scientific Notation?

Guided Practice:

Scientific Notation- when you are dealing with very large or very small numbers, it is helpful to be able to

write them in a shorter form.

Scientific Notation Standard Form

2.59 × 1011 = 259,000,000,000

Rule: A number is in Scientific Notation if:

1) The first factor is a single digit between 1 and 9, followed by a decimal point. Zero does not count as a digit.

2) Times the second factor which is a power of 10.

Exercise 1- Determine if the following numbers are written in scientific notation:

(1) 3.2 × 104 (2) 78.96 × 104 (3) 456.1 × 10−8 (4) 9. × 10−5

Scientific Notation: Positive Exponents and Negative Exponents

A number in scientific notation with ______________________ exponents represents a number

________________ than one (whole number).

A number in scientific notation with ________________________ exponents represents a number between 0

and 1 (decimal).

Remember:

Positive Exponent ________________________________________________

Negative Exponent ________________________________________________

4

Exercise 2- Determine if the following numbers below will be whole numbers or decimals.

(1) 1.2 × 105 (2) 5.8 × 10−5 (3) 6.8 × 10−9 (4) 3 × 109

Scientific Notation: Real Life Situations

When is it appropriate to use scientific notation in real life?

Exercise 3- determine if the number in scientific notation would be written as a positive or negative exponent:

(1) The weight of 10 Mack Trucks (2) The width of a grain of sand

Independent Practice:

1. Determine if the numbers below are written in scientific notation. Explain your reasoning.

(a) 4.1 × 1015 (b) 24.01 × 105 (c) 0.1 × 10−6

2. Determine if the number below are in whole numbers or decimals. Explain your reasoning.

(a) 2.1 × 1015 (b) 2.1 × 10−15 (c) 1.0 × 10−5

3. Determine if the number in scientific notation would be written with a positive or negative exponent.

Explain your reasoning.

(a) The size of a cheek cell (b) The mass of Earth

Examples of Large Numbers Examples of Small Numbers

5

Lesson 1 Homework

Determine if the numbers below are written in scientific notation. Explain your reasoning.

1) 1.5 x 104 2) 1.50 x 105 3) 0.42 x 102 4) 4. 56 + 106

5) 134, 987 6) 9.5 x 10-3 7) 17 x 10-16 8) 75.9 x 106

9) 1.3 x 10-23 10) 65 x 102

Determine if the following number in scientific notation would be written as a positive or negative exponent.

11) How many seconds in a year 12) The width of a piece of thread (in feet)

13) The weight of a skyscraper (in pounds) 14) The weight of an electron (in pounds)

Review Work:

21) 7 3 x 7-6 22) (1

4) -3

23) 4x + x – 8 = 5x + 12 24) 18

-3

6

Lesson 2 – Converting Scientific Notation

Aim: How can a number be expressed in scientific notation?

Warm Up: Tia was told to put her answer in scientific notation, so she wrote the following answer:

12.3 × 10−7. Is her response in the correct form? Explain.

Guided Practice:

Standard Form to Scientific Notation

1. Write the number placing the decimal point after the first non-zero digit

2. Write 𝑥 10

3. Count the number of digits you moved the decimal point and write it as the exponent.

Remember:

If it is a whole number ______________________________________________________________

If it is a decimal ______________________________________________________________

Exercise 1- Convert from standard form to scientific notation

(1) 245,000,000 (3) 500,000

(2) .00084 (4) .000007643

7

Scientific Notation to Standard Form

1. Move the decimal point to the number the number of places indicated by the exponent

2. If it’s a positive exponent, move the decimal point to the right (Whole number- make the number larger)

If it’s a negative exponent, move the decimal point to the left (Decimal-make the number smaller)

Exercise 2- Convert from scientific notation to standard form

(1) 5.9 × 103 (3) 8.32 × 10−4

(2) 4.765 × 108 (4) 1.9 × 10−7

Making Sure a Number is written in Scientific Notation

Rule:

If a decimal point needs to move to the left, the exponent increases 48.6 × 103

If the decimal point needs to move to the right, the exponent decreases . 48 × 103

** Be careful when the exponent is negative!

Exercise 3- Write each in Scientific Notation, if necessary:

(1) 68.7 × 109 ______________________________ (2) 6 × 105 _____________________________

(3) . 725 × 108 ______________________________ (4) . 292 × 10−4 ____________________________

(5) 326 × 10−8 ______________________________ (6) 7.5 × 10−9 ____________________________

LARS: Left Add Right Subtract

8


Complete the Foldable, then answer the following:

1. The speed of light in a vacuum is 299,792,458 meters per second. Which number, written in scientific

notation, is the best approximation of the speed of light?

