General Chemistry Fundamentals: Significant Figures, Scientific Notation, Classification of Matter, and Metric Conversions

Significant Figures and Calculations

Understanding Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They are crucial in reporting the precision of calculated results in chemistry.

• Definition: Significant figures reflect the precision of a measured or calculated quantity.

• Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros in a decimal number are significant.

• Calculations:

  • For multiplication/division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

  • For addition/subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Example: $\frac{4.386 \times 0.045}{2.80} = 0.070$ (2 significant figures)

Scientific Notation and Exponential Form

Expressing Numbers in Scientific Notation

Scientific notation is a way to express very large or very small numbers using powers of ten. It is commonly used in chemistry to simplify calculations and express measurements.

• Format: $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.

• Examples:

  • 5765 = $5.765 \times 10^3$

  • 0.000365 = $3.65 \times 10^{-4}$

  • 602,000,000,000 = $6.02 \times 10^{11}$

  • 0.00000240 = $2.40 \times 10^{-6}$

Converting Scientific Notation to Ordinary Numbers

To convert from scientific notation to ordinary numbers, multiply the coefficient by ten raised to the indicated power.

• Examples:

  • $6.75 \times 10^5 = 675,000$

  • $4.66 \times 10^{-4} = 0.000466$

  • $2.20 \times 10^3 = 2200$

  • $1.11 \times 10^{-2} = 0.011$

  • $2.3 \times 10^5 = 230,000$

Classification of Matter

Pure Substances vs. Mixtures

Matter can be classified as pure substances or mixtures. Mixtures can be further categorized as homogeneous or heterogeneous.

• Pure Substance: Matter with a fixed composition and distinct properties (e.g., elements, compounds).

• Mixture: A combination of two or more substances where each retains its own identity.

  • Homogeneous Mixture: Uniform composition throughout (e.g., gasoline).

  • Heterogeneous Mixture: Non-uniform composition (e.g., concrete, vegetable soup).

Sample	Classification
Concrete	Mixture, heterogeneous
Iodine crystals	Pure substance
Gasoline	Mixture, homogeneous
White chocolate macadamia nut cookies	Mixture, heterogeneous
Vegetable soup	Mixture, heterogeneous
Aluminum metal	Pure substance

Metric System and Unit Conversions

Performing Metric Conversions

The metric system is a decimal-based system of measurement used in science. Converting between units involves multiplying or dividing by powers of ten.

• Common Prefixes:

  • kilo- ($10^3$)

  • centi- ($10^{-2}$)

  • milli- ($10^{-3}$)

  • micro- ($10^{-6}$)

• Examples:

  • 65 cm = $0.65$ m

  • 9535 m = $9.535$ km

  • 79 g = $0.079$ kg

  • 0.00478 L = $4.78$ mL

Additional Practice: Significant Figures in Measurements

Counting Significant Figures

Determining the number of significant figures in a measurement is essential for proper reporting of data.

Measurement	Significant Figures
20.03 kg	4
1.90 x 104 L	3
120 M	2
0.00067 cm2	2
0.0580 in	3
35,500 people	3 (Additional info: If trailing zeros are not significant, otherwise 5)

Example Problem: Mass Conversion

Converting Mass of Aspirin

To convert the mass of aspirin from grams to pounds, use the conversion factor $1 \text{ lb} = 453.6 \text{ g}$.

• Given: 0.324 g of aspirin per tablet, 500 tablets.

• Total mass: $0.324 \text{ g} \times 500 = 162 \text{ g}$

• Convert to pounds: $\frac{162 \text{ g}}{453.6 \text{ g/lb}} = 0.357 \text{ lb}$

Example: A bottle containing 500 tablets of aspirin (0.324 g each) contains approximately 0.357 lb of aspirin.