A Guide to Using Significant Figures in Measurement

Understanding Significant Figures

Significant figures, or significant digits, are the digits in a number that carry meaningful information about its precision. The rules for determining significant figures help us convey the accuracy of our measurements. In this guide, we will explore the basic rules, calculations, and practical examples to clarify the concept.

Rules for Identifying Significant Figures

1. Non-zero digits are always significant.

   • Example: In 123.45, all five digits are significant.

2. Leading zeros (zeros before the first non-zero digit) are not significant.

   • Example: In 0.0045, only the 4 and 5 are significant (2 significant figures).

3. Captive zeros (zeros between non-zero digits) are always significant.

   • Example: In 1002, all four digits are significant.

4. Trailing zeros in a number without a decimal point are not significant.

   • Example: In 1500, only the 1 and 5 are significant (2 significant figures). In contrast, in 1500.0, all five digits are significant.

5. Trailing zeros in a number with a decimal point are significant.

   • Example: In 2.300, all four digits are significant.

Examples of Measurements and Significant Figures

• Example 1: Measurement of Length
  A ruler measures a length of 12.30 cm.

  • Significant Figures: 4 (1, 2, 3, and the trailing 0)

• Example 2: Measurement of Mass
  A balance reads 0.00560 g.

  • Significant Figures: 3 (5, 6, and the trailing 0)

• Example 3: Measurement of Volume
  A graduated cylinder shows 45.0 mL.

  • Significant Figures: 3 (4, 5, and the trailing 0)

Calculations Involving Significant Figures

When performing calculations, the results should reflect the precision of the measurements involved. Follow these rules:

• Multiplication and Division: The result should have the same number of significant figures as the measurement with the least significant figures.

  • Example: 3.24 (3 sig figs) × 2.1 (2 sig figs) = 6.804 → Rounded to 6.8 (2 sig figs).

• Addition and Subtraction: The result should have the same number of decimal places as the measurement with the least decimal places.

  • Example: 12.11 (2 decimal places) + 0.3 (1 decimal place) = 12.41 → Rounded to 12.4 (1 decimal place).

Practical Application

Understanding significant figures is vital in scientific measurements and reporting. For instance, in a chemistry experiment, if you accurately measure a liquid’s volume as 25.4 mL, reporting it with fewer significant figures would misrepresent the precision of your measurement.

Conclusion

Mastering significant figures is essential for accurate communication in science and mathematics. By applying the rules outlined in this guide, you can confidently report measurements and calculations while maintaining the integrity of your data.