Ms. Campos Math 8 Unit 11 Scientific Notation

Transcription

1 Ms. Campos Math 8 Unit 11 Scientific Notation Date Lesson Topic Homework T 3 3/15 1 Introduction to Scientific Notation Lesson 1 Page 4 F 4 3/16 2 Converting Scientific Notation Lesson 2 Page 8 M 5 3/19 3 Compare and Order Scientific Notation Lesson 3 Page 11 T 6 3/20 4 Multiply and Divide Lesson 4 Page 15 W 1 3/21 5 Add and Subtract Lesson 5 Page 19 T 2 3/22 Quiz Review Finish Review & Study! F 3 3/23 Quiz M 4 3/26 6 Scientific Notation with a Calculator Lesson 6 Page 27 T 5 3/27 7 Application of Scientific Notation Lesson 7 Page 31 W 6 3/28 Review Finish Review & Study! T 1 3/29 Test Name: # 1

2 Unit 11- Lesson 1 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 = 259,000,000,000 Rule: A number is in Scientific Notation if: 1) The first factor is a single digit followed by a decimal point 2) Times the second factor which is a power of 10. Exercise 1- Determine if the following numbers are written in scientific notation: (1) (2) (3) (4) 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 o and 1 (decimal). Remember: Positive Exponent Negative Exponent 2

3 Exercise 2- Determine if the following numbers below will be whole numbers or decimals. (1) (2) (3) (4) Scientific Notation: Real Life Situations When is it appropriate to use scientific notation in real life? Examples of Large Numbers Examples of Small Numbers 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 Problem Set: 1. Determine if the numbers below are written in scientific notation. Explain your answer. (a) (b) (c) Determine if the number below are in whole numbers or decimals. Explain your reasoning. (a) (b) (c) 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 3

4 Unit 11- Lesson Homework Determine if the numbers below are written in scientific notation. 1) 1.5 x ) 1.50 x ) 0.42 x ) ) 134, 987 6) 9.5 x ) 17 x ) 75.9 x ) 1.3 x ) 65 x 10 2 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) Write each in Scientific Notation if necessary: 15) 0.25 x 10 4 = 16) x 10 9 = 17) 16 x 10-3 = 18) 0.27 x 10-8 = 19) 6 x 10-5 = 20) x = Review Work: 21) 7 3 x ) ( 1 4 ) -3 23) 4x + x 8 = 5x )

5 Unit 11 Lesson 2 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: 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 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) (4)

6 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) (3) (2) (4) Making Sure a Number is written in Scientific Notation Rule: LARS If a decimal point needs to move to the left, the exponent increases If the decimal point needs to move to the right, the exponent decreases ** Be careful when the exponent is negative! Exercise 3- Write each in Scientific Notation, if necessary: (1) (2) (3) (4) (5) (6)

7 Problem Set: 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 10 7 meters per second (2) 0.3 x 10 8 meters per second (3) 3.0 x 10 7 meters per second (4) 3.0 x 10 8 meters per second 2. Expressed in scientific notation, is equivalent to: (1) (2) (3) (4) In 2013, JFK Airport had approximately 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 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: Is Anthony s answer correct? Explain your reasoning. 7

8 Unit 11 Lesson 2 Homework Converting- Standard Form and Scientific Notation Convert into scientific notation. Write the numbers below in standard form. 1) 3,400 5) x ) ) 8.65 x ) 101,000 7) 2.30 x ) ) 9.11 x

9 Unit 11 Lesson 3 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) (b) Investigation 1: Express each scientific notation in standard form- (a) (b) Which number is smaller? Which number is larger? Investigation 2: Express each scientific notation in standard form- (a) (b) 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? 9

10 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 decimals. Exercise 1: Exercise 2: Exercise 3- Order the countries according to the amount of money visitors spent in the United States from least to greatest. Problem Set: For the following problems, use >, <, or = to make the statement true. (1) (2) (3) (4) ,000,000 (5) 548,000, (6) (7) (8) (9) (10) (11) Compare the following problem. Be sure to explain your reasoning

11 Directions- Compare the following numbers: Unit 11 Lesson 3 Homework Comparing Number: Standard Form vs Scientific Notation Homework (1) (2) (3) (4) Directions-Order the numbers from least to greatest: ; ; ; Directions- The table lists the populations of five countries. List the countries from least to greatest. 11

12 Unit 11 Lesson 4 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) (b) (c) (d) 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 ( ) ( ) Exercise 2- Evaluate the following ( ) ( ) 12

13 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 Exercise 4- Evaluate the following Problem Set: 1. Evaluate the following ( ) ( ) Neurons are cells in the nervous system that process and transit information. An average neuron is about meter 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? 13

14 3. Central Park in New York City is rectangular in shape and measures approximately feet by feet. If one acre is equal to square feet, how many acres does Central Park cover? Round to the nearest hundredth. 4. In 2005, 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? 5. Which one does not belong? Prove your reasoning ; ( )( ); ; (3.4)(4.2) 10 (6+3) 6. Enrique is finding the quotient of and Revise & circle his mistake and correct it. 14

