Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Worksheet - Powers of Ten Large and small Name ___________________ Date _______ Per ___ Grp ___ numbers and Gravitation Part 1 Powers of Ten a) Positive powers - complete the tables 2 = 10 x = 100 104 = 10 x = 10,000 106 = = 1,000 = = 10 = b) Negative powers - complete the tables = 1 10 = 10-3 = 1 x 1 x 1 10 10 10 = 0.001 10-5 = 1 x 1 x 10 10 = 0.00001 10 10-1 0.0001 = 0.01 1 x 1 x 1 10 10 10 x = = = = 100 Special = Part 2 Writing Numbers in Power-of-Ten Notation a) Positive powers - Large numbers Calculators cannot handle huge numbers without changing the format mass of Earth = 6,000,000,000,000,000,000,000,000 kg mass of Jupiter = 1900,000,000,000,000,000,000,000,000 kg b) Negative powers - Small numbers 0.0002 = 2 x 1 x 1 x 1 x 1 10 10 10 10 0.000 000 5 = = 6.0 x = 1.9 x = 2 x 10-4 5 x 1 x 1 x 1 x 1 x 1 x 1 x 1 10 10 10 10 10 10 10 = 5 x 10-7 Part 3 Scientific Notation - How your calculator will give you an answer :the form is (number bet 1 and 10 ) x ( power of 10 ) example 1900 x 1024 = 1.9 x 1027 Large numbers NOT scientific notation This is scientific notation example 270,000,000 1. Put a pointer to the right of the first non zero digit 2. Count the spaces from the pointer to the decimal point 2^70,000,000 8 3. Replace the pointer with the new decimal point and x 108 multiply by 10 power # places If you move right from the pointer the power is PowTenStd 2.70 1 + POSITIVE 6/30/2017 Small numbers example 0.0000075 1. Put a pointer to the right of the first non zero digit 0.000007^5 2. Count the spaces from the pointer to the decimal point 3. Replace the pointer with the new decimal point and 6 7.5 x 10-6 multiply by 10 power # places If you move left from the pointer the power is Practice 1. Write in scientific notation a) 0.00567 - NEGATIVE b) 5670 c) 0.0000000567 d) 86,700 2. Write in decimal form a) 7.2 x 105 b) 2.88 x 10-4 ph 7 is neutral and the hydrogen ion concentration is 1 x 10-7 3. Chemistry ph 5 is acid rain - the hydrogen ion concentration is 1 x 10-5 Acid rain has ________x more hydrogen ions than neutral water. Part 4 Entering Scientific Notation with your calculator First find the correct key Large numbers ex simple calculator EXP or EE ( graphing calc 2nd EE) 1.75 x 1016 1. Enter the basic number 1.75 2. Hit the EE or EXP key 3. Enter the power Small numbers 16 1.75 E 16 should appear or 1.75 x 1016 ex 6.67 x 10-11 (Hit CLEAR before you continue) Casiofx300ms Casiofx250hc yours Enter basic number 6.67 6.67 6.67 Hit spec key EXP EXP Power - 11 11 then (+/-) key Display shows ** DO NOT ** enter 10 the EXP (EE) key knows you are doing powers of ten ** Older calculators - Do Not ** hit - before the power - use (+/-) key Practice 1. Interpreting your calculator - do on your calculator - write the answers in decimal form and scientific (3 sig figs) b) (570,000)2 a) 1/3300000 2. In the USA cars drive 4 billion miles /day (4 x 10 9) and use over 200 million gallons of gasoline a) what is the average miles/gallon b) how much gasoline would be saved / day if the mileage was raised to 30 miles/gallon c) how much oil would be saved? PowTenStd 2 6/30/2017 Part 5 Combining Numbers in Scientific Notation a) Multiplying to multiply two powers of 10 102 x 103 = 10 x 10 2 = + 3 add the powers x = 105 10 x 10 x 10 5 Practice Set 1 - do by hand 1. 2 x 104 x 3 x 109 = 2. 3 x 10-12 x 2 x 10-4 = 3. 2 x 10-2 x 2 x 1016 = Set 2 - do with your calculator 4. 2.08 x 104 x 3.12 x 109 = 5. 3.3 x 10-12 x 1.8 x 10-4 = b) Dividing to divide two powers of 10 subtract the powers 105 / 103 = 10 x 10 x 10 x 10 x 10 = 102 10 x 10 x 10 5 - 3 = 1. 3 x 1013 / 2 x 104 = 2. 2 x 1012 / 1 x 10-4 = 3. 6 x105 = 2 Practice a) do by hand / 4 x 10-11 b) do these with your calculator 1. 3.08 x 1013/ 2.12 x 104 = 2. 3.95 x 1015/ 2.05 x 109 = 3. 2 x 1030 = Sun Mass/ Earth Mass 4. 6 x 1024 / 7.4 x 1022 = Earth Mass/ Moon Mass / 6 x 1024 6. General Practice a) Physics Waves - for all types of waves the speed = wavelength x frequency i) Red light waves have wavelength 6.0x 10-7 m , frequency 5.0 x 10 14 per sec. What is the speed? ii) Radio waves have wavelength 100 m , frequency 3 x 106 per sec. What is the speed? iii) What did you notice about these wave speeds? PowTenStd 3 6/30/2017 b) Environmental i) In 2007 the world population was 7 billion ( 7 x 10 9) and the average CO2 production was 4.2 tons /person Find the world total CO2 ii) Use the table to calculate the CO2 / person Population CO2 metric tons China 1.34 billion 6.54 billion USA 310 million 5.84 billion Germany 81 million 787 million for China , USA and Germany iii) How does the USA CO2 rate compare with China, Germany and the entire world? CO2 per person c) Chemistry i) 12 g of Carbon contains 6.02 x 10 23 atoms. How many atoms are in 240 g of carbon? ii) 63 g of Iron has 6.02 x 10 23 atoms. How many atoms are in 6.3 kg of Iron ? Part 7 Universal Gravitation Applications (p 180 Plug and Chug Equation p 179 F = 1- 4) G = 6.67 x 10-11 Explain each part of the equation 1. Calculate the force of gravity on Mass of earth = 6 x 1024 kg 1 kg on the surface of the Earth Earth radius = 6.4 x 106 m 2. Calculate the force of gravity on Mass of earth = 6 x 1024 kg 1 kg twice as far from the center of the earth as #1 Earth radius = 6.4 x 106 m distance for this problem = 3. Calculate the force of gravity between the earth and the moon Mass of moon = 7.4 x 1022 kg Ave distance Earth - Moon = 3.8 x 108 m ( Use mass of Earth from #1) 4. Calculate the force of gravity between the earth and the sun Mass of sun = 2.0 x 1030 kg Ave distance Earth - Sun = 1.5 x 1011 m ( Use mass of Earth from #1) 5. Which pulls the Earth more strongly, the sun or the moon ? (use your calculation results from above) PowTenStd 4 6/30/2017