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Understanding Scientific Measurement: Accuracy, Precision, and Significant Figures

This chapter delves into the fundamentals of scientific measurement, distinguishing between qualitative and quantitative results. It clarifies the concepts of accuracy and precision, explaining how they influence measurement validation. The chapter also details the calculation of percent error and demonstrates the importance of significant figures in ensuring measurement precision. Additionally, it covers rounding methods and the use of scientific notation, providing practice problems to enhance comprehension of how to accurately present and calculate scientific values.

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Understanding Scientific Measurement: Accuracy, Precision, and Significant Figures

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  1. Chapter 3 Scientific Measurement

  2. Qualitative Gives results in a description, nonumerical form Quantitative Give results in a definite form, usually numbers and units Measurements

  3. Accuracy vs. Precision • Accuracy - how close a measurement is to the accepted value • Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

  4. Accuracy vs. Precision

  5. your value accepted value Percent Error • Indicates accuracy of a measurement

  6. % error = 2.9 % Percent Error • A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

  7. Percent Error • A technician experimentally determined the boiling point of octane to be 124.1ºC. The actual boiling point of octane is 125.7ºC. Calculate the error and percent error. Error= 1.6ºC Percent error= 1.273 %

  8. Significant Figures • Indicates precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.31 cm

  9. Significant Figures • Counting Sig Figs • All non-zero numbers are sig figs • Zeros depend on location in number: • LEADING zeros never count ---------0.0025 • EMBEDDED zeros always count---- 10,005 • TRAILING zeros only count if there is a point. --------------2,500 2,500. The underlined zeros do not count.

  10. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 3 sig figs 2. 402 2. 402 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  11. Rounding • Need to use rounding to write a calculation correctly • Calculator gives you lots of insignificant figures and you must round to the right place • When rounding, look at the digit after the one you can keep • Greater than or equal to 5, round up • Less than 5, keep the same

  12. Rounding • Round each measurement to 3 sig figs. • A. 87.073 meters • B. 4.3621 meters • C. 0.01552 meter • D. 9009 meters • E. 1.7777 meters • F. 629.55 meters 87.1meters 4.36 meters 0.0155 meter 9010 meters 1.78 meters 630 meters

  13. Scientific Notation • Round each measurement to the number of significant figure shown in parenthesis. Write the answers in scientific notation. • A. 314.721 meters (4) • B. 0.001775 meter (2) • C. 64.32 X 10-1 meters (1) • D. 8792 meters (2) 3.147 X 102 1.8 108 60 X 10-1 8.8 X 103

  14. Significant Figures • Calculating with Sig Figs (con’t) • Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350g  7.9 mL

  15. Significant Figures • C. 8.7 g + 15.43 g + 19 g = 43.13 g • D. 853.2 L – 627.443 L = 225.757 L • E. 5.47 m + 11m + 87.3000 m = 103.770m E. 5.47 11 + 87.3000 103.770 C. 8.7 15.43 + 19 43.13 D. 853.2 - 627.443 225.757 225.8 104 43

  16. Significant Figures • Calculating with Sig Figs (con’t) • Exact Numbers do not limit the # of sig figs in the answer. UNLIMITED SIG FIGS • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm

  17. 3 SF Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 324g

  18. 1. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL  3700 a. 67 X 55 = 3685  0.30 d. 0.034 X 8.8 = 0.2992

  19. Scientific Notation • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. • Large # (>1)  positive exponentSmall # (<1)  negative exponent • Only include sig figs. 65,000 kg  6.5 × 104 kg

  20. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  21. Scientific Notation • Convert between scientific notation and regular notation *without changing the # of sig figs* • A. 4.61 X 10-4 • B. 3.69 X 106 • C. 0.000597 • D. 23,000,000 • E. 8.00 X 102

  22. Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: (5.44 X10 (8.1X10 7) 4) ÷ EE EE ENTER = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

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