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

\