Identify the numbers in each of the following statements as measured or exact:
a. A patient has a mass of 67.5 kg.

Verified step by step guidance

1. Step 1: Understand the difference between measured and exact numbers. Measured numbers are obtained using a measuring tool and have a degree of uncertainty, while exact numbers are counted or defined and have no uncertainty.
2. Step 2: Analyze the given statement: 'A patient has a mass of 67.5 kg.' The number 67.5 is associated with the mass of the patient, which is typically determined using a scale or measuring device.
3. Step 3: Recognize that the use of a measuring device introduces uncertainty, even if the number is reported to a specific decimal place. This indicates that the number is a measured value.
4. Step 4: Confirm that mass is a physical quantity that cannot be counted or defined exactly, further supporting that 67.5 kg is a measured number.
5. Step 5: Conclude that the number 67.5 kg in the statement is a measured number because it was obtained using a measuring tool and has a degree of uncertainty.

Key Concepts

Measured Numbers

Measured numbers are values obtained through measurement and are subject to uncertainty. They include a degree of error based on the precision of the measuring instrument used. For example, the mass of a patient measured as 67.5 kg reflects the limitations of the scale, indicating that the true mass could vary slightly.

Exact Numbers

Exact numbers are values that are counted or defined and have no uncertainty associated with them. They are considered to be infinitely precise. Examples include the number of patients in a study or defined quantities like 100 centimeters in a meter, which do not vary regardless of measurement conditions.

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 maintaining precision in calculations.