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Measurement and Accuracy in Science

Learn about accuracy and precision in measurements, significant figures, scientific notation, and SI units in this comprehensive guide. Improve your understanding of measurement techniques and calculations.

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Measurement and Accuracy in Science

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  1. CH. 2 - MEASUREMENT Using Measurements

  2. 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

  3. 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 2.32 cm

  4. C. Significant Figures • Counting Sig Figs • Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500 • USA??

  5. 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

  6. 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

  7. 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. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  7.9 mL

  8. 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

  9. 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 • 18.9 g • - 0.84 g  18.1 g 18.06 g

  10. 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

  11. 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

  12. 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

  13. E. SI Units Quantity Symbol Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K Amount n mole mol

  14. M V D = F. Derived Units • Combination of base units. • Volume (m3 or cm3) • length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L • Density (kg/m3 or g/cm3) • mass per volume

  15. Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

  16. Density • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

  17. WORK: V = M D V = 25 g 0.87 g/mL Density • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g V = 29 mL

  18. kilo- mega- M k 106 103 deci- BASE UNIT d --- 100 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12 SI Prefix Conversions Prefix Symbol Factor move left move right

  19. SI Unit Conversions • King Henry Died__drinking chocolate milk • K H D __ d C M

  20. NUMBER = UNIT SI Prefix Conversions 0.532 532 m = _______ km NUMBER UNIT

  21. 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ____ mm 4) 805 dm = ______________ km SI Prefix Conversions 0.2 32 45,000 0.0805

  22. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  23. Dimensional Analysis • Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  24. qt mL  Dimensional Analysis • How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt) 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  25. lb cm3 Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. (1 kg = 2.2 lbs) 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

  26. cm in Dimensional Analysis • Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm) 8.0 cm 1 in 2.54 cm = 3.2 in

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