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OBJECTIVE/WARM-UP • Students will be able to distinguish between accuracy and precision. • Students will be able to use scientific notation. • • • • • • How many sig figs in each number? 3.400 0.00304 0.34090 0.0030 4500 NOTES-ACCURACY Word/Phrase: accuracy Definition: How close the measurement is to the real, true, or correct value Hints or diagram: Meaning in My own words: correctness NOTES-PRECISION Word/Phrase: precision Hints or diagram: Definition: How close measurements are to each other Meaning in My own words: repeatable On the TV show “The Biggest Loser”, weight loss is reported in whole pounds, but percentage weight loss is given with two decimal places. For example, if a 210 lb. person lost 4 pounds, the percent weight loss is reported as 1.90% weight loss. Write a letter to the producers of the show to explain how this is unfair and not correct precision in reporting the percentage weight loss. Suggest a way to correct this for future shows. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros. The Distance From the Sun to the Earth 93,000,000 Large Numbers Step 1 Move decimal left Leave only one number in front of decimal Step 2 Write number without zeros Step 3 Count how many places you moved decimal Make that your power of ten The power of ten is 7 because the decimal moved 7 places. 93,000,000 --Standard Form 9.3 x 107 --Scientific Notation Practice Problem Write in scientific notation. Decide the power of ten. 1) 98,500,000 = 9.85 x 10? 3) 279,000,000 = 2.79 x 10? 9.85 x 107 6.41 x 1010 2.79 x 108 4) 4,200,000 = 4.2 x 10? 4.2 x 106 2) 64,100,000,000 = 6.41 x 10? More Practice Problems On these, decide where the decimal will be moved. 1) 734,000,000 = ______ x 108 2) 870,000,000,000 = ______x 1011 3) 90,000,000,000 = _____ x 1010 1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010 Complete Practice Problems Write in scientific notation. 1) 50,000 2) 7,200,000 3) 802,000,000,000 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011 Scientific Notation to Standard Form Move the decimal to the right 3.4 x 105 in scientific notation 3.40000 --- move the decimal 340,000 in standard form Write in Standard Form 6.27 x 106 9.01 x 104 6,270,000 90,100 Small Numbers Step 1 Move decimal right Leave only one number in front of decimal Step 2 Write number without zeros Step 3 Count how many places you moved decimal Make that your power of ten The power of ten is -4 because the decimal moved 4 places. 0.000324 --Standard Form 3.24 x 10-4 --Scientific Notation Practice Problem Write in scientific notation. Decide the power of ten. 1) 0.000000985 = 9.85 x 10? 3) 2.79 = 2.79 x 10? 9.85 x 10-7 6.41 x 10-1 2.79 x 100 4) 0.042 = 4.2 x 10? 4.2 x 10-2 2) 0.641 = 6.41 x 10? Complete Practice Problems Write in scientific notation. 1) 0.005 2) 0.000072 3) 0.000802 1) 5 x 10-3 2) 7.2 x 10-5 3) 8.02 x 10-4 Scientific Notation to Standard Form Move the decimal to the left 3.4 x 10-5 in scientific notation 000034 --- move the decimal 0.000034 in standard form Write in Standard Form 6.27 x 10-6 9.01 x 10-4 0.00000627 0.000901 Scientific Notation Examples Change from scientific notation a) the distance from Pluto to the Sun is 5.9×10 12 meters b) the Milky Way disk radius is 3.9×1020 meters. c) The speed of light is 3 x 10 8 meters/second. d) the sun is 1.5x 1011 meters from earth e) Mass of proton : 1.6726 x 10-27 kg f) Mass of neutron: 1.6749 x 10-27 kg g) Mass of electron: 9.10939 × 10-31 kg Change into scientific notation h) 0.000 000 000 753 kg. is the mass of a dust particle! i) A proton has a diameter of approximately 0.000000000001 mm Quick Review When adding or subtracting: Make sure the exponents are the same and line up the decimal points. When multiplying: Add the exponents When dividing: Subtract the exponents