(1) 0.3 𝑥 107 meters per second




2. Expressed in scientific notation, 0.0000056 is equivalent to:

(1) 5.6 × 10−6

(2) 0.56 × 10−5

(3) 5.6 × 106

(4) 56 × 106

3. In 2013, JFK Airport had approximately 9.4 × 107 passengers pass through the airport. What is that number

written in standard form?

4. A virus is viewed under a microscope. It’s diameter is 0.00000002 meter. How would this length be

expressed in scientific notation?

5. Mrs. Bretscher gave her class the following problem: Convert the following number from standard form to

scientific notation 1,742,103,000.

Anthony’s Answer: 17.42103 × 108

Is Anthony’s answer correct? Explain your reasoning.

9

Lesson 2 Homework

Converting Standard Form and Scientific Notation

Convert into scientific notation. Write the numbers below in standard form.

1) 3,400

5) 1.901 x 10-7

2) 0.000023 6) 8.65 x 10-1

3) 101,000 7) 2.30 x 104

4) 0.010

8) 9.11 x 103

10

Lesson 3 – Compare and Order Scientific Notation

Aim: How do we compare numbers written in scientific notation? +

Warm Up: Are the following numbers written in scientific notation? If not, state the reason.

(a) 4.0701 + 107 (b) . 325 × 10−2

Investigation 1: Express each scientific notation in standard form.

(a) 4.3 × 102 (b) 2.5 × 103

Which number is smaller?

Which number is larger?

What do we observe about the exponents?

Investigation 2: Express each scientific notation in standard form.

(a) 2.1 × 104 (b) 1.5 × 104

Which number is smaller?

Which number is larger?

Is there a relationship between the value of the coefficient and which number is larger or smaller?

11

Guided Practice: Steps for Comparing Numbers in Scientific Notation Form

1. To compare two numbers given in scientific notation, first compare the _____________________.

The one with the greater exponent will be _________________________.

2. If the exponents are _______________, compare the coefficients (number with decimal).

Exercise 1: 1.06 × 1016 ________ 2.4 × 1015 Exercise 2: 2.78 × 107 ________ 278 × 107

Exercise 3- Order the countries according to the amount of money

visitors spent in the United States from least to greatest.

_____________________ _____________________

_____________________ _____________________

_____________________ _____________________

_____________________ _____________________


For the following problems, use >, <, 𝑜𝑟 = to make the statement true.

(1) 9.74 × 1021 _______ 2.1 × 1022 (2) 5.28 × 1012 ______ 95.4 × 1012

(3) 2.33 × 1010 _______ 7.6 × 1010 (4) 4.4 × 107 ______ 44,000,000

(5) 548,000,000 _______ 5.48 × 107 (6) 1.2 × 10−3 ______ 4.7 × 10−3

(7) 6.23 × 1014 ______ 8.912 × 1012 (8) 5.15 × 10−4 ______ 6.35 × 10−5

(9) 3.28 × 1017 ______ 4.25 × 1017 (10) −1.2 × 105 ______ −1.7 × 105

(11) Compare the following problem. Be sure to explain your reasoning.

12.8 × 103 ______ 1.4 × 103

12

Lesson 3 Homework

Comparing Standard Form and Scientific Notation

Compare the following numbers:

(1) 2.56 × 105 _______ 4.2 × 10−7

(2) 4.3 × 104 _______ 1.6 × 106

(3) 7.1 × 10−2 _______ 2.9 × 10−6

(4) 5.27 × 105 _______ 2.139 × 105

Order the numbers from least to greatest:

2.81 × 10−7; 2.01 × 103; 2.72 × 10−7; 9.45 × 10−4

_______________________________

_______________________________

_______________________________

_______________________________

The table lists the populations of five countries. List the countries from least to greatest.

