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Unit Conversion

Unit Conversion. What is 3 m m in m? A. 3 x 10 -9 m B. 3 x 10 -6 m C. 3 x 10 -3 m What is 2.5 h in s? A. 150 s B. 750 s C. 9000 s What is 120 km/h in m/s? A. 33.3 m/s B. 432 m/s C. 720 m/s. Unit Conversion. What is 3 m m in m?

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Unit Conversion

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  1. Unit Conversion • What is 3 mm in m? A. 3 x 10-9 m B. 3 x 10-6 m C. 3 x 10-3 m • What is 2.5 h in s? A. 150 s B. 750 s C. 9000 s • What is 120 km/h in m/s? A. 33.3 m/s B. 432 m/s C. 720 m/s

  2. Unit Conversion • What is 3 mm in m? A. 3 x 10-9 m B. 3 x 10-6 m C. 3 x 10-3 m • What is 2.5 h in s? A. 150 s B. 750 s C. 9000 s • What is 120 km/h in m/s? A. 33.3 m/s B. 432 m/s C. 720 m/s

  3. Unit Conversion • What is 3 mm in m? A. 3 x 10-9 m B. 3 x 10-6 m C. 3 x 10-3 m • What is 2.5 h in s? A. 150 s B. 750 s C. 9000 s • What is 120 km/h in m/s? A. 33.3 m/s B. 432 m/s C. 720 m/s

  4. Unit Conversion • What is 3 mm in m? A. 3 x 10-9 m B. 3 x 10-6 m C. 3 x 10-3 m • What is 2.5 h in s? A. 150 s B. 750 s C. 9000 s • What is 120 km/h in m/s? A. 33.3 m/s B. 432 m/s C. 720 m/s

  5. The Return of GUSS Featuring Significant Digits

  6. GUSS and Sig Digs: Learning Goal • The student will be able to express the results of any measurements or calculations involving data accurately and precisely, to the appropriate number of decimal places or significant digits. (A1.13)

  7. A Justification for “Sig Digs” Measurements are not perfect.

  8. A Justification for “Sig Digs” Measurements are not perfect. They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision.

  9. A Justification for “Sig Digs” Measurements are not perfect. They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision. Note that we are not talking about human errors here.

  10. Precision We indicate the precision to which we measured our quantity in how we write our measurement.

  11. Precision We indicate the precision to which we measured our quantity in how we write our measurement. For example, which measurement is more precise? • 15 cm • 15.0 cm

  12. Precision We indicate the precision to which we measured our quantity in how we write our measurement. For example, which measurement is more precise? • 15 cm • 15.0 cm  This one, obviously. Physicists are lazy. They wouldn’t bother to write the .0 if they didn’t mean it.

  13. What we mean When we write 15 cm, we mean that we’ve measured the quantity to be closer to 15 cm than to 14 cm or 16 cm BUT When we write 15.0 cm, we mean that we’ve measured the quantity to be closer to 15 cm than to 14.9 cm or 15.1 cm.

  14. Significance Digits that have been measured are said to be significant. • 15 cm  This measurement has 2. • 15.0 cm  This measurement has 3.

  15. The following rules are used to determine if a digit is significant: • All non-zero digits are significant e.g. 42.5 N has three significant digits

  16. The following rules are used to determine if a digit is significant: • All non-zero digits are significant • Any zeroes placed after other digits and behind a decimal are significant e.g. 1.50 kg has three significant digits

  17. The following rules are used to determine if a digit is significant: • All non-zero digits are significant • Any zeroes placed after other digits and behind a decimal are significant • Any zeroes placed between significant digits are significant e.g. 30.07 m has four significant digits

  18. The following rules are used to determine if a digit is significant: • All non-zero digits are significant • Any zeroes placed after other digits and behind a decimal are significant • Any zeroes placed between significant digits are significant • All other zeroes are not significant e.g. both 100 cm and 0.004 kg each have only one significant digit

  19. How can you say those digits are not significant? Both 100 cm and 0.004 kg each have only one sig dig? The zeros here are placeholders – they’re just there to show in which place the non-zeros belong. If the measurements are rewritten 1 m and 4 g, it becomes apparent that there’s only one sig dig.

  20. How can you say those digits are not significant? Both 100 cm and 0.004 kg each have only one sig dig? The zeros here are placeholders – they’re just there to show in which place the non-zeros belong. If the measurements are rewritten 1 m and 4 g, it becomes apparent that there’s only one sig dig. But what if you measured 100 cm exactly?

