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The Story of GUSS

The Story of GUSS. with a special appearance by Significant Digits. A Justification for “ Sig Digs ”. There are no "magic numbers" in science. A Justification for “ Sig Digs ”. There are no "magic numbers" in science. All numbers are generated by measurement.

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The Story of GUSS

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  1. The Story of GUSS with a special appearance by Significant Digits

  2. A Justification for “Sig Digs” There are no "magic numbers" in science.

  3. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement.

  4. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement. So each number has a set number of digits.

  5. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement. So each number has a set number of digits. All the measured digits +

  6. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement. So each number has a set number of digits. All the measured digits + an estimated digit.

  7. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement. So each number has a set number of digits. All the measured digits + an estimated digit. All these digits are significant.

  8. A Justification for “Sig Digs” There are no "magic numbers" in science. All numbers are generated by measurement. So each number has a set number of digits. All the measured digits + an estimated digit. All these digits are significant. Hence they are SIGNIFICANT DIGITS ("sig digs" for short) Big Sig Fig Gig

  9. For Example The measurement 21.6 cm has three sig digs

  10. The following rules are used to determine if a digit is significant:

  11. The following rules are used to determine if a digit is significant: • All non-zero digits are significant

  12. 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

  13. 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

  14. 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. 0.50 kg has two significant digits

  15. 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

  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 • Any zeroes placed between significant digits are significant e.g. 30.07 m has four 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 • All other zeroes are not significant

  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?

  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.

  21. 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.

  22. 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?

  23. Making Zeros Significant But what if you measured 100 cm exactly?

  24. Making Zeros Significant But what if you measured 100 cm exactly? You can show that a zero is significant by:

  25. Making Zeros Significant But what if you measured 100 cm exactly? You can show that a zero is significant by: • underscoring or overscoring the zero: e.g. 100 cm

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

  27. Making Zeros Significant They should look like this:

  28. And now for some practice. . . .

  29. How many significant digits are there in each of the following? • 12 m/s • 60 W • 305 K • 9.5 kg • 2.0 T • 0.8 N • 20450 cal

  30. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W • 305 K • 9.5 kg • 2.0 T • 0.8 N • 20450 cal

  31. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K • 9.5 kg • 2.0 T • 0.8 N • 20450 cal

  32. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K 3 s.d. • 9.5 kg • 2.0 T • 0.8 N • 20450 cal

  33. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K 3 s.d. • 9.5 kg 2 s.d. • 2.0 T • 0.8 N • 20450 cal

  34. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K 3 s.d. • 9.5 kg 2 s.d. • 2.0 T 2 s.d. • 0.8 N • 20450 cal

  35. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K 3 s.d. • 9.5 kg 2 s.d. • 2.0 T 2 s.d. • 0.8 N 1 s.d. • 20450 cal

  36. How many significant digits are there in each of the following? • 12 m/s 2 s.d. • 60 W 1 s.d. • 305 K 3 s.d. • 9.5 kg 2 s.d. • 2.0 T 2 s.d. • 0.8 N 1 s.d. • 20450 cal 4 s.d.

  37. How many significant digits are there in each of the following? • 1.40 W • 0.075 h • 102.5 MHz • 2500 J • 100.0 V • 40.20 A • 0.09030 km

  38. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h • 102.5 MHz • 2500 J • 100.0 V • 40.20 A • 0.09030 km

  39. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz • 2500 J • 100.0 V • 40.20 A • 0.09030 km

  40. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz 4 s.d. • 2500 J • 100.0 V • 40.20 A • 0.09030 km

  41. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz 4 s.d. • 2500 J 2 s.d. • 100.0 V • 40.20 A • 0.09030 km

  42. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz 4 s.d. • 2500 J 2 s.d. • 100.0 V 4 s.d. • 40.20 A • 0.09030 km

  43. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz 4 s.d. • 2500 J 2 s.d. • 100.0 V 4 s.d. • 40.20 A 4 s.d. • 0.09030 km

  44. How many significant digits are there in each of the following? • 1.40 W 3 s.d. • 0.075 h 2 s.d. • 102.5 MHz 4 s.d. • 2500 J 2 s.d. • 100.0 V 4 s.d. • 40.20 A 4 s.d. • 0.09030 km 4 s.d.

  45. 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.

  46. 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.

  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. • 2.715 kg to 2 s.d. • 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. • 0.987 V to 1 s.d. • 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. • 0.987 V to 2 s.d.

  50. 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.

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