15 1. Determine the product of ( ). Unit 11 Lesson 4 Homework 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 How much did each billionaire spend? 4. On weekdays, the average number of subway riders in CIty X is approximately 1 x 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? 15

16 Unit 11 Lesson 5 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. ( )( ) Can we simplify the following expressions? (a) 2x 2 + 3x (b) 4x x (c) x 3 + 3x 2 + 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: ( ) + ( ) ( ) + ( ) Exercise 2- Find the difference: ( ) ( ) ( ) ( ) 16

17 Exercise 3-Evalute the following expression: ( ) + 2,700,000 Problem Set: 1) ( ) ( ) 2) ( ) + ( ) 3) ( ) ( ) 4) ( ) + ( ) 5. In 2006, the US had a Gross Domestic Product (GDP) of The United Kingdom had a GDP of What were the combined GDPs of the Us and the UK, in 2006? 17

18 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 ,309,000 Oil ,000 Salt ,500 Show your work or explain, leaver 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? 18

19 Unit 11 Lesson 5 Homework Evaluate each expression. Express the result in scientific notation. Show all work! 1. ( ) + ( ) = 2. ( ) ( ) = 3. ( ) + ( ) = 4. ( ) 10,510,000 = 5. In 2012, people visited Central Park. That same year, people visited Yellowstone Park. How many more people visited Central Park than Yellowstone? 6. In 2006, China had internet users. That same year, Japan had internet users. How many Internet users did the two countries have combined? 19

20 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 10 2 = 6).17 x 10-7 = 7).052 x 10-4 = 8) x 10-6 = Lesson 2 Write each of the following in scientific notation: 9) 25,000 10) ) -4,700 12) 2 million Write each of the following in standard form: 13) x 10 14) 3 8 x 10 15) x 10 16) x 10 What is the value of the missing exponent (n): 17) What is the value of n in the problem: 50,200,000 = n 5.02 x 10 n = 18) What is the value of n in the problem: = 19) What is the value of n in the problem: 31,000 = n 3.2 x 10 n = n 3.1 x 10 n = 20) What is the value of n in the problem: = n 8.2 x 10 n = Lesson 3 20

21 Compare: Use <, >, or = 21) x 10 2,900,000 22) x x 10 23) x x 10 24) 7.6 x x 10 3 Lesson 4 Add, Subtract, Multiply, or Divide Without a Calculator 25) (2.8 x 10 7 ) + (4.1 x 10 7 ) = 26) (9.1 x 10 8 ) - (3.8 x 10 8 ) = 27) (4.0 x 10-4 ) x (2.1 x 10 9 ) = 28) (9.9 x ) (3.3 x 10 9 ) = Animal Weight in ounces Elephant 2.28 x 10 5 Cat 1.92 x 10 2 Mouse 3.2 x 10-1 Zebra 9.6 x ) 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) x 10 2 B) 1.45 x 10 2 C) 8.4 x 10 2 D) -8.4 x ) In the year 2000, approximately 169,000,000 personal computers were used in the United States. What is 21

22 this number expressed in scientific notation? A) B) C) D) ) A butterfly weighs only about 5.0 x 10-5 of a kilogram. What is the number written in standard form? A) B) C) 50,000 D) 500,000 36) The average distance from Pluto to the Sun is 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 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 22

23 39) Ming wrote the four numbers below in scientific notation 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 23

24 Unit 11 Lesson 6 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 10 4 ) can be inputted like this: ( 1. 2 x 10 ^ 4 = Examples: 1) (3.4 x 10 3 )(1.2 x 10 4 ) Enter the following: ( 3. 4 x 1 0 ^ 3 ) x ( 1. 2 x 1 0 ^ 4 ) Answer: (3.4 x 10 3 )(1.2 x 10 4 ) = 4.08 x x

25 Warm Up: Evaluate the following: What is the product of ( )( ) Guided Practice: Mixed Practice 1) ( ) + ( ) 2) ) ( ) ( ) 4) (4 10)( ) 25

26 Problem Set: 1) ) ( )( ) 3) ( ) ( ) 4) ( ) + ( ) 5) ( ) + ( ) 6) ( )( ) 7. Find the perimeter of the rectangle, if the area is cm 2 26

27 Unit 11 - Lesson 6 Homework 1. (8.4 x 10 2 )(2.5 x 10 6 ) 2. (2.63 x 10 4 ) + (1.2 x 10-3 ) 3. (7.83 x 10 8 )(1.161 x 10 7 ) 4. (8.4 x 10 2 ) (2.5 x 10 6 ) 5. (9 x ) - (2.4 x 10 8 ) 6. (9.45 x 10 5 ) (2.4 x 10 2 ) 7. 87,000,000 + (8.7 x 10 5 ) 8. (1.14 x 10 6 )(4.8 x 10-6 ) 9. (1.03 x 10-9 ) - (4.7 x 10 7 ) 10. (8.4 x 10 2 ) (2.5 x 10 6 ) 11. (9 x ) (2.4 x 10 8 ) 12. (9.45 x 10 5 ) + (2.4 x 10 2 ) Word problems: The table below shows the approximate populations of 3 countries. Country China France Australia Population 1.3 x x x 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 10 6 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. 27

