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8/29/11

8/29/11. 1. Room Map 2. Tally Skills Test 3. E-2 Significant figures notes 4. E-2 Practice Problems. Significant Figures.

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8/29/11

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  1. 8/29/11 • 1. Room Map • 2. Tally Skills Test • 3. E-2 Significant figures notes • 4. E-2 Practice Problems

  2. Significant Figures As you learned in the measurement activity, an appropriate measurement for the length of the rectangle below is 3.65 cm. Because the “3” and the “6” are certain, and the “5” is our guess, all three digits are intentional or “significant.” Thus 3.65 cm contains three significant figures. 0 1 2 3 4 5 cm

  3. Significant Figures The scale below is less precise, and so the rectangle’s length should be reported as just 3.5 cm. This measurement has just two significant figures: the “3” and the “5” and it is considered to be a weaker, less valuable measurement than 3.65 cm. 0 1 2 3 4 5 cm

  4. Significant Figures The scale below, however, is more precise, and a magnified view (shown at right) is helpful in making a good reading: 3.665 cm. This measurement has 4 significant figures: the “3.66…” which are certain, and the “5” which is the guess. (3.6) (3.7) 0 1 2 3 4 5 cm

  5. Significant Figures 3.5 cm has two significant figures, 3.65 cm has three significant figures, 3.665 cm has four significant figures. You might start to think that the number of significant figures is simply equal to the number of digits there are in a measurement, but that is not always the case…

  6. Significant Figures Consider the length of the rectangle below: 3500 mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant? 5000 4000 3000 2000 0 1000 mm

  7. Significant Figures Consider the length of the rectangle below: 3500 mm. The “3” is definite. The “5” is the guess. So what about the two zeroes at the end? Are they significant? NO! They are not considered significant. 5000 4000 3000 2000 0 1000 mm

  8. Significant Figures In 3500 mm, the zeroes are serving a very different purpose than the “3” and the “5.” These two zeroes are acting as place-keepers. They show the size of the measurement -- 3500 mm, not just 35 mm – but they do not make the measurement any more precise. 5000 4000 3000 2000 0 1000 mm

  9. Significant Figures Thus 3500 mm has just two significant figures, not four. 5000 4000 3000 2000 0 1000 mm

  10. Significant Figures Now consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.) 5000 4000 3000 2000 0 1000 mm

  11. Significant Figures Now consider the measurement below: 3450 mm. How many significant figures does it have? (Make a guess before continuing.) If you said three, you are correct! 5000 4000 3000 2000 0 1000 mm

  12. Significant Figures In 3450 mm, the “3” and “4” are definite and the “5” is the guess, so those are the three significant figures. The zero at the end is a place-keeping zero, and so it is not considered to be significant. 5000 4000 3000 2000 0 1000 mm

  13. Significant Figures Now what about the measurement below: 0.00275 m? How many significant figures do you think it has? (Make a guess before continuing.) 0.005 0.004 0.003 0.002 0 0.001 m

  14. Significant Figures Now what about the measurement below: 0.00275 m? How many significant figures do you think it has? (Make a guess before continuing.) If you said three, good job. 0.005 0.004 0.003 0.002 0 0.001 m

  15. Significant Figures In 0.00275 m, the “2” and “7” are definite and the “5” is the guess. Here the zeroes in the beginning of the number are place keepers. They make 0.00275 a small number, just as the zeroes in 3500 make it a big number. 0.005 0.004 0.003 0.002 0 0.001 m

  16. Significant Figures If you are good at converting numbers into scientific notation then this will help:

  17. Significant Figures If you are good at converting numbers into scientific notation then this will help: 170,000,000,000 converts into 1.7 x 1011.

  18. Significant Figures If you are good at converting numbers into scientific notation then this will help: 170,000,000,000 converts into 1.7 x 1011. And 0.00000563 converts into 5.63 x 10-6.

