1.3: significant figures in measurements

significant figures

  • significant figures: the digits in a measurement that were actually measured
  • all known numbers + one estimated number
  • communicate the uncertainty of a measurement
  • reflect the precision of the instrument with which a measurement is made

determining which digits are significant

  • all non-zero digits   * eg. 1245 (4 significant figures)   * 2.3 (2 significant figures)
  • all captive zeros (zeros between non-zero digits)   * 2021 (4 significant figures)   * 5000.1 (5 significant figures)
  • leading zeros are never significant   * 0.0012 (2 significant figures) → placeholders
  • zeros at the end of a number (trailing zeros) are   * not significant if there is no decimal point in the number:   * 230 (2 significant figures)   * 7000 (1 significant figure)
  • significant if there is a decimal point in the number   * 3.230 (4 significant figures)   * 7.0 (2 significant figures)

scientific notation

  • used to describe very large or very small numbers because   * it’s time-consuming to read/write   * easy to lose track of zeros and mess up
  • numbers are expressed with   * one digit to the left of the decimal, multiplied by a power of ten     * eg. 4.59x10^5     * 4.59 is the significand, 10 is the base, and 5 is the exponent.   * if x > 1, the exponent is positive, and if x < 1, the exponent is negative
  • scientific notation and significant figures   * significand determines number of significant figures     * eg. 4.590 x 10^5 => 5 sigfigs (4.590)
  • significant figures in calculations   * addition/subtraction—answer is rounded to the smallest significant decimal place   * multiplication/division—answer is rounded to the number of digits that corresponds with the least number of significant figures in any of the numbers used in the calculation

dimensional analysis

  • used to convert a measurement from one unit to another using conversion factors   * conversion factor: a ratio of equivalent measures (numerator = denominator)
  • when a measurement is multiplied by a conversion factor, the expression of measurement changes (because the units change) but the actual quantity measured remains the same

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