Indicate which of the following are exact numbers: (a) the mass of a 3- by 5-in. index card, (b) the number of ounces in a pound, (c) the volume of a cup of Seattle's Best coffee, (d) the number of inches in a mile, (e) the number of microseconds in a week, (f) the number of pages in this book.

Verified step by step guidance

1. Understand that exact numbers are those that are counted or defined, not measured.
2. Consider (a) the mass of a 3- by 5-in. index card. Mass is a measured quantity, so it is not exact.
3. Consider (b) the number of ounces in a pound. This is a defined quantity (16 ounces in a pound), so it is exact.
4. Consider (c) the volume of a cup of Seattle's Best coffee. Volume is typically measured, so it is not exact.
5. Consider (d) the number of inches in a mile. This is a defined quantity (63,360 inches in a mile), so it is exact.

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 that result from counting discrete items or from defined relationships, such as conversion factors. For example, there are exactly 12 inches in a foot, making it an exact number.

Measured Numbers

Measured numbers are values obtained from measurements and inherently include some degree of uncertainty. These numbers are influenced by the precision of the measuring instrument used. For instance, the mass of an index card is a measured number because it can vary slightly depending on the scale's accuracy.

Significant Figures

Significant figures are the digits in a number that contribute to its precision, including all non-zero digits, zeros between significant digits, and trailing zeros in a decimal. Understanding significant figures is crucial when performing calculations with measured numbers, as it helps convey the precision of the measurements involved.