28 Aim: I can apply scientific notation Unit 11 - Lesson 7 Warm up: 1. Which one doesn t belong? Explain your reasoning x 10 9 (3.4 x 10 6 )(4.2 x 10 3 ) 1.4 x 10 9 (3.4)(4.2) x 10 (6 + 3) Guided Practice: Use the table below for questions 2-4. The table below shows the debt of the three most populous states and the three least populous states. State Debt (in dollars) Population (2012) California 407,000,000, x 10 7 New York 337,000,000, x 10 7 Texas 276,000,000, x 10 7 North Dakota 4,000,000, x 10 4 Vermont 4,000,000, x 10 4 Wyoming 2,000,000, x What is the sum of the debts for the 3 most populous states? Express your answer in scientific notation. 2. What is the sum of the debts for the 3 least populous states? Express your answer in scientific notation. 3. How much larger is the combined debt of the three most populated states than that of the three least populated states? Express your answer in scientific notation. 4. Here are the masses of the so-called inner planets of the Solar System. Mercury: 3.3 x kg Earth: 5.9 x kg Venus: 4.8 x kg Mars: 6.4 x What is the average mass of all four inner planets? Write your answer in scientific notation. 28

29 6. What is the difference of and written in scientific notation? 1) 84 x ) 8.4 x ) 2 x ) 8.4 x What is the sum of 12 and expressed in scientific notation? 1) 4.2 x ) -4.2 x ) 42 x ) 42 x What is the product of,, and expressed in scientific notation? 1) 2) 3) 4) 9. What is the quotient of and? 1) 2) 3) 4) 10. What is the value of in scientific notation? 1) 2) 3) 4) 11. If the mass of a proton is gram, what is the mass of 1,000 protons? 1) g 2) g 3) g 4) g 29

30 12. 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) 13. If you could walk at a rate of 2 meters per second, it would take you 1.92 x 10 8 seconds to walk to the moon. Is it more appropriate to report this time as 1.92 x 10 8 or 6.02 years? 14. 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 (ml 2 ) Atlantic 2.96 x 10 7 Arctic 5.43 x 10 6 Indian 2.65 x 10 7 Pacific 6 x 10 7 Southern 7.85 x Mr. Murphy s yard is 2.4 x 10 2 feet by 1.15 x 10 2 feet. Calculate the area of Mr. Murphy s yard. 16. Every day, nearly 1.30 x 10 9 spam s are sent worldwide! Express in scientific notation how many spam s are sent each year. 17. In 2005, 8.1 x 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? 18. Let M = 993,456,789,098,765. Find the smallest power of 10 that will exceed M. 30

31 Unit 11 - Lesson 7 Homework 1. All planets revolve around the sun in elliptical orbits. Uranus s furthest distance from the sun is approximately x 10 9 km, and its closest distance is approximately x 10 9 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 inch. How is this number expressed in scientific notation? 1) x ) 3937 x ) 3937 x ) x The distance from Earth to the Sun is approximately 93 million miles. A scientist would write that number as 1) 93 x ) 9.3 x ) 93 x ) 9.3 x 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 x Gold x Hydrogen x Oxygen x Silver x A music download Web site announced that over 4 x 10 9 songs were downloaded by 5 x 10 7 registered users. What is the average number of downloads per user? 7. Sara s bedroom is 2.4 x 10 3 inches by 4.35 x 10 2 inches. How many carpeting would it take to cover her floor? Express your answer in scientific notation. 31

32 Name 8R Unit 11 Review Scientific Notation Write the following in Standard Form: 1) ) ) ) ) Write the following using Scientific Notation: 6) 120 7) 65,002,000 8) ).345 x ) 523 x 10 9 Find the value of the following. Write your answer in Scientific Notation. 11) ( )( ) 12) ( )( ) 13) ( ) 3 14) ) ( ) ( ) 16) ) ( ) + ( ) 18) ( ) ( ) 19) ( ) + ( ) Compare using < > = 20) 5.3 x x ) x

33 Word Problems: Add, Subtract, Multiple, or Divide 22) How many times larger is 9.8 x 10 6 than 6.32 x 10 5? 23) Find the mass of hydrogen atoms if the mass of one hydrogen atom is grams. 24) The distance from the Earth to the star Alpha Centauri is about kilometers. If light travels at a 5 speed of about kilometers per second, how long does it take light to travel from the star to Earth? ) In 1867, the United States purchased Alaska from Russia for $7.2 million. The total area of Alaska is about 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 10 7 and the population on Long Island is 1.68 x 10 5, 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 Planet B: x Planet C: x Planet D: x What is the average mass of all four planets? Write your answer in scientific notation. 33

34 Mixed Review Simplify: 29) 8x 2y + 6x y 30) -5(-2x + 7) 5 Simplify: 31) ) ) ) ) 6 0 Solve. 36) 4(-3x + 2) = 44 37) 4(x 2) = 3x ) 4x + 2 = 5x 3 x 39) Convert 68 degrees Fahrenheit to Celsius. C F ) 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 = πr 2 h) 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) 34