Significant Figures Rules and Examples

Overview

This lecture reviews the rules for identifying and using significant figures in measurements and calculations, including how to round results in multiplication, division, addition, and subtraction.

Counting Significant Figures

• All non-zero digits are significant.
• Zeros between non-zero digits (captive zeros) are always significant.
• Trailing zeros (right of a non-zero digit) are significant only if there is a decimal point.
• Leading zeros (to the left of the first non-zero digit) are never significant.

Examples of Significant Figures

• 846 has 3 significant figures.
• 3546 has 4 significant figures.
• 704 has 3 significant figures.
• 500 has 1 significant figure (no decimal point).
• 500. has 3 significant figures (decimal point present).
• 500.0 has 4 significant figures.
• 0.075 has 2 significant figures (only the 7 and 5).
• 0.00836 has 3 significant figures.
• 0.0050830 has 5 significant figures (trailing zero is significant due to decimal).

Practice Quiz Review

• 42.50 — 4 significant figures.
• 7080 — 3 significant figures (no decimal).
• 1050. — 4 significant figures (decimal present).
• 0.00703 — 3 significant figures.
• 0.08060 — 4 significant figures.
• 5030.0 — 5 significant figures.
• 750.064080 — 9 significant figures.

Rounding in Multiplication and Division

• When multiplying or dividing, round the final answer to the least number of significant figures in any original number.
• 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 and Subtraction

• When adding or subtracting, round the final answer to the least number of decimal places in any original number.
• Example: 2.36 + 12.1 = 14.46; round to 1 decimal place → 14.5.
• Example: 4.328 + 13 + 5.45 = 22.778; round to no decimal places → 23.

Key Terms & Definitions

• Significant Figures (Sig Figs) — Digits in a number that contribute to its measurement precision.
• Leading Zeros — Zeros before the first non-zero digit; not significant.
• Trailing Zeros — Zeros after the last non-zero digit; significant only with a decimal point.
• Captive Zeros — Zeros between non-zero digits; always significant.

Action Items / Next Steps

• Practice determining significant figures in different numbers.
• Review the longer video in the description for more challenging examples.
• Try additional problems involving rounding with significant figures.