R

1.2: error and uncertainty

numbers and chemistry

  • important number-related concepts in science
  • units of measurement
  • measurements vs. calculations
  • significant figures
  • dimensional analysis
  • accuracy and precision
  • accuracy: how close a measurement is to the real or accepted value of a quantity
    • correctness
  • precision: the proximity of several measurements to each other
    • reproducability

measurement

  • when we measure in science, we compare a physical quantity that we are interested in understanding to a known physical quantity
  • two issues must be confronted when measuring:
  • possibility of error
  • unavoidable uncertainty
  • error: the difference between a measurement and the actual or accepted value for the measurement
    • percent error = |[(measured value - accepted value)/accepted value] x 100|
    • uncertainty in measurement
  • different instruments of measurement have different degrees of precision and uncertainty
  • all measured numbers have some degree of inaccuracy
  • sources of measurement error
  • systematic error: unavoidable error
    • errors that consistently cause measurement values to be too large or too small
    • can be caused by faulty equipment
    • eg. mis-calibrated balances, inaccurate meter sticks
  • human error: avoidable error
    • can occur when equipment is used incorrectly
    • eg. reading from the wrong end of a meter stick, converting units incorrectly
  • random error: uncertainty—expected and unavoidable
    • when variations in the measurements occur without a predictable pattern
    • if repeated measurements are made, random error causes the measured value to vary, sometimes above or below the actual measured value
    • causes uncertainty in measurements
    • addressed by averaging measurements
    • can be minimized but not avoided entirely
  • measurements are inexact (uncertain)
  • measurements are inexact because scientific instruments have limitations
  • always a degree of uncertainty
  • some balances measure to ±0.01g and others to 0.0001g
  • exact numbers
  • counted
    • eg. there are exactly 13 donuts in the bakery box
  • are given as a definition (ie. conversion factors)
    • eg. there are 2.54cm in 1 inch