  21. Making Zeros Significant But what if you measured 100 cm exactly? You can show that a zero is significant by either: • underscoring or overscoring the zero: 100 cm (if the measurement is in a table) • rewriting the measurement in scientific notation: 1.00 x 102 cm

  22. Making Zeros Significant And yes, if you measure a zero, you must write it. Your lab tables should not look like this:

  23. Making Zeros Significant They should look like this:

  24. No ½ measurements Your tables also should not look like this:

  25. No ½ measurements If you can clearly measure .5 in one case, surely you could measure to the tenths place in the other cases too? We don’t use .5 to substitute for “about ½”: .5 means closer to .5 than to .4 or .6. Be exact.

  26. And now for some practice. . . .

  27. How many significant digits are there in each of the following? • 25 W • 60 km/h • 305 K • 3.6 kg • 5.0 mT • 0.1 N • 502500 cal

  28. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h • 305 K • 3.6 kg • 5.0 mT • 0.1 N • 502500 cal

  29. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K • 3.6 kg • 5.0 mT • 0.1 N • 502500 cal

  30. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K 3 s.d. • 3.6 kg • 5.0 mT • 0.1 N • 502500 cal

  31. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K 3 s.d. • 3.6 kg 2 s.d. • 5.0 mT • 0.1 N • 502500 cal

  32. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K 3 s.d. • 3.6 kg 2 s.d. • 5.0 mT 2 s.d. • 0.1 N • 502500 cal

  33. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K 3 s.d. • 3.6 kg 2 s.d. • 5.0 mT 2 s.d. • 0.1 N 1 s.d. • 502500 cal

  34. How many significant digits are there in each of the following? • 25 W 2 s.d. • 60 km/h 1 s.d. • 305 K 3 s.d. • 3.6 kg 2 s.d. • 5.0 mT 2 s.d. • 0.1 N 1 s.d. • 502500 cal 4 s.d.

  35. How many significant digits are there in each of the following? • 1.10 A • 0.017 h • 102.5 MHz • 2100 kJ • 250.0 W • 60.80 kg • 0.0018010 km

  36. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h • 102.5 MHz • 2100 kJ • 250.0 W • 60.80 kg • 0.0018010 km

  37. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz • 2100 kJ • 250.0 W • 60.80 kg • 0.0018010 km

  38. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz 4 s.d. • 2100 kJ • 250.0 W • 60.80 kg • 0.0018010 km

  39. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz 4 s.d. • 2100 kJ 2 s.d. • 250.0 W • 60.80 kg • 0.0018010 km

  40. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz 4 s.d. • 2100 kJ 2 s.d. • 250.0 W 4 s.d. • 60.80 kg • 0.0018010 km

  41. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz 4 s.d. • 2100 kJ 2 s.d. • 250.0 W 4 s.d. • 60.80 kg 4 s.d. • 0.0018010 km

  42. How many significant digits are there in each of the following? • 1.10 A 3 s.d. • 0.017 h 2 s.d. • 102.5 MHz 4 s.d. • 2100 kJ 2 s.d. • 250.0 W 4 s.d. • 60.80 kg 4 s.d. • 0.0018010 km 5 s.d.

  43. Round each measurement to the required significant digits: • 4080 J to 1 s.d. • 4080 J to 2 s.d. • 2.715 kg to 1 s.d. • 2.715 kg to 2 s.d. • 0.987 V to 1 s.d. • 0.987 V to 2 s.d.

  44. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. • 2.715 kg to 1 s.d. • 2.715 kg to 2 s.d. • 0.987 V to 1 s.d. • 0.987 V to 2 s.d.

  45. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. 4100 J • 2.715 kg to 1 s.d. • 2.715 kg to 2 s.d. • 0.987 V to 1 s.d. • 0.987 V to 2 s.d.

  46. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. 4100 J • 2.715 kg to 1 s.d. 3 kg • 2.715 kg to 2 s.d. • 0.987 V to 1 s.d. • 0.987 V to 2 s.d.

  47. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. 4100 J • 2.715 kg to 1 s.d. 3 kg • 2.715 kg to 2 s.d. 2.7 kg • 0.987 V to 1 s.d. • 0.987 V to 2 s.d.

  48. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. 4100 J • 2.715 kg to 1 s.d. 3 kg • 2.715 kg to 2 s.d. 2.7 kg • 0.987 V to 1 s.d. 1 V • 0.987 V to 2 s.d.

  49. Round each measurement to the required significant digits: • 4080 J to 1 s.d. 4000 J • 4080 J to 2 s.d. 4100 J • 2.715 kg to 1 s.d. 3 kg • 2.715 kg to 2 s.d. 2.7 kg • 0.987 V to 1 s.d. 1 V • 0.987 V to 2 s.d. 0.99 V

  50. Round each measurement to the required significant digits: • 13.5 N to 2 s.d. • 12.5 N to 2 s.d. • 12.51 N to 2 s.d. • 100.5 km to 3 s.d.

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