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Measurements and Conversions: Understanding Accuracy and Precision

Learn about measurements and conversions, including the SI system of units, conversion factors, significant digits, and scientific notation. Understand the concepts of accuracy and precision, as well as how to calculate percent error. Explore the use of graphs to represent relationships in scientific measurements. Review exercises are included.

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Measurements and Conversions: Understanding Accuracy and Precision

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  1. Chapter 2 Measurements and Calculations

  2. Scientific Method • 5 Steps • Hypothesize • Observe • Experiment • Conclusion • Pulication

  3. Units of Measurement • Measurements represent quantities • Le Système International d’Unités • SI System • Numbers written without comma • 24 000 not 24,000

  4. SI Measurement • Length • Meter • Mass • Quantity of mater • Kilogram • Time • Second • Temperature • Kelvin • Amount of substance • Mole

  5. SI Prefixes • Tera 1012 • Giga 109 • Mega 106 • Kilo 103 • Hecto 102 • Deka 101 • BASE 100 • Deci 10-1 • Centi 10-2 • Milli 10-3 • Micro 10-6 • Nano 10-9 • Pico 10-12 • Femto 10-15 • Atto 10-18

  6. Conversions • Conversion Factor - ratio derived from equality between two different units 4 quarters 1 dollar 0.25 dollar 1 dollar 4 quarters 1 quarter • How many quarters are in 12 dollars?

  7. Conversions 1000 g 1 kg 0.001 kg 1 kg 1000 g 1 g • How many grams are in 0.64 kg? • Express a mass of 5.712 grams in milligrams and in kilograms.

  8. Problems 10.5 g = _____ kg 1.57 km = _____ m 3.54 g = _____ g 3.5 mol = _____ mol 1.2 L = _____ mL 358 cm3 = ____ m3 548.6 mL = ____ cm3

  9. Accuracy vs. Precision • Accuracy closeness of measurements to accepted value • Precision  closeness of measurements in relationship to each other

  10. Percent Error • Calculation of the accuracy of measurements Percent Error = Valueaccepted - Valueexperimental x 100 Valueaccepted

  11. Sample Problems • Calculate the percent error in a length measurement of 4.25 cm if the correct value is 4.08 cm. • The actual density of a certain material is 7.44 g/cm3. A student measures the density of the same material as 7.30 g/cm3. What is the percent error of the measurement?

  12. Error in Measurement • There is always some error in measurement • The last digit in the measurement is an estimate • Include error estimate as ±0.01 cm, for example

  13. Significant Digits • Valid digits • Last digit is an estimate • 3.51 cm has 3 sig figs • 45.0 cm has 3 sig figs • Zeros not significant if holding decimal spot • 0.0024 kg has 2 sig figs • 0.0024030 kg has 5 sig figs

  14. Significant Digits • Nonzero digits are always significant. • All final zeros after the decimal point are significant • Zeros between two other sig figs are always significant • Zeros used only for spacing decimal point are not significant.

  15. Significant Digits • Mathematical operation cannot be more precise than least precise • Addition & Subtraction • Add/Subract values • Round to least number of decimal spot

  16. Significant Digits • Multiplication/Division • Calculate • Count number of digits • Round to this number • Conversion Factors • Consider exact/No uncertainty

  17. Scientific Notation • Used when referring to very large or small numbers • 6 000 000 000 000 000 000 kg • 0.000 000 000 000 000 000 mg • Scientific notation uses positive exponents

  18. Scientific Notation • First digit between 1 and 10 • Multiply by a whole-number power of 10 • M x 10n • 40 000 g = 4 x 104 g • 0.000 4 g = 4 x 10-4 g

  19. Graphs • Linear relationship • y = mx + b • Slope = rise/run • Quadratic relationship • y = kx2 • Parabolas • Inverse relationship • xy = k

  20. Chapter Review • Pg. 59 • 8,16,21,27,28,32,33,34,36,37,40,41

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