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Scientific notation classnotes September 28, 2015 Find your new seat today. You will need your laptop to begin. Go to https://todaysmeet.com/Scientificnotation Which is the more important invention the telescope or the microscope? Go to http://htwins.net/scale/ • Scale of the universe - zoom in and out and observe the numbers written in scientific notation. • Find one fact that is really small and one fact that is really big. • Compare the two numbers. • What is the difference between the two numbers? How did you calculate this? • What rule do all numbers in scientific notation follow? Scientific notation classnotes September 28, 2015 http://syrianrefugees.eu/ 6 x 10 Syrians have fled their homes since the outbreak of civil An estimated 99 million war in March 2.011x10 2011, taking refuge in neighbouring countries or within Syria itself. According to the United Nations High Commissioner for Refugees (UNHCR), over 3 6 million fled to Syria's immediate neighbours Turkey, Lebanon, Jordan and 3 x 10have Iraq. 6.5 x million 6.5 106 are internally displaced within Syria. Meanwhile, under 1.5 150,000 x 105 Syrians have declared asylum in the European Union, while member states have pledged to resettle a further 3.3 33,000 x 104Syrians. The vast majority of these resettlement spots 2.85 28,500 x 104 or 85% 8.5 x 10 are pledged by Germany. 3 Read this article and write the scientific notation as ordinary numbers. Scientific notation classnotes September 28, 2015 Calculations with scientific notation Write in scientific notation and as ordinary numbers. 1) 450 2) 8792 3) 0.15 4) 0.045 3 5) 64 x 10 -5 6) 0.015 x 10 Scientific notation classnotes Write in scientific notation 1) 2) 3) 4) September 28, 2015 Write as an ordinary number 5) 6) 7) 8) Write these correctly in standard form. 9) 10) 11) 12) Order from least to greatest 13) 14) Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Addition and Subtraction When adding or subtracting numbers in scientific notation follow these steps: 1) Write each number in parentheses as an ordinary number. for example 32000 4600 2) Add or subtract the two numbers. 32000 + 4600 = 36600 3) Write the final answer in scientific notation. 36600 = 3.66 x 104 Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Addition and Subtraction Using the example have a go at these questions: 1) 2) 3) 4) 5) srewsnA Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Multiplication When multiplying numbers in scientific notation follow these steps: 1) Write each number in parentheses as an ordinary number. for example 60000 200 2) multiply the two numbers. 200 x 60000 = 12000000 3) Write the final answer in scientific notation. 1200000 = 1.2 x 107 An alternative way would be: 1) Multiply the first number in the parentheses together. 2 x 6 = 12 2) Then multiply the base 10 in the parentheses together. 102 x 104 = 106 (from law of exponent an X am = an+m) 3) Combine the two answers together. 12 x 106 4) Then write the final answer in scientific notation. 12 x 106 = 1.2 x 107 Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Multiplication Use both methods to answer these multiplications to check whether your answer is correct. 1) 2) 3) 4) 5) Write down which method you prefer and why. Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Division When dividing numbers in scientific notation follow these steps: 1) Write each number in parentheses as an ordinary number. for example 300 90000000 2) Divide the two numbers. 90000000 ÷ 300 = 300000 3) Write the final answer in scientific notation. 300000 = 3 x 105 An alternative way would be: 1) Divide the first number in the parentheses together. 9÷3=3 2) Then divide the base 10 in the parentheses together. 107 ÷ 102 = 105 (from law of exponent an ÷ am = an-m) 3) Combine the two answers together. 3 x 105 4) Then write the final answer in scientific notation. 