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Dividing Numbers in Scientific Notation, Multiplying/Dividing Numbers in Scientific Notation, Distance/Rate/& Time Units Slide 2 Do Now - 4 + 49 /100 + 7 Please get out your guided notes from last week. Respond to Wednesdays Do Now: 1. Write an expression for the product of these two numbers:(3.2x10 9 )& (2.9x10 4 ) DO NOT SOLVE! 1. Solve. (2.4x10 5 ) x (5.2x10 7 ) Slide 3 Class Averages Slide 4 85% of Higher MATHLETES! 3 rd Period Gerardo Chyna Dezmond Luke DeRico 5 th Period Torez Katelyn Solomon Reggie Abdul Jalen Vicki Wesley Ceirsten Mario 6 th Period Jaycee Mallory Ellie 7 th Period Autumn Grace Jordan Slide 5 100% Math All-Stars! 3 rd Period JaWaun 5 th Period Tristan Aliciah Freeman Brandon 6 th Period Tylesha Steven Jayla Jim 7 th Period Kalei Jack Slide 6 Tracking Your Quiz You are to track your quiz on your own. Please write down your class average so you can do this on your own time. 3 rd period 66% 5 th period 86% 6 th period 63% 7 th period 68% Slide 7 Week Agenda Monday Dividing Numbers in Scientific Notation Tuesday Simplifying Scientific Notation Expressions Wednesday Adding/Subtracting Numbers in Scientific Notation Thursday Scientific Notation Word Problems Friday - Quiz Slide 8 Todays Agenda Do Now 6 minutes Quiz Return/ Shout Outs 4 minutes Agenda 1 minutes Rules of Exponents 5 minutes Dividing Numbers in Scientific Notation INM - 10 minutes Dividing Numbers in Scientific Notation GP & IP 15 minutes Exit Ticket 5 minutes Slide 9 Todays Objective SWBAT divide numbers in scientific notation. Slide 10 Computing with Scientific Notation Last week we worked with adding numbers in scientific notation and today we will divide numbers in scientific notation. Like last week, we will learn hand motions to help us remember the concept. Slide 11 Dividing Exponents When divide numbers with different exponents, you simply subtract the exponents, if the base number is the same. Example 1: 103 15 10 -10 If the base number is the same, you subtract the exponents. Solution: ____________________ Examples 2: 10 3 10 -4 If the base number is the same, you subtract the exponents. Solution: ____________________ Examples 3: 10 -20 10 3 If the base number is the same, you subtract the exponents. Solution: ____________________ Slide 12 Dividing Numbers in Scientific Notation If you remember, there are two factors to a number in scientific notation: 1. Factor 1: A number that is greater than 1, but less than 10. 2. Factor 2: A power of 10. When you divide numbers in scientific notation, we divide all factor 1 numbers, and then subtract the exponents of factor 2 together. Slide 13 Dividing Numbers in Scientific Notation Example 4: (8.4 x 10 3 ) (2.1 x 10 -4 ) First, we ID our factor 1 numbers. 8.4 & 2.1 Second, we divide our factor 1 numbers. 8.4 2.1 = 4 This is now our new factor 1 of our quotient. Third, we divide the numbers with exponents. 10 3 10 -4 Remember we subtract the exponents when the base is the same. 10 (3-(-4)) = 10 7 Fourth, we combine our factors to get our final answer. Factor 1: 4 Factor 2: 10 7 Final answer: 4 x 10 7 Slide 14 Dividing Numbers in Scientific Notation Example 5: (1.8 x 10 6 ) (7.5 x 10 2 ) First, we ID our factor 1 numbers. 1.8 & 7.5 Second, we divide our factor 1 numbers. 1.8 7.5 =.24 This is now our new factor 1 of our quotient. Third, we divide the numbers with exponents. 10 6 10 2 Remember we subtract the exponents when the base is the same. 10 (6-2) = 10 4 Fourth, we combine our factors to get our final answer. Factor 1:.24 Factor 2: 10 4 Temporary Final answer:.24 x 10 4 But your answer MUST BE IN CORRECT scientific notation form. We need to move the decimal point one place to the right so our factor 1 is greater than 1, but less than 10 2.4 When we do this, we must account for the change in factor 2. Factor 2 goes from 10 4 to 1o 3. Actual final answer: 2.4 x 10 3 Slide 15 Dividing Numbers in Scientific Notation Example 6: (1.2 x 10 -8 ) (9.6 x 10 12 ) First, we ID our factor 1 numbers. 