Uncertainty in Measurement

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Chapter 1.5

• Uncertainty in Measurement

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Exact Numbers

• Values that are known exactly
• Numbers obtained from counting
• The number 1 in conversions
• Exactly 2.54 cm in an inch

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Inexact Numbers

• Values with some uncertainty
• All numbers obtained by measurement
• Human error
• Equipment limitations
• Counting very large number of objects

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Precision

• Term used for describing uncertainties
• Measures how closely individual measurements
  agree with one another

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Accuracy

• Term used with uncertainties
• Measure of how closely individual measurements
  agree with the correct or true value

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A measurement can be precise while still being
inaccurate.
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Significant Figures

• Measured quantities are generally reported in
  such a way that only the last digit is uncertain.
• Think of a thermometer
• All digits, including the last one, are
  considered significant figures

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Rules for Sig Figs

• All nonzero digits are significant
• 678 has 3 sig figs
• Zeros between nonzero digits are significant
• 2034 has 4 sig figs
• Leading zeros are never significant
• 0.00006 has 1 sig fig
• Zeros at the end of a number are significant if
  the number contains a decimal point
• 0.003000 has 4 sig figs
• 980 has 2 sig figs

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Sig Figs in Calculations

• Least certain measurement limits certainty of
  final answer
• RULE 1 In multiplication and division- sig figs
  of the answer should be the same as the
  measurement with the fewest sig figs
• 6.221cm x 5.2cm 32.3492 cm2 32 cm2

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• RULE 2 For addition and subtraction- final
  answer has the same number of decimal places as
  the measurement with the fewest decimal places.
• 20.42 1.322 83.1 104.842 104.8

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Intermediate Answers

• Retain at least one additional digit past the sig
  figs.
• If using a calculator, enter numbers one after
  another