5 3 x 10 is already in scientific notation Scientific notation classnotes September 28, 2015 Calculating in scientific notation - Division Use both methods to answer these division to check whether your answer is correct. 1) 2) 3) 4) 5) Write down which method you prefer and why. Scientific notation classnotes September 28, 2015 Calculations with scientific notation Which number is smaller? 3.46 x 107 or 9.8 x 106 2.56 x 108 or 3.1 x 108 Explain why 4.2 x 10-5 is smaller than 3 x 10-4 Scientific notation classnotes September 28, 2015 Calculations with scientific notation Which number is smaller? 3.46 x 107 or 9.8 x 106 34600000 9800000 2.56 x 108 or 3.1 x 108 256000000 310000000 Explain why 4.2 x 10-5 is smaller than 3 x 10-4 0.000042 0.0003 Scientific notation classnotes September 28, 2015 For each question write your answer in scientific notation 1) What is the difference between 4.67 x 103 and 4.5 x 102? 2) What is the sum of 52300 and 7.62 x 103? 3) What is (0.056)(2.2 x 102)? Scientific notation classnotes September 28, 2015 For each question write your answer in scientific notation What is the difference between 1.243 x 107 and 1.0658 x 106? What is the sum of 4.89 x 105 and 12000 What is (3 x 102)(2.56)? Page 219 Qu 1, 3, 4, 5, 6 Scientific notation classnotes Using Scientific Notation in Real Life Situations September 28, 2015 Scientific notation classnotes September 28, 2015 nucleus of a human cell is about 7 x 10-6 meter in diameter. -8 A ribosome, another part of a cell, is about 3 x 10 meter in The diameter. Approximately how many times larger is a nucleus than a ribosome? 7 x 10-6 3 x 10-8 = 2.33... x 102 Scientific notation classnotes September 28, 2015 1.3 x 1025 27 The mass of Jupiter is about 4.2 x 10 The mass of Earth is about About how many times Earth's mass is Jupiter's mass? 4.2 x 1027 1.3 x 1025 = 3.230... x 102 Scientific notation classnotes September 28, 2015 Medium - answer questions 1, 3, 4, 6 Hard - answer questions 2, 5, 7 calculator Difficult - answer questions 2, 5, 7 non-calculator Scientific notation classnotes September 28, 2015 Question 1 A pixel on a computer screen is 2 × 10–2 cm long by 7 × 10–3 cm wide. What is the area of the pixel? Question 2 The star Betelgeuse is 1.8 × 1015 miles from Earth. Light travels at 1.86 × 105 miles per second. How many seconds does it take light to travel from Betelgeuse to Earth? Give your answer in scientific notation. Scientific notation classnotes September 28, 2015 Question 3 A typical adult has about 20 000 000 000 000 red corpuscles. Each red corpuscle weighs about 0.000 000 000 1 gram. Write both of these numbers in scientific notation and work out the total mass of red corpuscles in a typical adult. Question 4 Evaluate E M 2 3 when E = 1.5 × 10 and M = 3 × 10 , giving your answer in scientific notation. Question 5 Work out the value of giving your answer in scientific notation, correct to two significant figures. Scientific notation classnotes September 28, 2015 Question 6 Many people withdraw money from their banks by using holeinthewall machines. Each day there are eight million withdrawals from 32 000 machines. What is the average number of withdrawals per machine? Question 7 The mass of Saturn is 5.686 × 1026 tonnes. The mass of the Earth is 6.04 × 1021 tonnes. How many times heavier is Saturn than the Earth? Give your answer in standard form to a suitable degree of accuracy. Scientific notation classnotes September 28, 2015 Answers Qu 1 2 x 10-2 x 7 x 10-3 (2 x 7) x (10-2x 10-3) 14 x 10-5 1.4 x 10-4 Qu 3 2 x 1013 x 1 x 10-10 (2 x 1) x (1013x 10-10) 2 x 103 Qu 2 1.8 x 1015 ÷ 1.86 x 105 (1.8 ÷ 1.86) x (1015÷ 105) 0.96774... x 1010 9.6774... x 109 Qu 4 1.5 x 103 ÷ 3 x 10-2 (1.5 ÷ 3) x (103÷ 10-2) 0.5 x 105 5 x 104 Qu 6 3.2 x 104 ÷ 8 x 106 (3.2 ÷ 8) x (104÷ 106) 0.4 x 10-2 4 x 10-3 Qu 5 3.2 x 107 ÷ 1.4 x 102 (3.2 ÷ 4) x (107÷ 102) 2.2857... x 105 2.3 x 105 Qu 7 5.686 x 1026 ÷ 6.04 x 1021 (5.686 ÷ 6.04) x (1026÷ 1021) 0.94139.. x 105 9.4139 x 104