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Scientific Measurements Standards for Measurement

Scientific Measurements Standards for Measurement. Accuracy & Precision Significant Figures Scientific Notation. Precision vs. Accuracy. Precision: How closely individual measurements compare with each other The “fineness” of a measurement.

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Scientific Measurements Standards for Measurement

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  1. Scientific Measurements Standards for Measurement • Accuracy & Precision • Significant Figures • Scientific Notation

  2. Precision vs. Accuracy Precision: • How closely individual measurements compare with each other • The “fineness” of a measurement Accuracy: how closely individual measurements compare with the true or accepted value or correct value.

  3. Accurate or Precise? What is the temperature at which water boils? • Measurements: 95.0°C, 95.1°C, 95.3°C • True value: 100°C Precise! (but not accurate)

  4. Accurate or Precise? What is the temperature at which water freezes? • Measurements: 1.0°C, 1.2°C, -5.0°C • True value: 0.0°C Accurate! (it’s hard to be accurate without being precise)

  5. Accurate or Precise? What is the atmospheric pressure at sea level? • Measurements: 10.01 atm, 0.25 atm, 234.5 atm • True value: 1.00 atm Not Accurate & Not Precise (don’t quit your day job)

  6. Accurate or Precise? What is the mass of one Liter of water? • Measurements:1.000 kg, 0.999 kg, 1.002 kg • True value:1.000 kg Accurate & Precise (it’s time to go pro)

  7. A graduated cylinder: 41.2 mL (3 sig figs = very precise) 41.0 100 mL Beaker 50 mL Graduated cylinder A beaker: 40. mL (2 sig figs = not as precise) 50

  8. Uncertainty examples: • Measure time for a pencil to fall… compare a stopwatch and a wall clock. • Measure volume of a liquid… compare a graduated cylinder and a beaker. The stopwatch & graduated cylinder are more precise instruments…so the readings they produce will have more sig figs.

  9. Accuracy or Precision? When deciding on accuracy, precision, both, or neither….it is quantitative data (numerical), not qualitative (descriptive) 1. The recipe calls for 25 chocolate chips per cookie. The cookies analyzed have 34, 35, and 32 respectively. 2. The percent NaCl is 99%, 99%, and 98%. 3. The number of grams of KF required is 0.04 g. The amounts used were 0.038, 0.039, 0.041, and 0.040. 4. To win, Henry must earn 500 points. In his three trials, he earned 400, 480, and 395 points.

  10. Reporting Measurements • Using significant figures • Report what is known with certainty • Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

  11. Reading Lab equipment Interpolating Scale Values  1 2 3 4 5 6 Value - 3.66 (uncertainty ± 0.01 in 0.06) digit Meniscus 100 90 80 70 60 50 40 30 20 10  Value - 83.3 (uncertainty ±0.1 in 0.3)

  12. 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7th Edition, page 7

  13. Reporting Measurements

  14. Measurement of volume using a buret. The volume is read at the bottom of the liquid curve (called the meniscus). 20.16ml 20.17ml 20.15ml 20.18ml 20.16ml 20.17ml 20.15ml 20.18ml ±0.01ml ±0.01ml

  15. Thermometer:

  16. PACIFIC PACIFIC When are digits “significant”? The “Atlantic-Pacific” Rule “PACIFIC” Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit. 40603.23 ft2 = 7 sig figs 0.01586 mL = 4 sig figs

  17. ATLANTIC ATLANTIC When are digits “significant”? “ATLANTIC” Decimal point is ABSENT. Count digits from right side, starting with the first nonzero digit. 3 sig figs = 40600 ft2 1 sig fig = 1000 mL

  18. Examples • 0.00932 Decimal point present → “Pacific” → count digits from left, starting with first nonzero digit = 3 sig figs • 4035 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs • 27510 Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit = 4 sig figs

  19. Rules for Counting Significant Figures 1.All Non-zeros digits count as significant figures: 3456has 4 significant figures

  20. Rules for Counting Significant Figures Zeros 2. Trailing zerosare significant only if the number contains a written decimal point: 9.300 has 4 significant figures

  21. Rules for Counting Significant Figures Zeros 3. Zeros found between two significant digits count as significant figures: 16.07has 4 significant figures

  22. Rules for Counting Significant Figures Zeros 4. Leading zeroes (place holders) do not count as significant figures: 0.0486 has 3 significant figures

  23. Rules for Counting Significant Figures Two special situationshave an unlimited number of significant figures: 1. Counted items • 23 people, or 425 thumbtacks 2. Exactly defined quantities • 60 minutes = 1 hour

  24. Sig Fig Practice #1 How many significant figures in the following? 1.0070 m  5 sig figs 17.10 kg 4 sig figs These all come from somemeasurements 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 This is a counted value 5 dogs unlimited

  25. Rules for Counting Significant Figures • In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. • Sometimes, calculated values need to be rounded off.

  26. Rounding Calculated Answers • 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

  27. 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. • 6.80 + 11.934 = • 18.734  18.70

  28. Sig Fig Practice #2 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL *Note the zero that has been added.

  29. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sigfigs 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)

  30. Sig Fig Practice #3 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.05 cm2 0.04742 cm2 0.02 cm x 2.371 cm 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23ft 5872.786 lb·ft 2.9561 g/mL 2.96 g/mL 1.030 g x 2.87 mL

  31. Scientific Notation • “Writing a number as a power of 10.” • Why? • Very large and very small numbers more manageable to write and use. • Rule of thumb: Use when number is greater than 100 or smaller than 0.10. • The number of sig figs are clearly shown in a measurement.

  32. Scientific Notation How important is a change in the power of 10? Diameter of Earth’s orbit around the sun ≈ 100,000,000,000 m = 1.0 x 1011 m • Diameter of an atom • ≈ 0.0000000001 = 1.0 x 10-10 m

  33. Writing in scientific notation • Move the decimal point in the original number so that it is located to the right of the first nonzero digit. • Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved. • If the decimal point moves: • To the left, the power of 10 is positive. • To the right, the power of 10 is negative.

  34. SIGNIFICANCE OF THE EXPONENT n

  35. Scientific Notation: • EXPONENT

  36. Write the following measurements in scientific notation, then record the number of sig figs. • 789 g • 96,875 mL • 0.0000133 J • 8.915 atm • 0.94°C 3 sig figs 7.89 x 102 g 5 sig figs 9.6875 x 104 mL 1.33 x 10-5 J 3 sig figs 4 sig figs 8.915 atm 2 sig figs 9.4 x 10-1 °C

  37. Rounding Look at digit following specified rounding value. If it is 5 or greater, then round up. If not, truncate (cut off the rest of the numbers). • Round to the nearest tenth • 6.7512 • 6.7777 • 6.7499 • 6.9521 6.8 6.8 6.7 7.0

  38. Practice Problems 1. State the abbreviation for each of the following units: • milligram • kilogram • meter • nanometer • angstrom • microliter 2. State the number of significant figures in each of the following numbers: • 40.0 • 0.081 • 129,042 • 4.090 x 10-3 3 Round each of the following numbers to three significant figures: • 8.8726 • 21.25 • 129.509 • 1.995 x 106 4. Write each of the following numbers in exponential (scientific) notation: • 0.0456 • 4082.2 • 40.30 • 12,000,000 mg kg m nm A 8.87 21.3 130. or 1.30 x 102 2.00 x 106 L 3 2 6 4 4.56 x 10-2 4.08 x 103 4.03 x 101 1.20 x 107

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