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Significant Figures and Rounding Rules

Oct 3, 2025

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Overview

This lecture reviews the rules for determining significant figures (sig figs), how to round answers based on them, and applies these concepts to multiplication, division, addition, and subtraction.

Counting Significant Figures

  • Every nonzero digit is significant.
  • Zeros between nonzero digits (captive zeros) are significant.
  • Trailing zeros (to the right of nonzero digits) are only significant if there is a decimal point.
  • Leading zeros (before nonzero digits) are never significant.

Examples & Practice

  • 846: 3 sig figs; 3546: 4 sig figs.
  • 704: 3 sig figs; 5006: 4 sig figs.
  • 500 (no decimal): 1 sig fig.
    1. (decimal present): 3 sig figs; 500.0: 4 sig figs.
  • 0.075: 2 sig figs; 0.00836: 3 sig figs.
  • 0.0050830: 5 sig figs (trailing zero counts due to decimal).

Quiz Review

  • 42.50: 4 sig figs.
  • 7080 (no decimal): 3 sig figs.
    1. (with decimal): 4 sig figs.
  • 0.00703: 3 sig figs.
  • 0.08060: 4 sig figs.
  • 5030.0: 5 sig figs.
  • 750.064080: 9 sig figs.

Rounding with Multiplication & Division

  • Round the answer to the least number of sig figs found in any input value.
  • Example: 4.6 × 3.52 = 16.192 → 16 (2 sig figs).
  • Example: 5.64 × 12.458 = 70.26312 → 70.3 (3 sig figs).
  • Example: 96.752 ÷ 3.541 = 27.32335498 → 27.32 (4 sig figs).

Rounding with Addition & Subtraction

  • Round the answer to the least number of decimal places found in the numbers being added or subtracted.
  • Example: 2.36 + 12.1 = 14.46 → 14.5 (rounded to one decimal place).
  • Example: 4.328 + 13 + 5.45 = 22.778 → 23 (rounded to the nearest whole number).

Key Terms & Definitions

  • Significant Figures (Sig Figs) — Digits in a number that carry meaning about its precision.
  • Leading Zeros — Zeros before the first nonzero digit; not significant.
  • Trailing Zeros — Zeros after nonzero digits; significant only if a decimal is present.
  • Captive Zeros — Zeros between nonzero digits; always significant.

Action Items / Next Steps

  • Practice counting sig figs and rounding calculations in homework problems.
  • Watch the extended YouTube video for more challenging examples.
  • Review additional practice problems as assigned or suggested.

Full transcript