Maths calculations

  • Objective: Recap fundamental math concepts relevant to the course.

  • Key Topics:

    • Rearranging formulas.

    • SI units.

    • Calculating uncertainty from experimental results.

    • Upcoming: Mole calculations and percentage yield (to be covered in two classes).

Rearranging Formulas

  • Comfort level with rearranging formulas varies among students.

  • Important skills:

    • Line multiplication, division, addition, and subtraction.

    • Remember terms: Numerator (top) and Denominator (bottom).

Mathematical Operations

  • Multiplications:

    • Two positive numbers yield a positive result.

    • Positive multiplied by negative gives a negative result.

    • Two negatives produce a positive.

  • Division Concepts:

    • Recall terminology (Numerator and Denominator).

Percentages and Ratios

  • A percentage is a fraction where the denominator is 100100.

  • Example: calculate percentage of daily intake from yogurt:

    • Yogurt energy: 695695 kilojoules, daily intake: 87008700 kilojoules.

    • Calculation: 6958700×100=8\frac{695}{8700}\times 100 = 8% of daily intake.

Algebra Techniques

Triangle Method for Rearranging Formulas

  • Useful when working with moles:

    • b=a×cb = a \times c

    • Rearranging involves basic algebra principles.

  • Example of rearrangement:

    • To find cc: If aa = bc\frac{b}{c}, multiply by cc to isolate and solve for cc.

Graphing Data

  • When graphing, identify X and Y axes:

    • Independent variable on X, dependent variable on Y.

  • Importance of linear relationships in graphs for predictions (e.g., temperature vs. volume).

Scientific Notation

  • Large numbers expressed in scientific notation simplify calculations:

    • Example: 12301230 -> 1.23×1031.23 \times 10^{3}

  • Key concept: Moving decimal to the left for negative exponents.

Conversion Factors

  • Converting between units:

    • Example: Convert micrometers to millimeters by understanding their relative sizes (10−310^{-3}).

  • Formula to convert: Value in millimeters=Value in micrometers1000\text{Value in millimeters} = \frac{\text{Value in micrometers}}{1000}

SI Units

  • Fundamental SI Units: Meter (length), Kilogram (mass), Second (time), Kelvin (temperature), Mole (amount of substance).

  • Consistent unit conversions are key in calculations (e.g., area = length x width).

Density Formula

  • Density defined as: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

  • Multiple units can represent density: kg/m³, g/cm³, or g/mL.

Upcoming Topics

  • Focus on uncertainty calculations.

  • Mole and percentage yield will be emphasized in the following classes.

Closing Remarks

  • Encourage questions and clarification on material covered.

  • Reminder to engage in practice problems during the next session.