1.2 & 9.6 Second, we divide our factor 1 numbers. 1.2 9.6 =.125 This is now our new factor 1 of our quotient. Third, we divide the numbers with exponents. 10 -8 10 12 Remember we subtract the exponents when the base is the same. 10 (-8-12) = 10 -20 Fourth, we combine our factors to get our final answer. Factor 1:.125 Factor 2: 10 -20 Temporary Final answer:.125 x 10 -20 But your answer MUST BE IN CORRECT scientific notation form. We need to move the decimal point one place to the right so our factor 1 is greater than 1, but less than 10 1.25 When we do this, we must account for the change in factor 2. Factor 2 goes from 10 -20 to 1o -21. Actual final answer: 1.25 x 10 -21 Slide 16 Dividing Numbers in Scientific Notation Example 7: (3.4 x 10 3 ) (6.8 x 10 -2 ) First, we ID our factor 1 numbers. 3.4 & 6.8 Second, we divide our factor 1 numbers. 3.4 6.8 =.5 This is now our new factor 1 of our quotient. Third, we divide the numbers with exponents. 10 3 10 -2 Remember we subtract the exponents when the base is the same. 10 (3-(-2) = 10 5 Fourth, we combine our factors to get our final answer. Factor 1:.5 Factor 2: 10 5 Temporary Final answer:.5 x 10 5 But your answer MUST BE IN CORRECT scientific notation form. We need to move the decimal point one place to the right so our factor 1 is greater than 1, but less than 10 5 When we do this, we must account for the change in factor 2. Factor 2 goes from 10 5 to 10 4. Actual final answer: 5 x 10 4 Slide 17 Dividing Numbers in Scientific Notation Example 8: (9 x 10 -11 ) (2.4 x 10 8 ) Slide 18 Dividing Numbers in Scientific Notation Example 9: (9.45 x 10 10 ) (1.5 x 10 6 ) Slide 19 Dividing Numbers in Scientific Notation Work on this one with your partner. Example 10: (3.24 x 10 -4 ) (8.1 x 10 -7 ) Slide 20 Dividing Numbers in Scientific Notation Work on this one with your partner. Example 11: (4.2 x 10 -8 ) (1.68 x 10 -2 ) Slide 21 Dividing Numbers in Scientific Notation Work on this one on your own. Example 12: (4.64 x 10 -4 ) (2.9 x 10 -6 ) Slide 22 Dividing Numbers in Scientific Notation Work on this one on your own. Example 13:(3.7x 10 5 ) (2.9 x 10 11 ) Slide 23 Dividing Numbers in Scientific Notation Example 14: Which one of these expressions correctly identifies the quotient of these two numbers(7.9 x 10 -2 ) (9.5 x 10 -4 )? a) (7.9 x 9.5) x 10 (-2+-4) b) (7.9 x 9.5) x 10 (-2--4) c) (7.9 9.5) x 10 (-2+-4) d) (7.9 9.5) x 10 (-2--4) Slide 24 Exit Ticket Each of you will complete your exit ticket on a note card. There are 3 problems. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK Math Book Page 120: #s 5-8 & 20-25! Slide 25 Exit Ticket 1. (3.4 X 10 6 ) (2 X 10 8 ) = 2. (4.8 X 10 -5 ) (3.2 X 10 -6 ) = 3. (10.5 X 10 20 ) ( 1.2 X 10 -14 ) = HOMEWORK Math Book Page 120: #s 5-8 & 20-25 & STUDY FOR QUIZ! Slide 26 Do Now - 81 / 81+81 Please pick up your guided notes and respond to the following SILENTLY & INDEPENDENTLY. 1. Solve.