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