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Accuracy, Dimensional Analysis

numerical uncertainty - measurements are ALWAYS inexact  

  • precision - how closely measurements agree w/ each other
  • accuracy - how closely measurements agree w/ the right answer
  • precision doesn't lead to accuracy
  • trials are done to get a better accuracy

significant figures - all digits of a quantity, including an uncertain one  

  • measured quantities are reported so that the last digit is uncertain
  • more significant figures means more certainty in the measurement
  • all non-zero digits are significant
    • 3456 - 4 significant figures
    • 3.13245 - 6 significant figures
    • 22 - 2 significant figures
  • zeros between non-zero digits are significant
    • 34000005 - 8 significant digits
    • 345.0003 - 7 significant digits
    • 60.7 - 3 significant digits
  • zeros at the beginning of the number aren't significant
    • 0.00000000006 - 1 significant digit
    • 0000234 - 3 significan digits
    • 0.0005042 - 4 signifcant digits
  • zeros at the end of the number are significant
    • 34000. - 5 significant digits
    • 34.00 - 4 significant digits
    • 5.01000 - 6 significant digits
  • zeros at the end of numbers w/o a decimal point may or may not be significant
    • 450 - 2 or 3 significant digits
    • 3000 - 1, 2, 3, or 4 significant digits
  • w/ multiplication/division, the result should have the same number of significant figures as the number w/ the least significant figures
  • w/ addition/subtraction, result can't have more decimal places than the number w/ the least number of decimal places

dimensional analysis - guarantees that the result has the proper units  

  • conversion factor - fraction where the numerator/denominator are the same quantity in different units
  • given unit x desired unit / given unit = desired unit
  • multiple conversion factors can also be used
  • derived SI units may require multiple conversion factors to get the desired unit
  • Convert 0.076L to mL
    • 0.076L x 1000mL / 1L = 76 mL
  • Convert 1.55kg/m3 to g/L
    • 1.55kg / 1m3 x 1m3 / 1000dm3 = 0.00155 kg/dm3
    • 0.00155kg / 1dm3 x 1000g / 1kg = 1.55g/dm3
    • 1.55g / 1dm3 x 1dm3 / 1L = 1.55 g/L
Subject: 
Chemistry
Subject X2: 
Chemistry

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