(6.5 x 10 -6 ) (4.5 x 10 9 ) 2. Solve. Slide 27 Todays Agenda Do Now 6 minutes Agenda 1 minutes Computing Numbers in Scientific Notation Investigation 10 minutes Computing Numbers in Scientific Notation IP 5 minutes GP & IP 14 minutes Exit Ticket 5 minutes Slide 28 Todays Objective SWBAT simplify scientific notation expressions. Slide 29 Math Investigation You are in groups of 4. Together, you will work together to try to solve the problem given to you. You may use your notes, your partners, but not your calculators. Together, you CAN solve the problem Use your rules of exponents to help you! I will be cycling around to monitor your progress and check your final answers. Slide 30 Simplifying Scientific Notation Expressions Example 1: Simplify. First, we take care of the numerator. Multiply the factor 1 numbers: 2 x 3 = 6 Multiply factor 2 numbers by adding exponents: 10 -3 x 10 7 = 10 4 Combine both factors to get your product: 6 x 10 4 Second, divide your new product by the denominator. Your new problem is: Divide factor 1 numbers: 6 2 = 3 Divide factor 2 numbers by subtracting exponents: 10 (4-(-8)) = 10 12 Last, combine your factors. Final answer: 3 x 10 12 Slide 31 Simplifying Scientific Notation Expressions Example 2: Simplify. First, we take care of the numerator. Multiply the factor 1 numbers: 6 x 2 = 12 Multiply factor 2 numbers by adding exponents: 10 4 x 10 7 = 10 11 Combine both factors to get your product: 12 x 10 11 Second, divide your new product by the denominator. Your new problem is: Divide factor 1 numbers: 12 4 = 3 Divide factor 2 numbers by subtracting exponents: 10 (11-10) = 10 1 Last, combine your factors. Final answer: 3 x 10 1 Slide 32 Simplifying Scientific Notation Expressions Example 3: Simplify. First, we take care of the numerator. Multiply the factor 1 numbers: 7 x 1 = 7 Multiply factor 2 numbers by adding exponents: 10 -12 x 10 6 = 10- 6 Combine both factors to get your product: 7 x 10- 6 Second, divide your new product by the denominator. Your new problem is: Divide factor 1 numbers: 7 14 = 0.5 Divide factor 2 numbers by subtracting exponents: 10 (-6-(-8)) = 10 2 Last, combine your factors. Final answer: 0.5 x 10 2 CORRECT SCIENTIFIC NOTATION ANSWER: 5 x 10 1 Slide 33 Simplifying Scientific Notation Expressions Example 4: Simplify. Slide 34 Simplifying Scientific Notation Expressions Example 5: Simplify. Slide 35 Simplifying Scientific Notation Expressions Example 6: Simplify. Slide 36 Simplifying Scientific Notation Expressions Example 7: Simplify. Slide 37 Simplifying Scientific Notation Expressions Example 8: Simplify. Slide 38 Simplifying Scientific Notation Expressions Example 9: Simplify. Slide 39 Simplifying Expressions in Scientific Notation Example 10: Simplify. Slide 40 Exit Ticket Each of you will complete your exit ticket on a note card. There are 2 problems. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK Worksheet! Slide 41 Exit Ticket Slide 42 Do Now 1. 3x 10 = 17 2. 5x 10 = -20 3. - x + 8 = -4 4. x + 9 = 35 5. -9= 8 16x Slide 43 Do Now (9) 2 /361/16 + 64 Please respond to the following on the Wednesday area of your guided notes SILETNLY & INDEPENDENTLY. 1. Simplify. 2. Write the steps to the problem you just solved above. Slide 44 Todays Agenda Do Now 8 minutes Agenda 1 minutes Adding & Subtracting Number in Scientific Notation INM 10 minutes GP & IP 26 minutes Exit Ticket 5 minutes Slide 45 Todays Objective SWBAT add and subtract number in scientific notation. Slide 46 Adding and Subtracting Numbers in Scientific Notation After multiplying, dividing, and combining operations with numbers in scientific notation, we will finish computing with the numbers by adding and subtracting them. Before we begin, work with your partner and come up with 2 examples of where we would need to add and subtract numbers in scientific notation. Slide 47 Adding and Subtracting Numbers in Scientific Notation There are two different ways to adding and subtract numbers in scientific notation. I will model both to you, and then you can chose which one works best for you! Slide 48 Adding and Subtracting Numbers in Scientific Notation Example 1: (6.89 x 10 4 ) + (9.24 x 10 5 ) Method One: 1. Convert all numbers into standard form. 6.89 x 10 4 = 68,900 9.24 x 10 5 = 924,000 2. Complete the operation indicated to solve. 