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Accuracy vs Precision in Scientific Notation - Understanding Sig Figs

Learn to distinguish between accuracy and precision, use scientific notation, and determine the number of significant figures in each number. Discuss the unfairness of reporting percentage weight loss in the TV show "The Biggest Loser" and suggest a correction. Practice problems included.

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Accuracy vs Precision in Scientific Notation - Understanding Sig Figs

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  1. 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

  2. Notes-Accuracy How close the measurement is to the real, true, or correct value accuracy correctness

  3. Notes-Precision precision How close measurements are to each other repeatable

  4. 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.

  5. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

  6. The Distance From the Sun to the Earth 93,000,000

  7. Large Numbers

  8. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

  9. Step 2 • Write number without zeros 93,000,000 = 9.3

  10. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  11. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

  12. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

  13. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

  14. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

  15. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

  16. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

  17. 6.27 x 106 9.01 x 104 6,270,000 90,100 Write in Standard Form Move the decimal to the right.

  18. Small Numbers

  19. Step 1 • Move decimal right • Leave only one number in front of decimal 0.000324 = 00003.24

  20. Step 2 • Write number without zeros 0.000324 = 3.24

  21. -4 0.000324 = 3.24 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  22. The power of ten is -4 because the decimal moved 4 places. -4 0.000324 = 3.24 x 10

  23. 0.000324 --- Standard Form • 3.24 x 10-4 --- Scientific Notation

  24. 9.85 x 10-7 -----> 6.41 x 10-1 -----> 2.79 x 100 -----> 4.2 x 10-2 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 0.000000985 = 9.85 x 10? • 0.641 = 6.41 x 10? • 2.79 = 2.79 x 10? • 0.042 = 4.2 x 10?

  25. Complete Practice Problems Write in scientific notation. • 0.005 • 0.000072 • 0.000802 Answers 1) 5 x 10-3 2) 7.2 x 10-5 3) 8.02 x 10-4

  26. 000034 --- move the decimal <--- Scientific Notation to Standard Form Move the decimal to the left • 3.4 x 10-5 in scientific notation • 0.000034 in standard form

  27. 6.27 x 10-6 9.01 x 10-4 0.00000627 0.000901 Write in Standard Form Move the decimal to the left.

  28. Scientific Notation Examples Change from scientific notation • the distance from Pluto to the Sun is 5.9×10 12 meters • the Milky Way disk radius is 3.9×1020 meters. • The speed of light is 3 x 10 8 meters/second. • the sun is 1.5x 1011 meters from earth • Mass of proton : 1.6726 x 10-27 kg • Mass of neutron: 1.6749 x 10-27 kg • Mass of electron: 9.10939 × 10-31 kg Change into scientific notation • 0.000 000 000 753 kg. is the mass of a dust particle! • A proton has a diameter of approximately 0.000000000001 mm

  29. 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

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