Significant Figures

Introduction to Significant Figures

  • Significant figures are crucial for determining the precision of measurements.

Determining Significant Figures

  • Non-zero digits: Always significant.

    • Example: 846 has 3 significant figures.

  • Leading zeros: Never significant.

    • Example: 0.075 has 2 significant figures (the 7 and the 5).

  • Zeros between non-zero digits: Always significant.

    • Example: 704 has 3 significant figures; 5,006 has 4 significant figures.

  • Trailing zeros: Depends on the presence of a decimal point.

    • 500 (no decimal) has 1 significant figure.

    • 500.0 (with decimal) has 4 significant figures.

      1. has also 3 significant figures.

  • Complex examples: Evaluate zeros based on position and decimal points.

    • Example: 0.0050830 has 5 significant figures.

Practice Questions

  • Determine significant figures for the following numbers:

    1. 4250: 3 significant figures (0 not counted; no decimal)

    2. 7,080: 3 significant figures (0 on the right not counted; no decimal)

    3. 30,050: 5 significant figures (trailing zeros counted because of decimal)

    4. 0.00703: 3 significant figures (leading zeros not counted)

    5. 0.08060: 4 significant figures (the trailing zero counted due to decimal)

    6. 5,030.0: 5 significant figures (decimals make trailing zero significant)

    7. 750.064080: 9 significant figures (all zeros significant due to decimal)

Rounding with Significant Figures

  • When multiplying/dividing, the final answer should have the same number of significant figures as the measurement with the least significant figures.

  • Example Calculation: 4.6 (2 sig figs) × 3.52 (3 sig figs) = 16.192; round to 2 sig figs.

    • Rounded answer: 16 (as last digit 6 is rounded down).

Additional Problems for Practice

  • Multiply: 5.64 × 12.458; round based on significant figures.

  • Divide: 96.752 ÷ 3.541; also round based on significant figures.