Measurement Uncertainty, Accuracy, and Precision - Intro to Chemistry Study Guide 2024 | Fiveable (2024)

Measurement and are crucial in chemistry. measures closeness to true values, while reflects consistency in repeated measurements. Understanding these concepts helps interpret data reliability and experimental results.

, rules, and error analysis are essential tools for managing uncertainty. These techniques ensure meaningful data interpretation, allowing chemists to communicate results effectively and make informed decisions based on experimental outcomes.

Measurement and Uncertainty

Accuracy vs precision in measurements

  • Accuracy measures how close a result is to the true or accepted value
    • High accuracy indicates the measured value is very close to the true value (bullseye on a dartboard)
    • Low accuracy means the measured value differs significantly from the true value (off-center hits on a dartboard)
  • Precision describes how close multiple measurements are to each other, regardless of their accuracy
    • High precision means the measurements are tightly clustered, even if they are not centered around the true value (tightly grouped darts, but not necessarily in the bullseye)
    • Low precision indicates the measurements are widely dispersed, even if their average is close to the true value (scattered darts across the board)
  • Measurements can be categorized as:
    • Accurate and precise: close to the true value and tightly clustered (bullseye with tightly grouped darts)
    • Accurate but imprecise: close to the true value but widely dispersed (darts centered around the bullseye but scattered)
    • Precise but inaccurate: tightly clustered but far from the true value (tightly grouped darts off-center)
    • Neither accurate nor precise: far from the true value and widely dispersed (scattered darts off-center)

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      Exact vs uncertain chemical data

      • Exact numbers have no uncertainty and are not subject to significant figure rules
        • Counted values (5 molecules)
        • Defined values (1 kg = 1000 g)
        • Integers in chemical formulas (H2SO4)
      • Uncertain measurements have inherent uncertainty and follow significant figure rules
        • Measured values (5.3 g, 10.2 mL)
        • Calculated values derived from measured values (density = mass ÷ volume)

      Significant figures for uncertainty

      • Significant figures represent the number of certain digits plus one uncertain digit in a measurement
        • Non-zero digits are always significant (1, 2, 3, ..., 9)
        • Zeros between non-zero digits are significant (1.0023)
        • Leading zeros are not significant (0.0012 has two significant figures)
        • Trailing zeros are significant only with a decimal point (1.200 has four significant figures, 1200 has two)
      • When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures
        • 5.2×3.10=16.125.2 \times 3.10 = 16.125.2×3.10=16.12, rounded to 16 (two significant figures)
      • When adding or subtracting, the result should have the same number of decimal places as the measurement with the fewest decimal places
        • 5.2+3.10=8.305.2 + 3.10 = 8.305.2+3.10=8.30, rounded to 8.3 (one decimal place)

      Rounding rules in calculations

      • If the digit to the right of the last significant figure is less than 5, round down (12.44 rounds to 12.4)
      • If the digit to the right of the last significant figure is 5 or greater, round up (12.45 rounds to 12.5)
      • If the digit to the right of the last significant figure is 5 followed by zeros:
        1. Round up if the last significant figure is odd (12.350 rounds to 12.4)
        2. Round down if the last significant figure is even (12.450 rounds to 12.4)

      Sources of Error and Statistical Analysis

      • Systematic error: consistent deviation from the true value due to flaws in equipment or methodology (e.g., uncalibrated instruments)
      • Random error: unpredictable fluctuations in measurements due to limitations in precision (e.g., human reaction time)
      • Standard deviation: a measure of the spread of data points around the mean, indicating precision
      • Confidence interval: a range of values that likely contains the true value, based on the standard deviation
      • Calibration: the process of adjusting instruments to reduce systematic errors and improve accuracy
      • Error propagation: the way uncertainties in individual measurements combine to affect the uncertainty of a final calculated result

      Key Terms to Review (7)

      Accuracy: Accuracy refers to how close a measured value is to the true or accepted value. It indicates the correctness of a measurement.

      Exact number: An exact number is a value that is known with complete certainty, often through counting or defined quantities. Exact numbers have an infinite number of significant figures and do not contribute to measurement uncertainty.

      Precision: Precision refers to the consistency of a set of measurements or results. It indicates how close the measurements are to each other, regardless of their accuracy.

      Rounding: Rounding is a mathematical technique used to reduce the number of significant digits in a number while keeping its value close to the original. In scientific measurements, rounding helps in reporting values with appropriate precision.

      Significant digits: Significant digits (or significant figures) represent the meaningful digits in a measured or calculated quantity, reflecting its precision. They indicate the accuracy of a number by showing which digits are known reliably.

      Significant figures: Significant figures are the digits in a measurement that carry meaningful information about its precision. They include all certain digits plus one uncertain or estimated digit.

      Uncertainty: Uncertainty in measurements is the range within which the true value is expected to lie. It reflects the limitations of measurement instruments and methods.

      Measurement Uncertainty, Accuracy, and Precision - Intro to Chemistry Study Guide 2024 | Fiveable (2024)
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