1 / 37

NOTES: 3.1, part 2 - Significant Figures

NOTES: 3.1, part 2 - Significant Figures. Significant Figures:. The “sig figs” in a measurement include all of the digits that are known , plus a last digit that is estimated The # of sig figs in a measurement depends on the precision of the instrument being used

forbes
Download Presentation

NOTES: 3.1, part 2 - Significant Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. NOTES: 3.1, part 2 - Significant Figures

  2. Significant Figures: • The “sig figs” in a measurement include all of the digits that are known, plus a last digit that is estimated • The # of sig figs in a measurement depends on the precision of the instrument being used • How do we determine which digits are significant?

  3. THE “RULES” FOR SIG FIGS!!

  4. 1) All non-zero numbers are significant. • EXAMPLES: • 672 - • 34 - • 1,245 - • 24,346 -

  5. 1) All non-zero numbers are significant. • EXAMPLES: • 672 - 3 sig figs • 34 - 2 sig figs • 1,245 - 4 sig figs • 24,346 - 5 sig figs

  6. 2) Zeroes between two non zero numbers are significant. • EXAMPLES: • 202 - • 1.01 - • 1,305 - • 10,001 - • 3,002 - • 62,004 -

  7. 2) Zeroes between two non zero numbers are significant. • EXAMPLES: • 202 - 3 sig figs • 1.01 - 3 sig figs • 1,305 - 4 sig figs • 10,001 - 5 sig figs • 3,002 - 4 sig figs • 62,004 - 5 sig figs

  8. 3) “Leading” zeroes are not significant (just placeholders) • EXAMPLES: • 0.0012 - • 0.000231 - • 0.00855 - • 0.0022 - • 0.0006469 -

  9. 3) “Leading” zeroes are not significant (just placeholders) • EXAMPLES: • 0.0012 - 2 sig figs • 0.000231 - 3 sig figs • 0.00855 - 3 sig figs • 0.0022 - 2 sig figs • 0.0006469 - 4 sig figs

  10. 4) Final or trailing zeroes are not significant UNLESS there is a decimal point in the number. • EXAMPLES: • 150 - • 22.0 - • 12,500 - • 0.00240 - • 5,250 - • 0.02300 - • 0.000350 -

  11. 4) Final or trailing zeroes are not significant UNLESS there is a decimal point in the number. • EXAMPLES: • 150 - 2 sig figs • 22.0 - 3 sig figs • 12,500 - 3 sig figs • 0.00240 - 3 sig figs • 5,250 - 3 sig figs • 0.02300 - 4 sig figs • 0.000350 - 3 sig figs

  12. 5) Powers of ten are not significant • EXAMPLES: • 1.50 X 102 - • 8.890 x 104 - • 7.0 x 108 - • 4.010500 x 1010 - • 6.35 x 10-12 -

  13. 5) Powers of ten are not significant • EXAMPLES: • 1.50 X 102 - 3 sig figs • 8.890 x 104 - 4 sig figs • 7.0 x 108 - 2 sig figs • 4.010500 x 1010 - 7 sig figs • 6.35 x 10-12 - 3 sig figs

  14. PRACTICE: Determine how many significant figures are in each of the following measurements • 0.0034050 L ___________ • 33.600 m ___________ • 7500.0 g ___________ • 47,900 mm ___________ • 7,000,000,001 miles ___________ • 8.07 Hz ___________

  15. PRACTICE: Determine how many significant figures are in each of the following measurements • 0.0034050 L ___________ • 33.600 m ___________ • 7500.0 g ___________ • 47,900 mm ___________ • 7,000,000,001 miles ___________ • 8.07 Hz ___________ 5 5 5 3 10 3

  16. Sig Figs in Calculations: • Find the area of a floor that measures 7.7 meters by 5.4 meters: • AREA =

  17. Sig Figs in Calculations: • Find the area of a floor that measures 7.7 meters by 5.4 meters: • AREA = 41.58 m2

  18. But wait!... • The calculated answer has 4 sig figs, but each measurement used in the calculation only had 2! • The calculated area cannot be more precise than the measured values used to obtain it! • SO…we “round” the answer to the appropriate # of sig figs

  19. ROUNDING: • After you have determined how many sig figs the answer can have, round to that many digits: • If the last significant digit is less than 5: leave the last sig fig as is; • If the last significant digit is 5 or greater: round up!

