Significant Figures Rules and Calculations

Overview

This lecture reviews the rules for identifying significant figures (sig figs) in numbers and their application in calculations, including multiplication, division, addition, and subtraction.

Identifying Significant Figures

• Every non-zero digit counts as a significant figure.
• Zeros between non-zero digits are significant (e.g., 704 has 3 sig figs).
• Trailing zeros (zeros to the right) are significant only if there is a decimal point (e.g., 500 vs. 500.0).
• Leading zeros (zeros before non-zero digits) are not significant (e.g., 0.075 has 2 sig figs).
• Zeros in between non-zero digits are always counted as significant.

Examples of Counting Significant Figures

• 846 → 3 sig figs
• 3546 → 4 sig figs
• 704 → 3 sig figs
• 5006 → 4 sig figs
• 500 (no decimal) → 1 sig fig
• 500. → 3 sig figs
• 500.0 → 4 sig figs
• 0.075 → 2 sig figs
• 0.00836 → 3 sig figs
• 0.0050830 → 5 sig figs

Practice Quiz Review

• 42.50 → 4 sig figs
• 7080 → 3 sig figs
• 1050. → 4 sig figs
• 0.00703 → 3 sig figs
• 0.08060 → 4 sig figs
• 5030.0 → 5 sig figs
• 750.064080 → 9 sig figs

Rounding in Calculations: Multiplication and Division

• Final answer should have as many sig figs as the input with the fewest sig figs.
• Example: 4.6 × 3.52 = 16.192 → rounded to 16 (2 sig figs).
• Example: 5.64 × 12.458 = 70.3 (3 sig figs).
• Example: 96.752 ÷ 3.541 = 27.32 (4 sig figs).

Rounding in Addition and Subtraction

• Final answer should have as many decimal places as the number with the least decimal places.
• Example: 2.36 + 12.1 = 14.46 → rounded to 14.5 (1 decimal place).
• Example: 4.328 + 13 + 5.45 = 22.778 → rounded to 23 (no decimal places).

Key Terms & Definitions

• Significant Figure (Sig Fig) — a digit in a number that contributes to its precision.
• Trailing Zeros — zeros to the right of a non-zero digit; only significant with a decimal point.
• Leading Zeros — zeros to the left of all non-zero digits; not significant.
• Rounding (Sig Figs) — adjusting the result of a calculation to reflect the correct number of significant figures.

Action Items / Next Steps

• Practice identifying and rounding significant figures in sample problems.
• Review additional examples in the suggested detailed video if needed.