____________________ ____________________

____________________ ____________________

____________________ ____________________

____________________ ____________________

____________________ ____________________

____________________ ____________________

13

Lesson 4 – Multiply and Divide

Aim: How can we find the product and quotient of numbers written in scientific notation?

Warm Up: Answer the following questions (without a calculator)

(a) 2.7 × 3.4 (b) 8.04 ÷ 6.7

(c) 103 × 105 (d) 1012

104

Guided Practice:

To find the product of numbers that are in scientific notation:

1. Multiply the first factors (the numbers before the multiplication sign)

2. Keep the base of ten

3. Add the exponents

Exercise 1- Evaluate the following (7.2 × 103) (1.6 × 104)

Exercise 2- Evaluate the following (8.4 × 102) (2.5 × 106)

14

To find the quotient of numbers that are in scientific notation:

1. Divide the first factors (the numbers before the multiplication sign)

2. Keep the base of ten

3. Subtract the exponents

Exercise 3- Evaluate the following 9.45×1010

1.5×106

Exercise 4- Evaluate the following 1.14 × 106

4.8 × 103


1. Evaluate the following

(2.63 × 104) (1.2 × 10−3)

9 × 10−11

2.4 × 108

2. Neurons are cells in the nervous system that process and transit information. An average neuron is about

5 × 10−6meter in diameter. A standard table tennis ball is 0.04 meter in diameter. About how many times as

great is the diameter of a ball than a neuron?

Scientific Notation ______________________

Standard Form _________________________

15

3. Central Park in New York City is rectangular in shape and measures approximately 1.37 × 104 feet by

2.64 × 102 feet. If one acre is equal to 4.356 × 104 square feet, how many acres does Central Park cover?


Standard Form _________________________

4. In 2005, 8.1 × 1010 text messages were sent in the United States. In 2010, the number of annual text

messages had risen to 1,810,000,000,000. About how many times as great was the number of text messages in

2010 than 2005?


Standard Form _________________________

5. Which one does not belong? Prove your reasoning.

(a) 14.28 × 109;

(b) (3.4 × 106)(4.2 × 103);

(𝑐) 1.4 × 109;

(d) (3.4)(4.2) × 10(6+3)

6. Enrique is finding the quotient of 6.63 × 10−6 and 5.1 × 10−2. Revise & circle his mistake and correct it.

16

Lesson 4 Homework

1. Determine the product of 800.5 × (2 × 106).

2. One terabyte of data storage is approximately 1,100,000,000,000 bytes of data. About how many bytes

are in four terabytes? Express your answer in scientific notation.

3. Three billionaires chipped in to buy an island worth $3.66 𝑥 1012. How much did each billionaire

spend?

4. On weekdays, the average number of subway riders in City X is approximately 1 𝑥 106. The average

number of subway riders In City Y is approximately 50,000. How many times as great is the average

number of riders in City X as in City Y?

17

Lesson 5 – Add and Subtract

Aim: How does scientific notation make it easier to compute by adding and subtracting very large or very small

numbers?

Warm Up: Simplify each expression

1. (1.1 × 10−3)(2.5 × 109) 2. 9.9 × 1011

1.1 × 108

3. Can we simplify the following expressions?

(a) 2𝑥2 + 3𝑥 (b) 4𝑥 − 𝑥 (c) 𝑥3 + 3𝑥2 + 7𝑥

Guided Practice: Steps for Adding and Subtracting with Scientific Notation

1. Look to see if the exponents are the same. (If they are, skip to step 3)

2. If the exponents are different, move the decimal point in the

coefficient to change the exponent.

a) If you moved the decimal to the left, add the exponent

b) If you moved the decimal to the right, subtract the exponent.