  20. Practice Problems: How many sig figs in each of the following? 1) 123 meters - 2) 40,506 meters - 3) 9.8000 x 104 m - 4) 0.07080 m - 5) 98,000 m -

  21. Practice Problems: How many sig figs in each of the following? 1) 123 meters - 3 sig figs 2) 40,506 meters - 5 sig figs 3) 9.8000 x 104 m - 5 sig figs 4) 0.07080 m - 4 sig figs 5) 98,000 m - 2 sig figs

  22. More practice…Round the following measurements off so that they each contain 3 significant figures. 1) 366.2 L ___________ 2) 9,047,022 mg ___________ 3) 12.76 g ___________ 4) 999.9 J ___________

  23. More practice…Round the following measurements off so that they each contain 3 significant figures. 1) 366.2 L ___________ 2) 9,047,022 mg ___________ 3) 12.76 g ___________ 4) 999.9 J ___________ 366 L 9,050,000 mg 12.8 g 1.00 x 103 J Notice this one must be in scientific notation to have 3 sig. figs.

  24. NOTES: 3.1, part 2 –Operations With Significant Figures!!

  25. ADDITION AND SUBTRACTION • First add or subtract, then round the answer to the last decimal place they have in common. 25.46 1.6251 + 221.3 -0.543 = = = =

  26. ADDITION AND SUBTRACTION • First add or subtract, then round the answer to the last decimal place they have in common. 25.46 1.6251 + 221.3 -0.543 = 246.76 = 246.8 = 1.0821 = 1.082

  27. Example: 123.25 + 46.0 + 86.257 = =

  28. Example: 123.25 + 46.0 + 86.257 = 255.507 = 255.5 The answer is expressed as 255.5 since 46.0 has only one decimal place.

  29. Examples: a. 15.2 b. 10.8164 + 5.0892 - 8.22 = = = = c. 17.1 d. 2.1 + 4.235 + 3.92 - 0.77 = = = =

  30. Examples: a. 15.2 b. 10.8164 + 5.0892 - 8.22 = 20.2892 = 20.3 = 2.5964 = 2.60 c. 17.1 d. 2.1 + 4.235 + 3.92 - 0.77 = 16.33 = 16.3 = 10.255 = 10.3

  31. MULTIPLICATION AND DIVISION • Multiply or divide first, then round the answer to the same number of sig figs as the smallest number you started with. 1.311 x 2.20 = = 6.884 / 2 = =

  32. MULTIPLICATION AND DIVISION • Multiply or divide first, then round the answer to the same number of sig figs as the smallest number you started with. 1.311 x 2.20 = 2.8842 = 2.88 6.884 / 2 = 3.441 = 3

  33. Example: 23.0 x 432 x 19 = =

  34. Example: 23.0 x 432 x 19 = 188,784 = 190,000 The answer is expressed as 190,000 or 1.9 x 105 since 19 has only two sig. figs.

  35. Examples: a. 3.214 x 4.24 = b. 6.8 x 3.145 = c. 122.82 / 2.00 = d. 0.072 / 4.36 = e. 5.82 x 760 x 325 = 723 x 273

  36. Examples: a. 3.214 x 4.24 = 13.6 b. 6.8 x 3.145 = 21 c. 122.82 / 2.00 = 61.4 d. 0.072 / 4.36 = 0.17 e. 5.82 x 760 x 325 = 7.3 723 x 273

  37. Perform the following calculations. Round your answers to the proper # of sig. figs. 1) 36.57 m / 3.21 s = ___________ 2) 41.376g + 13.3g + 42.9g = ___________ 3) 5.67 m x 13.44 m = ___________ 4) (5.83 m / 2.67 s) / 2.1 s = ___________ 5) 9.374 V x 6.0 = ___________ 11.4 m/s 97.6 g 76.2 m2 1.0 m/s2 56 V From now on, we will round all our answers to the correct # of significant figures.

More Related