Chapter 1-7 Significant Figures Review Flashcards

Rules for Counting Significant Figures

  • Pacific / Atlantic Rule:
    • Present Decimal: Count from the Pacific (left) side starting at the first non-zero digit and count all remaining digits.
    • Absent Decimal: Count from the Atlantic (right) side starting at the first non-zero digit and count all remaining digits.
  • Overline / Bar Notation: A bar placed over a zero indicates that the zero is significant when a decimal point is absent; counting starts at the barred zero.
  • Decimal Indication: Adding an explicit decimal point at the end of a whole number (e.g., 2,500.2,500.) marks the decimal as present, requiring counting from the Pacific side.
  • Scientific Notation: Significant figures are determined solely by the coefficient (e.g., 5.00×1035.00 \times 10^{3} has 33 significant figures).

Exact Numbers and Placeholders

  • Placeholder Zeros: Non-significant zeros used strictly to maintain the magnitude of a number.
  • Exact Numbers: Possess infinite significant figures and do not limit precision in calculations. Examples include:
    • Counted objects (e.g., 10 molecules10\,\text{molecules}, 3 atoms3\,\text{atoms}).
    • Defined conversion values (e.g., 12 inches=1 foot12\,\text{inches} = 1\,\text{foot}, 5,208 feet=1 mile5,208\,\text{feet} = 1\,\text{mile}).
    • Exponential terms in scientific notation (e.g., 10310^{3}).
    • Sample sizes or replicate counts (nn) in average calculations.

Rules for Rounding

  • Standard Rounding:
    • Identify the target last significant digit and observe the adjacent digit to the right.
    • If the adjacent digit is less than 55, leave the last digit unchanged.
    • If the adjacent digit is greater than or equal to 55, round up the target digit.
  • Magnitude Preservation: Insert non-significant placeholder zeros when rounding whole numbers to avoid changing the number's magnitude (e.g., 11,18211,182 rounded to 44 significant figures is 11,18011,180).

Significant Figures in Basic Calculations

  • Multiplication and Division:
    • Round the final result to the least number of significant figures present in any input value.
  • Addition and Subtraction:
    • Round the final result to the least number of decimal places (least precise place value) present in any input value.

Combined Operations and Special Cases

  • Multi-Step Calculations:
    • Follow standard order of operations.
    • Retain extra intermediate digits throughout multi-step operations and round only once at the final step.
  • Percent Error:
    • Formula: Percent Error=∣Experimental−Accepted∣Accepted×100%\text{Percent Error} = \frac{|\text{Experimental} - \text{Accepted}|}{\text{Accepted}} \times 100\%
    • The subtraction in the numerator must be evaluated for decimal place precision before determining significant figures for division.
  • Mean (Average) Calculation:
    • Formula: Mean=∑xn\text{Mean} = \frac{\sum x}{n}
    • The replicate count nn has infinite significant figures.
    • The calculated mean must be rounded to match the same number of decimal places as the component measurements being averaged.