General Chemistry Study Notes: Measurement, Precision, Metric Conversions, and Significant Figures

1. Data Quality in Measurements: Accuracy vs. Precision

• Accuracy: Refers to how close a measured value is to the true or accepted value.
• Precision: Refers to how close a series of measurements are to each other.
• Archery Analogy:
  • Accurate and Precise: Arrows are tightly clustered together in the center target. This is the ideal goal in scientific measurements.
  • Precise but Not Accurate: Arrows are clustered tightly together, but located away from the center.
  • Accurate but Not Precise: Arrows are scattered around the center, close to the target on average, but not clustered together.
  • Neither Accurate nor Precise: Arrows are scattered randomly away from the center.

2. Systems of Measurement

• Unit: A standardized system used to label measurements, defining quantities such as mass, length, or volume.
• Imperial System: Used primarily in the United States (e.g., inches, feet, miles, pounds, gallons, ounces).
• Metric System: Used universally in scientific research and by most countries worldwide. It is structured around multiples of $10$.

3. Metric Conversions and Base Units

• The metric system uses prefixes applied to base units (such as grams or meters):

  • Larger Units (greater than $1$ base unit):
  • Mega ($\text{M}$): $1 imes 10^6$ base units ($1,000,000$
  • Kilo ($\text{k}$): $1 imes 10^3$ base units ($1,000$
  • Smaller Units (less than $1$ base unit):
  • Centi ($\text{c}$): $10^{-2}$ base units ($0.01$
  • Milli ($\text{m}$): $10^{-3}$ base units ($0.001$
  • Micro ($\mu$): $10^{-6}$ base units
  • Nano ($\text{n}$): $10^{-9}$ base units

• Key equivalencies to remember:

  • $1\,\text{kilo-} = 1000\,\text{base units}$
  • $1\,\text{base unit} = 100\,\text{centi-}$
  • $1\,\text{base unit} = 1000\,\text{milli-}$
  • $1\,\text{base unit} = 10^6\,\text{micro-}$
  • $1\,\text{base unit} = 10^9\,\text{nano-}$

4. Dimensional Analysis

• Conversion Factor: An equality expressed as a fractional ratio used to convert between different units (e.g., $\frac{1\,\text{m}}{1000\,\text{mm}}$ or $\frac{1000\,\text{mm}}{1\,\text{m}}$).

• Process:

  1. Identify the given value and target unit.
  2. Set up conversion factors so that unwanted units appear in opposite positions (numerator vs. denominator) to cancel out.
  3. Perform calculations and verify the final unit.

• Example: Imperial to Metric Conversion:

  • Convert $5.80\,\text{ft}$ to meters using $1\,\text{ft} = 12\,\text{in}$, $1\,\text{in} = 2.54\,\text{cm}$, and $1\,\text{m} = 100\,\text{cm}$:
    $5.80\,\text{ft} imes \frac{12\,\text{in}}{1\,\text{ft}} imes \frac{2.54\,\text{cm}}{1\,\text{in}} imes \frac{1\,\text{m}}{100\,\text{cm}} = 1.76784\,\text{m}$

5. Rules for Significant Figures (Sig Figs)

Significant figures determine the meaningful digits in a measured value.

1. Non-zero digits: Always significant.
   • Example: $398$ has $3$ significant figures.
   • Example: $459.1$ has $4$ significant figures.
2. Sandwiched Zeros: Zeros located between two non-zero digits are significant.
   • Example: $101$ has $3$ significant figures.
3. Leading Zeros: Zeros at the beginning of a number are place holders and are NOT significant.
   • Example: $0.0015$ has $2$ significant figures.
4. Trailing Zeros with a Decimal: Zeros at the end of a number that contains a decimal point are significant.
   • Example: $25.20$ has $4$ significant figures.
5. Trailing Zeros without a Decimal: Zeros at the end of a whole number without a decimal point are NOT significant.
   • Example: $100$ has $1$ significant figure.
   • Exception: If written as $100.$ (with a trailing decimal point), all $3$ digits are significant.