68,900 + 924,000 = 992,900 Slide 49 Adding and Subtracting Numbers in Scientific Notation Example 2: (6.89 x 10 4 ) + (9.24 x 10 5 ) Method Two: 1. Check to see if the powers of 10 have the same exponent. 2. Convert numbers to the same by power of 10 by moving the decimal point. 6.89 x 10 4 = 6.89 x 10 4 9.24 x 10 5 = I want the power to be 4, so I need to subtract 1 from the exponent. When I subtract I move the decimal right. = 92.4 x 10 4 3. Add the factor ones and keep the power of ten to solve. 92.4 + 9.89 = 99.29 x 10 4 4. Convert to proper scientific notation form. 99.29 x 10 4 = 9.929 x 10 5 Slide 50 Adding and Subtracting Numbers in Scientific Notation After seeing both methods, I want you to think, why would I want to know how to use both methods? When would the standard form method be useful? When would the exponent method be useful? You will have one minute to think about this with your partner. Slide 51 Adding and Subtracting Numbers in Scientific Notation Example 3: (7.38 x 10 8 ) (1.161 x 10 7 ) Method 1Method 2 Slide 52 Adding and Subtracting Numbers in Scientific Notation Example 4: (8.41 x 10 3 ) + (9.71 x 10 4 ) Method 1Method 2 Slide 53 Adding and Subtracting Numbers in Scientific Notation Work on this one with your partner. Example 5: (1.263 x 10 9 ) (1.525 x 10 7 ) Slide 54 Adding and Subtracting Numbers in Scientific Notation Work on this one with your partner. Example 6: (2.85 x 10 7 ) + (1.61 x 10 9 ) Slide 55 Adding and Subtracting Numbers in Scientific Notation Work on this one with your partner. Example 7: (8.23 x 10 6 ) + (6.91 x 10 5 ) Slide 56 Adding and Subtracting Numbers in Scientific Notation Work on this one on your own. Example 8: (4.9 x 10 18 ) + (5.8 x 10 15 ) Slide 57 Adding and Subtracting Numbers in Scientific Notation Work on this one on your own. Example 9: (9.3 x 10 -5 ) (3.25 x 10 -3 ) Slide 58 Adding and Subtracting Numbers in Scientific Notation Work on this one on your own. Example 10: (5.12 x 10 -4 ) (2.9 x 10 -3 ) Slide 59 Adding and Subtracting Numbers in Scientific Notation Work on this one on your own. Example 11: (4.1 x 10 -2 ) + (8.4 x 10 -3 ) Slide 60 Adding and Subtracting Numbers in Scientific Notation Work on this one on your own. Example 12: (3.5 x 10 13 ) + (7.3 x 10 12 ) Slide 61 Exit Ticket Each of you will complete your exit ticket on a note card. There are 2 problems. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK Math book page 120: 10 13 & page 121: 28 - 35! Slide 62 Exit Ticket 1. (2.18 x 10 10 ) (5.61 x 10 8 ) 2. (6.85 x 10 6 ) + (9.7 x 10 5 ) HOMEWORK Math book page 120: 10 13 & page 121: 28 - 35! Slide 63 Do Now 3 2 / 4 2 + 2 2 Please get out your guided notes and respond to the following on the Thursday area SILENTLY & INDEPENDENTLY. 1. (3.5 x 10 4 ) + (2.76 x 10 5 ) 2. (7.34 x 10 15 ) (4.67 x 10 14 ) Slide 64 Todays Agenda Do Now 8 minutes Agenda 1 minute Scientific Notation Word Problems INM 10 minutes GP & IP 25 minutes Exit Ticket 5 minutes Quiz Topics 1 minute Slide 65 Todays Objective SWBAT solve word problems involving scientific notation. Slide 66 Scientific Notation Word Problems Example 1: In 2006, Blue Ridge Parkway was visited by about 1.9 x 10 7 people. That same year, Great Smoky Mountains National Park was visited by about 9.3 x 10 6 people. How many more people visited Blue Ridge Parkway than Great Smoky Mountains National Park in 2006? What operation will be used to solve this problem? Slide 67 Scientific Notation Word Problems Example 2: In 2006, the US had a Gross Domestic Product (GDP) of 1.313 x 10 13. The United Kingdom had a GDP of 1.93 x 10 12. What were the combined GDPs of the US and the UK in 