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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

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