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# Physics 1.1 Scientific Notation

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A simple discussion of the concept of orders of magnitude.

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### Physics 1.1 Scientific Notation

1. 1. Topic 1 – Physical Measurements 1.1 - Orders of Magnitude
2. 2. Scientific Notation <ul><li>When recording values for quantities we often use scientific notation.
3. 3. We always write a number as a number between 1 and 10 with 2 or 3 significant figures followed by an exponent of 10. </li><ul><li>e.g. the speed of light is 299742548 ms -1
4. 4. In Sci. this is 3.00x10 8 ms -1 </li></ul><li>We use an appropriate number of sig figs based on the instrument made to make the measurement. </li><ul><li>If in doubt, choose 3 sig figs </li></ul></ul>
5. 5. Scientific Notation <ul><li>Write the following values in scientific notation. </li><ul><li>The mass of a peanut = 1.6084g
6. 6. Two hectares of land = 20000m 2
7. 7. Seconds in a year = 31556926s
8. 8. The atomic clock frequency = 9192631770Hz </li></ul></ul>
9. 9. Working with Scientific Notation <ul><li>Addition and Subtraction </li><ul><li>Multiply the number with the larger exponent repeatedly by 10 until the exponents are the same.
10. 10. Now simply add or subtract the numbers
11. 11. Finally simplify back into Scientific Notation </li><ul><li>example
12. 12. 4.1x10 2 + 3.8x10 3 = (4.1 + 38)x10 2 = 42.1x10 2 =4.21x10 3
13. 13. question
14. 14. Find: 6.8x10 99 – 4.5x10 97 </li></ul></ul></ul>
15. 15. Working with Scientific Notation <ul><li>Multiplication and Division </li><ul><li>Multiply or divide the numbers in the normal way.
16. 16. If multiplying then ADD the exponents; if dividing then SUBTRACT the exponents
17. 17. Finally simplify back into Scientific notation. </li><ul><li>Example
18. 18. 1.5x10 -5 x 4.0x10 2 = (1.5 x 4.0)x10 (-5 + 2) =6x10 -3
19. 19. Question
20. 20. Find: 8x10 78 / 5x10 45 </li></ul></ul></ul>
21. 21. Orders of Magnitude <ul><li>Often, we only want to compare the orders of magnitude of two quantities.
22. 22. The order of magnitude is simply the exponent part of scientific notation. </li><ul><li>Think of it as a inaccurate approximation. </li></ul><li>We use the tilde ~ to signify order of magnitude. </li><ul><ul><li>Example
23. 23. The speed of light is 299742548ms -1 . Its order of magnitude is ~10 8 ms -1 </li></ul></ul></ul>
24. 24. Orders of Magnitude <ul><li>Use WolframAlpha ( http://www.wolframalpha.com ) to find values of (in Sci.) and the order of magnitudes of: </li><ul><li>The atomic diameter of iron
25. 25. The nuclear diameter of lead
26. 26. The size of visible Universe.
27. 27. The mass of the electron.
28. 28. The mass of the Universe.
29. 29. The age of the Universe. </li></ul></ul>
30. 30. <ul><li>Comparing orders of magnitudes allows us to work out how many times bigger something is. </li><ul><ul><li>Example
31. 31. How many times smaller is the nucleus than an atom?
32. 32. 10 -15 / 10 -10 = 10 -5 times smaller OR 5 orders of magnitude.
33. 33. Questions
34. 34. How many times more massive is the Universe than an electron?
35. 35. How many times older is the Universe than the passage of light across an atom? </li></ul></ul></ul>How many times smaller is …?
36. 36. Estimation <ul><li>Using your experience of the world estimate in Scientific notation and order of magnitude : </li><ul><li>The length of a 747 Jet
37. 37. The area of a tennis court
38. 38. The mass of a basketball
39. 39. The height of an average man
40. 40. The mass of an average man
41. 41. The mass of an average car. </li></ul></ul>