Significant Figures in Chemistry

Significant Figures

• Significant figures (sig figs) communicate the precision of measurements.
• They indicate how confidently others can rely on the exactness of your measurements and findings.

Identifying Significant Figures

• Non-zero digits: Always significant.
  • Example: In the number 45, both 4 and 5 are significant.
• Zeros: Can be significant or not, depending on their location.
  • Zeros between non-zero digits: Always significant.
    • Example: In the number 405, the zero is significant.
  • Zeros to the left of all non-zero digits: Not significant.
    • Example: In the number 0.405, the first zero is not significant.
  • Zeros to the right of all non-zero digits: Significant only if a decimal point is present in the number.
    • Example: In the number 0.4050, the last zero is significant because of the decimal point.
    • The measurement 0.4050 grams contains four sig figs.

Practice

• 1234.00 has six sig figs. Zeros are significant because a decimal point is present.
• 1.02 has three sig figs. The zero between 1 and 2 is significant.
• 250 has two sig figs. The zero after 5 is not significant because there is no decimal point.
• 2.0 has two sig figs. The zero after 2 is significant because there is a decimal point.

Scientific Notation

• Apply significant figure rules to the number before the power of 10.
• The 10 and the exponent are exact and do not impact your significant figure count.

Sig Figs in Calculations

Multiplication and Division

• Round the calculated result to have the same number of sig figs as the involved value with the smallest number of sig figs.
• Example: $4.6 \text{ ml} \div 0.78 \frac{\text{g}}{\text{ml}} = 5.897… \approx 5.9 \text{ g}$.
  • 4. 6 ml has two sig figs, and 0.78 g/ml has two sig figs. The answer should be rounded to two sig figs.
  • The calculator displays 5.897…, which is rounded to 5.9 g.

Exact Values and Unit Definitions

• When using the definition of a unit, the conversion factor is an exact value and does not impact your number of allowed sig figs.
• Example: Converting 25.04 ml to liters.
  • $25.04 \text{ ml} * \frac{1 \text{ L}}{1000 \text{ ml}} = 0.02504 \text{ L}$
  • The result should have four sig figs because 25.04 ml has four sig figs.

Addition and Subtraction

• Pay attention to the digits after the decimal point.
• The answer can have the same number of digits after the decimal point as the involved value with the smallest number of digits after the decimal point.
• Example: $4.23 \text{ ml} - 0.5 \text{ ml} = 3.73 \approx 3.7 \text{ ml}$.
  • 0. 5 ml has one digit after the decimal point so the answer is rounded to one digit after the decimal point.

Practice Problems

• $4.8 \text{ ATM} - 0.3 \text{ ATM} = 4.5 \text{ ATM}$
  • The answer is reported to one digit after the decimal point because 0.3 ATM has one digit after the decimal point.
• $\frac{431.04 \text{ grams}}{50.0 \text{ moles}} = 8.62 \frac{\text{grams}}{\text{mole}}$
  • The answer is reported with three sig figs because 50.0 moles has three sig figs.

Conclusion

• Significant figures communicate how well a measurement is known, and that information needs to follow through any calculation involving the measurement.
• Get comfortable recognizing sig figs and the rules of their use in calculations so that it becomes second nature to consider.