Indicate which of the following are exact numbers: (a) the mass of a 32-oz can of coffee, (b) the number of students in your chemistry class, (c) the temperature of the surface of the Sun, (d) the mass of a postage stamp, (e) the number of milliliters in a cubic meter of water, (f) the average height of NBA basketball players.

Key Concepts

Exact Numbers

Exact numbers are values that are counted or defined and have no uncertainty associated with them. They are typically whole numbers, such as the number of students in a class or the number of milliliters in a liter. Unlike measured values, exact numbers do not have significant figures and are considered to be infinitely precise.

Measured Numbers

Measured numbers are values obtained through measurement and inherently include some degree of uncertainty. For example, the mass of a can of coffee or the temperature of the Sun are measured quantities, which depend on the precision of the measuring instrument used. These numbers are expressed with significant figures to reflect their precision.

Significant Figures

Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for interpreting measured numbers, as they indicate the reliability of the measurement and help in performing calculations accurately.