Overview
This lecture covers solving mixed operation problems in chemistry, emphasizing correct order of operations and the rules for significant figures (sig figs).
Order of Operations in Mixed Problems
- Always follow order of operations: parentheses, then multiplication/division, then addition/subtraction.
- Perform addition or subtraction steps first if they are within parentheses.
Significant Figures Rules
- Track significant figures (sig figs) at each step of multi-operation problems.
- For addition/subtraction, limit the answer to the least precise decimal place.
- For multiplication/division, limit the answer to the smallest number of sig figs from the inputs.
Common Traps in Exams
- Exams often try to trick students with mixed operations and incorrect sig fig choices.
- Do not round your intermediate results; only round the final answer.
- Carry insignificant digits as subscript or notation until the last calculation.
Example Problem Steps
- Convert all numbers to the same exponent when adding/subtracting numbers in scientific notation.
- Example: 9.6 × 10⁷ + 7.4 × 10⁶ → convert both to ×10⁷; answer is 1.03 × 10⁸ (3 sig figs).
- Use the addition result (with correct precision) for subsequent multiplication/division.
- Example: 3.45 × 1.03 × 10⁸ ÷ 8.348 × 10³ = 4.27 × 10⁴ (3 sig figs).
Practice Example Walkthrough
- When subtracting numbers of different magnitudes, adjust to the higher power and write zeros as needed.
- Track and correctly assign sig figs based on the last shared decimal place.
- Multiply/divide using results from previous steps and round only at the final answer.
Key Terms & Definitions
- Order of Operations — The sequence in which mathematical operations are performed: parentheses, exponents, multiplication/division, addition/subtraction.
- Significant Figures (Sig Figs) — Digits in a number that express its precision; rules differ for addition/subtraction and multiplication/division.
- Scientific Notation — Expressing numbers as a product of a coefficient and a power of ten for clarity and precision.
Action Items / Next Steps
- Practice similar mixed operation problems, focusing on sig fig rules.
- Review examples in your textbook or provided worksheets.
- Be prepared for further examples in the next lecture.