Intro

Units of Measure

• Standard systems of units:
  • English system (e.g. feet, pounds, quarts)
  • Metric system (e.g. meters, kilograms, liters)
• SI system (the international system) for scientific units of measurement.
  • International agreement based on the metric system.
• Fundamental SI units:
  • Mass: kilogram (kg)
  • Length: meter (m)
  • Time: second (s)
  • Temperature: kelvin (K)
  • Electric current: ampere (A)
  • Amount of substance: mole (mol)
  • Luminous intensity: candela (cd)
• Volume (not a fundamental SI unit): derived from length.
  • $1~cm^3 = 1~mL$, $1~dm^3=1~L$
• Metric prefixes (to change the size of a unit):
  • kilo (k) = $10^3$
  • hecto (h) = $10^2$
  • deka (da) = $10^1$
  • BASE (-) = $10^0$
  • deci (d) = $10^{-1}$
  • centi (c) = $10^{-2}$
  • milli (m) = $10^{-3}$
  • micro ($\mu$) = $10^{-6}$
  • nano (n) = $10^{-9}$

Making Measurements

• Measurement: quantitative observation that always consists of a number and scale (unit).
• Analog measurements: guess once; record all certain digits (markings on device) and the first uncertain/estimated digit.
  • More precise measuring device = more certain digits.
  • Volume: record from the bottom of the meniscus of a graduated cylinder, pipette, buret, volumetric flask, etc.
• Digit measurements: record given value (all digits).
  • Mass: use chemical balance (weighing on a chemical balance involves comparing the mass of an object to a standard mass).
    • Mass vs. weight:
      • Mass: measure of the resistance an object to change in its state of motion; force necessary to give an object acceleration (use the force that gravity exerts on an object to measure mass).
      • Weight: force that gravity exerts on an object; response of mass to gravity, varies with the strength of the gravitational field.

Uncertainty in Measurement

• A measurement always has some degree of uncertainty that depends on the precision of the measuring device.
• A conclusion based on a series of measurement depends on the certainty of the measurements (uncertainty needs to be indicated by significant figures).
• Reliability of measurements:
  • Accuracy: agreement of a particular value with the true value.
  • Precision: degree of agreement among several measurements of the same quantity, reflects the reproducibility of a given type of measurement.
• Types of errors:
  • Random error (indeterminate error): measurement has an equal probability of being too high or too low, occurs in estimating the value of the uncertain digit (last digit).
    • Could be caused by poor technique, imprecise measuring device, etc.
    • Average a series of precise measurements to average out random errors and get to the true value (random errors have an equal probability of being too high or too low → error minimized).
  • Systematic error (determinate error): occurs in the same direction each time (either always too high or always too low)
    • Could be caused by poor technique (e.g. always measuring to the top of the meniscus), problem with measuring device (e.g. reads 1.0 kg too high), etc.
    • Averaging a series of precise measurements does not remove systematic errors.
    • High precision $\neq$ accuracy if systematic errors are present.

Significant Figures

<aside> 🧪 Significant figures indicate the uncertainty of a measurement.

</aside>

• Significant figures of a measurement are all certain digits and the first uncertain (estimated) digit.
  • The last number (estimated number) usually has a certainty of $\pm1$ (e.g. 1.86 kg is $1.86\pm1$ kg → it could be 1.85 kg or 1.87 kg; 25 mL is between 24 mL and 26 mL, more precise 25.00 mL is between 24.99 mL and 25.01 mL).