3. Add or subtract the coefficients

4. Check to make sure your answer is in Scientific Notation; if it’s not in the correct form, convert it!!

Exercise 1- Find the sum: (2.3 × 103) + (6.9 × 103)

(4.81 × 103) + (7.913 × 105)

18

Exercise 2- Find the difference:

(6.1 × 104) − (2.43 × 102) (7.61 × 106) − (2.87 × 104)

Exercise 3-Evalute the following expression: (6.3 × 105) + 2,700,000


1) (7.38 × 108) − (1.61 × 107) 2) (8.41 × 103) + (9.71 × 104)

3) (1.263 × 109) − (1.525 × 107) 4) (2.85 × 107) + (1.61 × 109)

19

5. In 2006, the US had a Gross Domestic Product (GDP) of 1.313 × 1013. The United Kingdom had a GDP of

1.93 × 1012. What were the combined GDPs of the Us and the UK, in 2006?

6. Factories A and B produced potato chips. Last year, each factory reported the amount of each ingredient.

Factory A reported their amounts in scientific notation and Factory B reported their amounts in standard form.

Ingredient Factory A

(amount used in pounds)

Factory B

(amount used in pounds)

Potato 4.87 × 106 3,309,000

Oil 5.61 × 105 356,000

Salt 2.87 × 105 193,500

Show your work or explain, leave your answers in scientific notation.

a) Which factory used more oil last year? By how much?

b) What is the total amount of salt used by both factories?

c) What is the total weight of all the ingredients in Factory A?

20

Lesson 5 Homework

Evaluate each expression. Express the result in scientific notation. Show all work!

1. (5.69 × 105) + (6.97 × 105) =

2. (9.47 × 108) − (4.9 × 108) =

3. (3.67 × 107) + (6.4 × 107) =

4. (9.87 × 107) − 10,510,000 =

5. In 2012, 1.9 × 107 people visited Central Park. That same year, 9.3 × 106 people visited Yellowstone Park.

How many more people visited Central Park than Yellowstone?

6. In 2006, China had 1.311 × 108 internet users. That same year, Japan had 9.09 × 107 internet users. How

many Internet users did the two countries have combined?

21

Scientific Notation Lessons 1 – 5 Quiz Review

Lesson 1

Determine if the number in scientific notation would be written with a positive or negative exponent.

1) Total weight of 18-wheel truck ______________ 2) Population in China ______________

3) Size of a computer pixel _____________ 4) Weight of an atom_____________

Write each number in correct scientific notation

5) 29 x 102 = ______________________ 6) .17 x 10-7 = ________________________

7) .052 x 10-4 = ______________________ 8) 386.4 x 10-6 = ______________________

Lesson 2

Write each of the following in scientific notation:

9) 25,000 __________________________________ 10) .000302 __________________________________

11) -4,700__________________________________ 12) 2 million__________________________________

Write each of the following in standard form:

13) 7104.2 x _______________________________ 14) 3108x _________________________________

15) 4101.8 x _______________________________ 16) 51003.4 x ______________________________

What is the value of the missing exponent (n):

17) What is the value of n in the problem: 50,200,000 = nx1002.5 n = ______

18) What is the value of n in the problem: 0.00032 = nx102.3 n = ______

19) What is the value of n in the problem: 31,000 = nx101.3 n = ______

20) What is the value of n in the problem: 0.0000082 = nx102.8 n = ______

22

Lesson 3

Compare: Use < , >, or =

21) 6109.2 x 2,900,000 22) 3104.2 x 31041.2 x

23) 5101.2 x 7101.1 x 24) 5106.7 x 3108.4 x

Lesson 4 Add, Subtract, Multiply, or Divide Without a Calculator

25) (2.8 x 107) + (4.1 x 107) = ____________________ 26) (9.1 x 108) - (3.8 x 108) = _______________

27) (4.0 x 10-4) x (2.1 x 109) = ____________________ 28) (9.9 x 1010) ÷ (3.3 x 109) = ______________

Animal Weight in ounces

Elephant 2.28 x 105

Cat 1.92 x 102

Mouse 3.2 x 10-1

Zebra 9.6 x 103

29) Add - Cat and Zebra 30) Subtract - Elephant minus Cat

31) Multiply - Mouse and Zebra 32) Divide - Zebra and Mouse

Mixed Review

33) Which expression has the greatest value?

