Overview
This lecture reviews how to count significant figures, rules for identifying them in different types of numbers, and how to round answers properly during calculations involving significant figures.
Counting Significant Figures
- Non-zero digits are always significant (e.g., 846 has 3 significant figures).
- Zeros between non-zero digits are significant (e.g., 704 has 3; 5006 has 4).
- Trailing zeros (zeros to the right of a non-zero digit) are significant only if there is a decimal point (e.g., 500 = 1 sig fig, 500. = 3 sig figs, 500.0 = 4 sig figs).
- Leading zeros (zeros before the first non-zero digit) are never significant (e.g., 0.075 has 2 sig figs).
- In decimal numbers, trailing zeros are significant (e.g., 0.0050830 has 5 sig figs).
Practice Examples (Number of Significant Figures)
- 42.50 → 4 sig figs
- 7080 → 3 sig figs
- 1000.50 → 6 sig figs
- 0.00703 → 3 sig figs
- 0.08060 → 4 sig figs
- 5030.0 → 5 sig figs
- 750.064080 → 9 sig figs
Rounding in Multiplication & Division
- Multiply or divide as normal, then round the result to the same number of significant figures as the input with the least sig figs.
- Example: 4.6 × 3.52 = 16.192 → round to 2 sig figs → 16.
- Example: 5.64 × 12.458 = 70.26312 → round to 3 sig figs → 70.3.
- Example: 96.752 ÷ 3.541 = 27.32335498 → round to 4 sig figs → 27.32.
Rounding in Addition & Subtraction
- Add or subtract as normal, then round the result so it has the same number of decimal places as the number with the least decimal places in the original problem.
- Example: 2.36 + 12.1 = 14.46 → round to 1 decimal place → 14.5.
- Example: 4.328 + 13 + 5.45 = 22.778 → round to whole number → 23.
Key Terms & Definitions
- Significant Figures (Sig Figs) — The digits in a number that are meaningful in terms of accuracy.
- Trailing Zeros — Zeros to the right of the last non-zero digit; significant if a decimal point is present.
- Leading Zeros — Zeros before the first non-zero digit; never significant.
Action Items / Next Steps
- Practice determining significant figures in various numbers.
- Complete multiplication/division and addition/subtraction problems, rounding appropriately.
- For more challenging examples, watch the longer YouTube video linked in the description.