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

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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

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