A) 1.045 x 10 2 B) 1.45 x 10 2 C) 8.4 x 10 2 D) -8.4 x 10 2

23

34) In the year 2000, approximately 169,000,000 personal computers were used in the United States. What is

this number expressed in scientific notation?

A) 1.69 × 10-8 B) 16.9 × 10-7 C) 16.9 × 107 D) 1.69 × 108

35) A butterfly weighs only about 5.0 x 10 -5 of a kilogram. What is the number written in standard form?

A) 0.00005 B) 0.000005 C) 50,000 D) 500,000

36) The average distance from Pluto to the Sun is 3.65 × 10 9 miles. What is this number written in

standard form?

A) 365,000,000 B) 3,650,000,000 C) 36,500,000,000 D) 365,000,000,000

Extended Response:

37) The radius of a hydrogen atom is about 0.000000106 millimeter. Write the length of this radius in scientific

notation.

Answer __________ millimeter(s)

On the lines below, explain how you determined your answer.

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

38) The table below shows geographic information about Antarctica.

Write the numbers, in standard form, for the area and the lowest elevation of Antarctica.

Answer:

Area __________________________ square kilometers

Lowest elevation _________________________ meters

24

39) Ming wrote the four numbers below in scientific notation.

5.5 × 105 1.2 × 103 2.8 × 106 7.4 × 102

Put them in order least to greatest.

________________________________________________________________________________

40) Connor is researching four types of memory modules for his computer. The data are shown in the

table below.

Connor wants to buy the module with the most memory. Which module should he buy? ______________

41) The table below shows the number of Earth days it takes for two of Jupiter’s moons to make one full orbit

around Jupiter.

How much longer, in Earth days, does it take for Themisto to orbit Jupiter than it does for Callisto to orbit

Jupiter? Write your answer in standard form.

Show your work.

Answer _________________ Earth days

25

Lesson 6 – Scientific Notation with a Calculator

Aim: How can I evaluate scientific notation using all operations? *Calculator

Rules for Multiplying and Dividing Numbers in Scientific Notation

1 - Put your calculator in Sci. Not. Mode

2 - Type the problem into the calculator EXACTLY how it is written.

How to multiply and divide numbers in scientific notation:

You MUST use parentheses ( ) when inputting each number in

scientific notation!

To input an exponent, enter the base then hit ( ^ ) before entering

the exponent.

Hit (−) first if you need to make a number negative.

Simple numbers like (1.2 x 104) can be inputted like this:

( 1 . 2 x 1 0 ^ 4 )

Examples:

1) (3.4 x 103)(1.2 x 104)

Enter the following:

( 3 . 4 x 1 0 ^ 3 ) x ( 1 . 2 x 1 0 ^ 4 )

Answer: (3.4 x 103)(1.2 x 104) = 4.08 x 107

4.08 x1007

26

Warm Up: Evaluate the following: What is the product of (2.2 × 104)(1.5 × 103)

Guided Practice: Mixed Practice. State answers in Scientific Notation and Standard Form

1) (8 × 105) + (5 × 104)

2) 7×106

2×103

3) (3 × 104) − (5 × 102)

4) (4 × 10)(2 × 103)

27


1) 9.8 × 103

2 × 102

2) (8 × 103)(3 × 104)

3) (5.13 × 108) − (2.7 × 106)

4) (7 × 105) + (6 × 107)

5) (4 × 102) + (9 × 104) 6) (2 × 103)(5 × 104)

7. Find the perimeter of the rectangle, if the area is 5.612 × 1014 cm2

28

Lesson 6 Homework

1. (8.4 x 102)(2.5 x 106) 2. (2.63 x 104) + (1.2 x 10-3) 3. (7.83 x 108)(1.161 x 107)

4. (8.4 x 102) ÷ (2.5 x 106) 5. (9 x 10-11) - (2.4 x 108) 6. (9.45 x 105) ÷ (2.4 x 102)

7. 87,000,000 + (8.7 x 105) 8. (1.14 x 106)(4.8 x 10-6) 9. (1.03 x 10-9) - (4.7 x 107)

10. (8.4 x 102) (2.5 x 106) 11. (9 x 10-11) ÷ (2.4 x 108) 12. (9.45 x 105) + (2.4 x 102)

Use the table to solve questions 13 – 16. The table shows the approximate populations of 3 countries.

