Significant Figures and Exact Numbers in Chemistry

Measurement and Problem Solving

Exact vs. Inexact Numbers

In chemistry, numbers encountered in calculations are classified as either exact or inexact. Understanding this distinction is crucial for proper measurement and reporting of results.

• Exact Numbers: Values that are known with complete certainty. These include:

  • Counting numbers (e.g., 3 apples, 12 students)

  • Defined quantities (e.g., 1 dozen = 12, 1000 g = 1 kg)

  • Numbers that appear in definitions or as part of a calculation that does not involve measurement uncertainty

• Inexact Numbers: Values obtained from measurements, which always involve some degree of uncertainty.

Example: The mass of a bronchodilator administered to a patient is 10.50 mg. This is an inexact number because it is measured.

Significant Figures

Significant figures are the digits in a measurement that contribute to its precision. They include all certain digits plus one uncertain or estimated digit.

• All nonzero digits are significant.

• Any zeros between significant digits are significant.

• Leading zeros (zeros to the left of the first nonzero digit) are not significant.

• Trailing zeros in a number containing a decimal point are significant.

• Trailing zeros in a whole number with no decimal shown are ambiguous and should be avoided by using scientific notation.

Number	Significant Figures	Explanation
0.00340	3	Leading zeros are not significant; trailing zero after decimal is significant.
1.0050	5	All nonzero digits and zeros between/after nonzero digits (with decimal) are significant.
1200	2 (ambiguous)	Trailing zeros without decimal are ambiguous; use scientific notation to clarify.
1.20 × 103	3	Scientific notation shows 3 significant figures.

Example: Determine the number of significant figures in 0.00340:

• There are 3 significant figures (3, 4, and the trailing 0).

Practice Problems

• How many significant figures does each number contain?

  • 10.100: 5 sig figs

  • 0.00340: 3 sig figs

  • 1.20 × 103: 3 sig figs

  • 10 apples: infinite (exact number)

• Indicate the number of significant figures in 1.019 g: 4 sig figs

Additional info: Significant figures are essential for reporting scientific measurements accurately and for ensuring that calculated results reflect the precision of the measurements used.