2006? What operation will be used to solve this problem? Slide 68 Scientific Notation Word Problems Example 3: One cell has a diameter of 4.5 x 10 -6. If there are 20 cells growing in a lab, what is their combined diameters? What operation will be used to solve this problem? Slide 69 Scientific Notation Word Problems Example 4: The average distance from Earth to the Sun is 1.46 x 10 8 kilometers. The average distance from Earth to the Moon is 3.84 x 10 5 kilometers. About many more times as great is the distance from Earth to the Sun than to the Moon? What operation will be used to solve this problem? Slide 70 Scientific Notation Word Problems Example 5: About 8.73 x 10 8 people in the world speak Chinese. About 3.22 x 10 8 speak Spanish. In scientific notation, how many more people speak Chinese than Spanish? What operation will be used to solve this problem? Slide 71 Scientific Notation Word Problems Example 6: Great Lake Superior covers an area of 3.17 x 10 4 square miles. The smallest Great Lake, Ontario, covers an area of 7.34 x 10 3 square miles. About how many times as great is the area covered by Lake Superior than Lake Ontario? What operation will be used to solve this problem? Slide 72 Scientific Notation Word Problems Example 7: The income following incomes are recorded for music artists in 2010. How much more money did Jay-Z make over Yo Gotti? What operation will be used to solve this problem? Artist2010 Income Jay-Z2.56 x 10 7 Yo Gotti5.1 x 10 6 Slide 73 Scientific Notation Word Problems Example 8: The distance between Memphis and Sand Francisco is 1.2 x 10 3 miles. The distance between Memphis and Nashville is 2.5 x 10 2. How much further is San Francisco than Nashville from Memphis? What operation will be used to solve this problem? Slide 74 Scientific Notation Word Problems Example 9: The largest planet in our solar system is Jupiter with a diameter of about 1.43 x 10 5 kilometers. The smallest planet in our solar system is Mercury with a diameter of about 4.9 x 10 3 kilometers. About how many times greater is the diameter of Jupiter than the diameter of Mercury? What operation will be used to solve this problem? Slide 75 Scientific Notation Word Problems Example 10: In 2006, China had 1.311 x10 8 internet users. That same year, Japan had 9.09 x 10 7 internet users. How many internet users did the two countries have combined? What operation will be used to solve this problem? Slide 76 Scientific Notation Word Problems Example 11: With nearly 3.0 x 10 8 books, the Library of Congress is the largest library in the US. The University of Tennessee has about 2.97 x 10 7 books in its library. How many more books does the Library of Congress have than the University of Tennessee? What operation will be used to solve this problem? Slide 77 Exit Ticket Each of you will complete your exit ticket on a note card. There are 2 problems. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK Worksheet & Study for Quiz! Slide 78 Exit Ticket 1. The average distance from star A to the star B is 3.56 x 10 9 kilometers. The average distance from Star A to Star C is 4.8 x 10 12 kilometers. About much further is the distance from Star A to Star C than to Star B? What operation will be used to solve this problem? 2. In 2010, USA had 2.31 x10 5 IPhone users. That same year, Europe had 1.49 x 10 4 IPhone users. How many IPhone users did the USA and Europe have combined? What operation will be used to solve this problem? Homework Worksheet & Study! Slide 79 Do Now - 81 / 25 - 2 2 Please clear off your desk of everything except a pencil, calculator, and a plain sheet of paper (to cover your quiz with). The longer it takes you to complete this, the less time you will have for your quiz.