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Measurement and Accuracy in Science

Understand precision and accuracy in measurements, learn about percent error, significant figures rules, and scientific notation usage for better scientific calculations. Explore direct and inverse proportions in graphs.

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Measurement and Accuracy in Science

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  1. CH. 2 - MEASUREMENT I. Using Measurements (p. 44 - 57)

  2. (1) Use one word to describe precision and one word to describe accuracy

  3. A. 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. (2) What is the equation for percent error?

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

  6. % error = 2.9 % B. 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. (3) What is the purpose for significant figures?

  8. C. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

  9. (4) What are two rules for significant figures? (zero rules)

  10. C. Significant Figures • Counting Sig Figs (Table 2-5, p.47) • Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500

  11. C. 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

  12. (5) What are the multiplication rules?

  13. 3 SF C. 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

  14. (6) What is the rule for adding and subtracting significant figures?

  15. C. 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 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.9 mL

  16. (7) What about exact numbers in calculations?

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

  18. 5. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF C. Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 6. 18.9 g - 0.84 g  18.1 g 18.06 g

  19. (8) What do we use in science to help us work with larger numbers?

  20. D. 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

  21. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm D. Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

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

  23. (9) How does the graphs of inverse and direct proportion differ?

  24. y y x x E. Proportions • Direct Proportion • Inverse Proportion

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