Country China France Australia

Population 1.3 x 109 6.48 x 107 2.15 x 107

13. What is the total population of China, France, and Australia?

14. How many more people live in France than in Australia?

15. The area of Australia is 2.95 x 106 square miles. What is the approximate average number

of people per square mile in Australia?

16. How many times greater is the population of China than the population of France?

Write your answer in standard notation.

29

Lesson 7 – Application of Scientific Notation

Aim: I can apply scientific notation

Warm up:

1. Which one doesn’t belong? Explain your reasoning.

14.28 x 10 9 (3.4 x 106)(4.2 x 103) 1.4 x 109 (3.4)(4.2) x 10 (6 + 3)

Guided Practice:

Use the table below for questions 1-3. The table below shows the debt of the three most populous states and the

three least populous states.

Express all answers

in Scientific Notation

1. What is the sum of the debts for the 3 most populous states?

2. What is the sum of the debts for the 3 least populous states?

3. How much larger is the combined debt of the three most populated states than that of the three least

populated states?

4. Here are the masses of the so-called inner planets of the Solar System.

Mercury: 3.3 x 1023 kg Earth: 5.9 x 1024 kg

Venus: 4.8 x 1024 kg Mars: 6.4 x 1023

What is the average mass of all four inner planets? Write your answer in scientific notation.

State Debt (in dollars) Population

(2012)

California 407,000,000,000 3.8 x 107

New York 337,000,000,000 1.9 x 107

Texas 276,000,000,000 2.6 x 107

North Dakota 4,000,000,000 6.9 x 104

Vermont 4,000,000,000 6.26 x 104

Wyoming 2,000,000,000 5.76 x 104

30

5. What is the difference of and written in scientific notation?

6. What is the sum of 12 and expressed in scientific notation?

1) 4.2 x 106

2) -4.2 x 106

3) 42 x 106

4) 42 x 107

7. What is the product of , , and expressed in scientific notation?

1) 2) 3) 4)

8. What is the quotient of and ?

1) 2) 3) 4)

9. What is the value of in scientific notation?

1) 2) 3) 4)

10. If the mass of a proton is gram, what is the mass of 1,000 protons?

1) g

2) g

3) g

4) g

1) 84 x 108

2) 8.4 x 109

3) 2 x 105

4) 8.4 x 108

31

11. If the number of molecules in 1 mole of a substance is , then the number of molecules in 100

moles is

1) 2) 3) 4)

12. If you could walk at a rate of 2 meters per second, it would take you 1.92 x 108 seconds to walk to the

moon. Is it more appropriate to report this time as 1.92 x 108 or 6.02 years?

13. The areas of the world’s oceans are listed in the table. Order the oceans according to their area from least to

greatest.

Ocean Area (ml2)

Atlantic 2.96 x 107

Arctic 5.43 x 106

Indian 2.65 x 107

Pacific 6 x 107

Southern 7.85 x 106

14. Mr. Murphy’s yard is 2.4 x 102 feet by 1.15 x 102 feet. Calculate the area of Mr. Murphy’s yard.

15. Every day, nearly 1.30 x 109 spam E-mails are sent worldwide! Express in scientific notation how many

spam e-mails are sent each year.

16. In 2005, 8.1 x 1010 text messages were sent in the United States. In 2010, the number of annual text

messages had risen to 1,810,000,000,000. About how many times as great was the number of text

messages in 2010 than 2005?

32

Lesson 7 Homework

1. All planets revolve around the sun in elliptical orbits. Uranus’s furthest distance from the sun is

approximately 3.004 x 109 km, and its closest distance is approximately 2.749 x 109 km. Using this

information, what is the average distance of Uranus from the sun?

2. A micron is a unit used to measure specimens viewed with a microscope. One micron is equivalent to

0.00003937 inch. How is this number expressed in scientific notation?

