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Measurement

Measurement. September 2007. Today 9/13/07. Review of Measurement Metric system Uncertainty Significant Figures The Lab. Units of Measurement. English (Imperial) used in U.S. metric most common, worldwide used in science (not engineering) SI – offshoot of metric

hermione-woodard
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Measurement

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  1. Measurement September 2007

  2. Today 9/13/07 • Review of Measurement • Metric system • Uncertainty • Significant Figures • The Lab

  3. Units of Measurement • English (Imperial) • used in U.S. • metric • most common, worldwide • used in science (not engineering) • SI – offshoot of metric • only seven base units

  4. Système Internationale • Fundamental Quantity Unit Abbrev. • Mass Kilogram kg • Length Meter m • Time Second sec

  5. Prefixes

  6. Metric units • Mass (distinct from weight) • gram (g) is the base metric unit • 1 kg = 2.2 pounds • Length • meter (m) is the base unit • 1 m = 1.094 yd = 3.281 ft = 39.37 in

  7. Metric units • Temperature • Celsius scale (°C) • °C = 5/9 (°F – 32) • °F = 9/5(°C) + 32 • Kelvin scale (K) • K = °C + 273.15 • Absolute temperature

  8. Metric units • Volume (derived unit in SI) • liter (l or L) is the base unit • 1 l = 1 dm3 = 1.06 qt • 1 ml = 1 cm3 = 1 cc • 1 m3

  9. Metric units • Density • mass/volume • g/ml or g/cc (liquids) • g/ cm3 (solids) • Density of liquid water is 1.0 g/ml • Density often confused with weight

  10. Uncertainty in Measurement • Measurements are inexact • Two terms dealing with uncertainty: • accuracy • correctness • precision • grouping

  11. Significant Figures • Expression of uncertainty • How do we know how uncertain a value is? • What is the difference between • 1 m and 1.00 m? • 25 ml and 25.00 ml? • 34 °C and 34.0 °C

  12. Rounding • Method 1 • < 5 rounds down (1.2 -> 1) • ≥ 5 rounds up (1.5 -> 2) • Method 2 • < 5 rounds down (1.2 -> 1) • > 5 rounds up (1.5 -> 2) • 5 rounds to nearest even number • 1.5 -> 2 • 2.5 -> 2

  13. Significant Figures • Nonzero digits are always significant • Zeros between nonzero digits are always significant • Zeros to the right of the decimal and to the right of a nonzero digit are always significant • Exact numbers have infinite significant digits (e.g., there are exactly 100 cm in 1 m)

  14. Significant Figures • What if we want to measure something that is 100 m ±1 m? • Three ways • 100. m • 100 m • 1.00 x 102 m (Scientific notation)

  15. Significant Figures in Calculations • Multiplication/Division • keep least number of significant figures • 2.5 x 3.76 x 4.986 = 46.8684 -> 47 • Addition/Subtraction • round to least precise value

  16. Dimensional Analysis • By carrying units all the way through the calculation, and cancelling where appropriate, we can more easily solve scientific problems • Consider the relationship 1 cm = 2.54 in

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