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50643763-1-4-Significant-figures-and-calculations.pptx

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1. The scientific method 2. Units of measurement 3. Uncertainty in measurement precision and accuracy 4. Significant figures and calculations 5. Dimensional analysis 1.4 MEASUREMENTS
1.4 SIGNIFICANT FIGURES AND CALCULATIONS 1.4
1.4 Significant figures and calculations All certain digits plus one estimated digit 1.4
Significant Figures in Measurements Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated. Measurements must be reported to the correct number of significant figures. 1.4
Any digit that is not zero is significant 2.234 kg 4 significant figures Zeros between nonzero digits are significant 607 m 3 significant figures Zeros to the left of the first nonzero digit are not significant 0.07 L 1 significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 5.0 mg 2 significant figures If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant 0.00520 g 3 significant figures 1.4 1.8 Significant Figures You must be within 1 sig fig it does not need to be perfect, but sig figs DO count!
Rules for Counting Significant Figures Two special situations have an unlimited number of significant figures: 1. Counted items a) 23 people, or 425 thumbtacks 2 Exactly defined quantities b) 60 minutes = 1 hour 1.4
Sig Fig Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 mL 2 sig figs unlimited 5 dogs These all come from some measurements This is a counted value 1.4
1.4 How many significant figures are in each of the following measurements? 24 mL 2 significant figures 3001 g 4 significant figures 0.0320 m3 3 significant figures 6.4 x 104 molecules 2 significant figures 560 kg 2 significant figures 1.8
Rounding Calculated Answers 1.4 Rounding Decide how many significant figures are needed Round to that many digits, counting from the left Is the next digit less than 5? Drop it. Next digit 5 or greater? Increase by 1 3.016 rounded to hundredths is 3.02 3.013 rounded to hundredths is 3.01 3.015 rounded to hundredths is 3.02 3.045 rounded to hundredths is 3.04 3.04501 rounded to hundredths is 3.05
Rounding Calculated Answers Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem.Examples: 1.4
Examples 1.4 Make the following have 3 sig figs: 761.50 762 14.334 14.3 10.44 10.4 10789 10800 8024.50 8020 203.514 204
Rounding Calculated Answers 1.4 Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem.
Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 13 (2 sig figs) 1.4
Significant Figures in Calculations 1.4 In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Ever heard that a chain is only as strong as the weakest link? Sometimes, calculated values need to be rounded off.
Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 23 m2 100.0 g 歎 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m 歎 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 1.030 g 歎 2.87 mL 5872.786 lb揃ft 2.9561 g/mL 5870 lb揃ft 2.96 g/mL 1.4
Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) 89.332 +1.1 90.432 3.70 -2.9133 0.7867 one significant figure after decimal point round off to 90.4 two significant figures after decimal point round off to 0.79 1.4
Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 1818.2 lb + 3.37 lb 709.228 L 1821.57 lb 709.2 L 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL 1.4

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50643763-1-4-Significant-figures-and-calculations.pptx

  • 1. 1. The scientific method 2. Units of measurement 3. Uncertainty in measurement precision and accuracy 4. Significant figures and calculations 5. Dimensional analysis 1.4 MEASUREMENTS
  • 3. 1.4 Significant figures and calculations All certain digits plus one estimated digit 1.4
  • 4. Significant Figures in Measurements Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated. Measurements must be reported to the correct number of significant figures. 1.4
  • 5. Any digit that is not zero is significant 2.234 kg 4 significant figures Zeros between nonzero digits are significant 607 m 3 significant figures Zeros to the left of the first nonzero digit are not significant 0.07 L 1 significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 5.0 mg 2 significant figures If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant 0.00520 g 3 significant figures 1.4 1.8 Significant Figures You must be within 1 sig fig it does not need to be perfect, but sig figs DO count!
  • 6. Rules for Counting Significant Figures Two special situations have an unlimited number of significant figures: 1. Counted items a) 23 people, or 425 thumbtacks 2 Exactly defined quantities b) 60 minutes = 1 hour 1.4
  • 7. Sig Fig Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs 3.29 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 mL 2 sig figs unlimited 5 dogs These all come from some measurements This is a counted value 1.4
  • 8. 1.4 How many significant figures are in each of the following measurements? 24 mL 2 significant figures 3001 g 4 significant figures 0.0320 m3 3 significant figures 6.4 x 104 molecules 2 significant figures 560 kg 2 significant figures 1.8
  • 9. Rounding Calculated Answers 1.4 Rounding Decide how many significant figures are needed Round to that many digits, counting from the left Is the next digit less than 5? Drop it. Next digit 5 or greater? Increase by 1 3.016 rounded to hundredths is 3.02 3.013 rounded to hundredths is 3.01 3.015 rounded to hundredths is 3.02 3.045 rounded to hundredths is 3.04 3.04501 rounded to hundredths is 3.05
  • 10. Rounding Calculated Answers Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem.Examples: 1.4
  • 11. Examples 1.4 Make the following have 3 sig figs: 761.50 762 14.334 14.3 10.44 10.4 10789 10800 8024.50 8020 203.514 204
  • 12. Rounding Calculated Answers 1.4 Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem.
  • 13. Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 13 (2 sig figs) 1.4
  • 14. Significant Figures in Calculations 1.4 In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Ever heard that a chain is only as strong as the weakest link? Sometimes, calculated values need to be rounded off.
  • 15. Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 23 m2 100.0 g 歎 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m 歎 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 1.030 g 歎 2.87 mL 5872.786 lb揃ft 2.9561 g/mL 5870 lb揃ft 2.96 g/mL 1.4
  • 16. Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) 89.332 +1.1 90.432 3.70 -2.9133 0.7867 one significant figure after decimal point round off to 90.4 two significant figures after decimal point round off to 0.79 1.4
  • 17. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 1818.2 lb + 3.37 lb 709.228 L 1821.57 lb 709.2 L 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL 1.4