1) 3.937 𝑥 105 3) 3937 𝑥 108

2) 3937 𝑥 10−8 4) 3.937 𝑥 10−5

3. The distance from Earth to the Sun is approximately 93 million miles. A scientist would write that

number as:

1) 93 𝑥 107 3) 9.3 𝑥 106

2) 93 𝑥 1010 4) 9.3 𝑥 107

4. By the year 2050, the world population is expected to reach 10 billion people. When 10 billion is written

in scientific notation, what is the exponent of the power of ten?

5. The table shows the mass in grams of one atom of each of several elements. List the elements in order

from the least mass to greatest mass per atom.

Element Mass per Atom

Carbon 1.995 x 10-23

Gold 3.272 x 10-22

Hydrogen 1.674 x 10-24

Oxygen 2.658 x 10-23

Silver 1.792 x 10-22

6. A music download Web site announced that over 4 x 109 songs were downloaded by 5 x 107 registered users.

What is the average number of downloads per user?

7. Sara’s bedroom is 2.4 x 103 inches by 4.35 x 102 inches. How many carpeting would it take to cover her

floor? Express your answer in scientific notation.

33

Unit 11 Review -- Scientific Notation

Write the following in Standard Form:

1) 6.3 × 107 2) 5.23 × 10−4 3) 8.08 × 100 4) 4.2 × 10−1 5) 9.24 × 1010

Write the following using Scientific Notation:

6) 120 7) 65,002,000 8) 0.0000233 9) .345 x 104 10) 523 x 109

Find the value of the following. Write your answer in Scientific Notation.

11) (4.3 × 107)( 2.2 × 103) 12) (5 × 1012)(4.77 × 10−5) 13) (3.6 × 10−5)3

14) 6.2×109

2×102 15) (3.45 × 106) ÷ (8.01 × 10−5) 16)

1.6332×1011

1.6332×1011

17) (4.3 × 107) + ( 7.2 × 107) 18) (5.32 × 1012) − ( 2.9 × 103) 19) (2 × 107) + ( 5.6 × 106)

Compare using < > =

20) 5.3 x 103 4.5 x 103 21) 2300 2.3 x 103

34

Word Problems: Add, Subtract, Multiple, or Divide

22) How many times larger is 9.8 x 106 than 6.32 x 105?

23) Find the mass of 15107.2 hydrogen atoms if the mass of one hydrogen atom is 241067.1 grams.

24) The distance from the Earth to the star Alpha Centauri is about 131007.4 kilometers. If light travels at a

speed of about 5100.3 kilometers per second, how long does it take light to travel from the star to Earth?

25) In 1867, the United States purchased Alaska from Russia for $7.2 million. The total area of Alaska is about

81078.3 acres. What was the price per acre?

26) Consider a person whose heart beats 70 times per minute, and lives to be 85 years old. How many times

would their heart beat in their lifetime (excluding leap years)? Write your answer in scientific notation.

27) If the population in New York City is 3.2 x 107 and the population on Long Island is 1.68 x 105, how many

people live in these two areas combined? Express your answer in scientific notation.

28) The masses of the following planets in a given solar system are listed below.

Planet A: 3.24 x 1024 Planet B: 5.673 x 1025

Planet C: 2.178 x 1025 Planet D: 3.923 x 1024

What is the average mass of all four planets? Write your answer in scientific notation.

35

Mixed Review. Simplify:

29) 8x – 2y + 6x – y 30) -5(-2x + 7) – 5

Simplify:

31) 55 ∙ 57 32) 26 ∙ 2−9 33) 98

94 34) 6−10 ÷ 63 35)

6

0

Solve.

36) 4(-3x + 2) = 44 37) 4(x – 2) = 3x + 5 38) 4x + 2 = 5x – 3 – x

39) Convert 68 degrees Fahrenheit to Celsius. 3295

FC

40) Find the slope of the line which passes through points (6,3) and (4, -5)

41) Find the volume of a prism when l = 10, w = 8, and h = 6

42) Find the volume of a cylinder when r = 5 and h = 8 (𝑉 = 𝜋𝑟2ℎ)

43) Write the equation of a line whose slope = 2 and y-intercept = -6

44) Reflect point A (2,5) over the x axis. 45) Reflect point B (-5,6) over the y axis.

Name the type of slope.

46) 47) 48) 49)

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