  19. Significant Figures If you are good at converting numbers into scientific notation then this will help: 170,000,000,000 converts into 1.7 x 1011. And 0.00000563 converts into 5.63 x 10-6. Notice how scientific notation separates out all the significant figures and puts them in the beginning… 1.7 x 1011 5.63 x 10-6

  20. Significant Figures If you are good at converting numbers into scientific notation then this will help: 170,000,000,000 converts into 1.7 x 1011. And 0.00000563 converts into 5.63 x 10-6. Notice how scientific notation separates out all the significant figures and puts them in the beginning…and it changes all the place- keeping zeroes into a power of ten 1.7 x 1011 5.63 x 10-6

  21. Significant Figures 3500 has two significant figures, 0.00275 has three significant figures. You might start to think that zeroes are never significant, but that is not always the case…

  22. Significant Figures Consider the measurement shown below: 30.5 cm. 50 40 30 20 0 10 cm

  23. Significant Figures Consider the measurement shown below: 30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “5” is the guess. 50 40 30 20 0 10 cm

  24. Significant Figures Consider the measurement shown below: 30.5 cm. Here the zero is one of the significant figures: the “3” and the “0” are definite, and the “6” is the guess. 30.5 cm has three significant figures. 50 40 30 20 0 10 cm

  25. Significant Figures And consider the measurement shown below: 23.0 cm. 50 40 30 20 0 10 cm

  26. Significant Figures And consider the measurement shown below: 23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess. 50 40 30 20 0 10 cm

  27. Significant Figures And consider the measurement shown below: 23.0 cm. Here the zero is also one of the significant figures: the “2” and the “3” are definite, and this time the “0” is the guess. 23.0 cm has three significant figures. 50 40 30 20 0 10 cm

  28. Rules recap thusfar: Rules for identifying significant figures in a measurement: All non-zero digits are significant (i.e. 1-9). 2. All zeros or groups of zeros between non zero digits are significant (ex. ALL the zeros in 703 g, 8.001 mL, and 7010.02 cm are all significant because of rule #2a.) AND all zeros between a non-zero digit on the left and a decimal on the right are also significant (ex. ALL the zeros in 140. cm, 6000. mL, are 1800. g are all significant because of rule #2b.). These 2 types of zeros can be referred to as “squeezed zeros.” 3. All zeros or groups of zeros to the right of the decimal AND at the end of the number are significant (ex. ALL the zeros in 2.30 cm, 7.00 mL, and 56.9000 g are all significant because of rule #3.). These zeros can be referred to as “trailing zeros.” **ALL other types of zeros are NOT significant and serve only as place holders(ex. The zeros in 300 cm and 0.0071 mL ARE NOT significant since they are neither “squeezed zeros” nor “trailing zeros”). Remember, significant means measured, not important (Place holder zeros ARE still important even if they aren’t significant!)!

  29. All those rules seem a bit tough to keep straight? While you should remember why we do sig figs, and what makes something “significant,” here’s a handy trick to help you count your sig figs: If the decimal point is Absent, count from the Atlantic. If the decimal point is Present, count from the Pacific. ________________________________________________________________ For example: 6702000 has no decimal point. The Altantic rule applies! |<---- starting from the “Atlantic,” heading “west,” the first non-zero digit we hit is the 2, and everything after that is also significant. So 6702000 has 4 significant figures!

  30. SHORTCUT! HANDY TRICK! If the decimal point is Absent, count from the Atlantic. If the decimal point is Present, count from the Pacific.

  31. We’ll stop here for Day 1 of E2 Day 1 Homework: Bottom of page 10 in WB #1 ALL, #2 a-h Want more practice? Keep going on these slides from the blog (MHSchemistry.wordpress.com)! There’s a good recap at slide #130, just before Day 2 notes pick up.

  32. Significant Figures Now, let’s see how much you have learned about significant figures. What follows are 50 different problems. For each one, simply think of the how many significant figures there are, then go to the next slide to see if you are correct. If you are correct, go on to the next problem. If not, try to figure out why your answer is incorrect.

  33. Significant Figures 34.84 cm

  34. Significant Figures 34.84 cm 4 sig figs

  35. Significant Figures 63 g

  36. Significant Figures 63 g 2 sig figs

  37. Significant Figures 109 m

  38. Significant Figures 109 m 3 sig figs

  39. Significant Figures 17.03 cm

  40. Significant Figures 17.03 cm 4 sig figs

  41. Significant Figures 290 mm

  42. Significant Figures 290 mm 2 sig figs

  43. Significant Figures 0.00037 s

  44. Significant Figures 0.00037 s 2 sig figs

  45. Significant Figures 0.00405 kg

  46. Significant Figures 0.00405 kg 3 sig figs

  47. Significant Figures 70400 mL

  48. Significant Figures 70400 mL 3 sig figs

  49. Significant Figures 0.03040 L

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