Exact vs Inexact Numbers and Significant Figures in Chemistry

Exact vs Inexact Numbers

Definition and Distinction

In chemistry, numbers encountered in measurements and calculations are classified as either exact or inexact. Understanding the difference is crucial for proper data reporting and calculation accuracy.

• Exact Number: A value or integer obtained from counting objects or as part of a definition. These numbers are considered to have infinite precision and do not limit the number of significant figures in calculations.

  • Example: There are 125 students in your lecture.

  • Example: There are 12 objects in a baker's dozen.

• Inexact Number: A value obtained from calculations or measurements that contain some uncertainty. These numbers are limited by the precision of the measuring instrument.

  • Example: Your textbook is measured at a length of 12.53 inches.

Example: Determine if the following statement deals with an exact or inexact number: The combined mass of all doses of a bronchodilator administered to a patient measure 10.0 mg. Inexact number

Significant Figures

Definition and Importance

Significant Figures are the digits in a number that contribute to its precision. They are associated with any measured value and indicate the reliability of the measurement.

• Significant figures are used to express the certainty of measurements and calculations.

• They help communicate the precision of scientific data.

Rules for Identifying Significant Figures

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros (zeros before the first nonzero digit) are not significant.

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

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

Examples of Significant Figures

Number	Significant Figures	Explanation
0.000250	3	Leading zeros are not significant; trailing zeros after decimal are significant.
8.03 × 105	3	All nonzero digits and zeros between them are significant.
125 students	Infinite	Exact number from counting; all digits are significant.
12 eggs	Infinite	Exact number from definition; all digits are significant.

Example: Determine the number of significant figures in the following value: 0.003840. 4 sig figs

Practice Problems

• a) 100 min: 3 sig figs

• b) 17.3 × 103 objects: 3 sig figs

• c) 10 apples: infinite sig figs (exact number)

Additional info: Significant figures are essential in reporting scientific data, as they reflect the precision of measurements and calculations. Always use the correct number of significant figures in your final answer to maintain scientific accuracy.